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0.1 About this book
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0.2 How to read
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Chapter 1. Encounter with algorithms
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1.1 Algorithms are everywhere
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1.2 What is an algorithm
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Chapter 2. Complexity analysis
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2.1 Algorithm efficiency assessment
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2.3 Time complexity
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2.4 Space complexity
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Chapter 3. Data structures
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Chapter 3. Data structures
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3.1 Classification of data structures
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3.2 Basic data types
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3.3 Number encoding *
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3.4 Character encoding *
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Chapter 4. Array and linked list
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4.1 Array
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4.4 Memory and cache *
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Chapter 5. Stack and queue
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Chapter 5. Stack and queue
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5.1 Stack
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5.3 Double-ended queue
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Chapter 6. Hash table
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6.1 Hash table
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6.2 Hash collision
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6.3 Hash algorithm
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6.3 Hash algorithm
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6.3.1 Goals of hash algorithms
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6.3.2 Design of hash algorithms
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6.3.3 Common hash algorithms
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Chapter 7. Tree
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Chapter 7. Tree
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7.1 Binary tree
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7.2 Binary tree traversal
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7.3 Array Representation of tree
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7.4 Binary Search tree
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7.5 AVL tree *
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Chapter 8. Heap
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8.1 Heap
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8.2 Building a heap
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8.3 Top-k problem
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9.1 Graph
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9.2 Basic graph operations
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9.3 Graph traversal
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10.1 Binary search
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10.2 Binary search insertion
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10.3 Binary search boundaries
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10.4 Hashing optimization strategies
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10.5 Search algorithms revisited
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10.6 Summary
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Chapter 11. Sorting
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Chapter 11. Sorting
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11.1 Sorting algorithms
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11.2 Selection sort
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11.3 Bubble sort
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11.4 Insertion sort
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11.5 Quick sort
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11.6 Merge sort
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11.7 Heap sort
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11.8 Bucket sort
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11.9 Counting sort
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11.10 Radix sort
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11.11 Summary
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Chapter 12. Divide and conquer
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Chapter 12. Divide and conquer
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12.1 Divide and conquer algorithms
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12.2 Divide and conquer search strategy
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12.3 Building binary tree problem
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12.4 Tower of Hanoi Problem
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12.5 Summary
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Chapter 13. Backtracking
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Chapter 13. Backtracking
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13.1 Backtracking algorithms
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13.2 Permutation problem
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13.3 Subset sum problem
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13.4 n queens problem
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13.5 Summary
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Chapter 14. Dynamic programming
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Chapter 14. Dynamic programming
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14.1 Introduction to dynamic programming
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14.2 Characteristics of DP problems
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14.3 DP problem-solving approach¶
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14.4 0-1 Knapsack problem
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14.5 Unbounded knapsack problem
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14.6 Edit distance problem
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14.7 Summary
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Chapter 15. Greedy
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Chapter 15. Greedy
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15.1 Greedy algorithms
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15.2 Fractional knapsack problem
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15.3 Maximum capacity problem
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15.4 Maximum product cutting problem
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15.5 Summary
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Chapter 16. Appendix
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16.1 Installation
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16.2 Contributing
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16.3 Terminology
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References
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References
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Table of contents
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6.3.1 Goals of hash algorithms
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6.3.2 Design of hash algorithms
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6.3.3 Common hash algorithms
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< h1 id = "63-hash-algorithms" > 6.3 Hash algorithms< a class = "headerlink" href = "#63-hash-algorithms" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > The previous two sections introduced the working principle of hash tables and the methods to handle hash collisions. However, both open addressing and chaining can < strong > only ensure that the hash table functions normally when collisions occur, but cannot reduce the frequency of hash collisions< / strong > .< / p >
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< p > If hash collisions occur too frequently, the performance of the hash table will deteriorate drastically. As shown in Figure 6-8, for a chaining hash table, in the ideal case, the key-value pairs are evenly distributed across the buckets, achieving optimal query efficiency; in the worst case, all key-value pairs are stored in the same bucket, degrading the time complexity to < span class = "arithmatex" > \(O(n)\)< / span > .< / p >
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< p > < a class = "glightbox" href = "../hash_algorithm.assets/hash_collision_best_worst_condition.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Ideal and worst cases of hash collisions" class = "animation-figure" src = "../hash_algorithm.assets/hash_collision_best_worst_condition.png" / > < / a > < / p >
< p align = "center" > Figure 6-8 Ideal and worst cases of hash collisions < / p >
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< p > < strong > The distribution of key-value pairs is determined by the hash function< / strong > . Recalling the steps of calculating a hash function, first compute the hash value, then modulo it by the array length:< / p >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "nv" > index< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > hash< span class = "o" > (< / span > key< span class = "o" > )< / span > < span class = "w" > < / span > %< span class = "w" > < / span > capacity
< / code > < / pre > < / div >
< p > Observing the above formula, when the hash table capacity < code > capacity< / code > is fixed, < strong > the hash algorithm < code > hash()< / code > determines the output value< / strong > , thereby determining the distribution of key-value pairs in the hash table.< / p >
< p > This means that, to reduce the probability of hash collisions, we should focus on the design of the hash algorithm < code > hash()< / code > .< / p >
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< h2 id = "631-goals-of-hash-algorithms" > 6.3.1 Goals of hash algorithms< a class = "headerlink" href = "#631-goals-of-hash-algorithms" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > To achieve a "fast and stable" hash table data structure, hash algorithms should have the following characteristics:< / p >
< ul >
< li > < strong > Determinism< / strong > : For the same input, the hash algorithm should always produce the same output. Only then can the hash table be reliable.< / li >
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< li > < strong > High efficiency< / strong > : The process of computing the hash value should be fast enough. The smaller the computational overhead, the more practical the hash table.< / li >
< li > < strong > Uniform distribution< / strong > : The hash algorithm should ensure that key-value pairs are evenly distributed in the hash table. The more uniform the distribution, the lower the probability of hash collisions.< / li >
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< / ul >
< p > In fact, hash algorithms are not only used to implement hash tables but are also widely applied in other fields.< / p >
< ul >
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< li > < strong > Password storage< / strong > : To protect the security of user passwords, systems usually do not store the plaintext passwords but rather the hash values of the passwords. When a user enters a password, the system calculates the hash value of the input and compares it with the stored hash value. If they match, the password is considered correct.< / li >
< li > < strong > Data integrity check< / strong > : The data sender can calculate the hash value of the data and send it along; the receiver can recalculate the hash value of the received data and compare it with the received hash value. If they match, the data is considered intact.< / li >
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< / ul >
< p > For cryptographic applications, to prevent reverse engineering such as deducing the original password from the hash value, hash algorithms need higher-level security features.< / p >
< ul >
< li > < strong > Unidirectionality< / strong > : It should be impossible to deduce any information about the input data from the hash value.< / li >
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< li > < strong > Collision resistance< / strong > : It should be extremely difficult to find two different inputs that produce the same hash value.< / li >
< li > < strong > Avalanche effect< / strong > : Minor changes in the input should lead to significant and unpredictable changes in the output.< / li >
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< / ul >
< p > Note that < strong > "Uniform Distribution" and "Collision Resistance" are two separate concepts< / strong > . Satisfying uniform distribution does not necessarily mean collision resistance. For example, under random input < code > key< / code > , the hash function < code > key % 100< / code > can produce a uniformly distributed output. However, this hash algorithm is too simple, and all < code > key< / code > with the same last two digits will have the same output, making it easy to deduce a usable < code > key< / code > from the hash value, thereby cracking the password.< / p >
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< h2 id = "632-design-of-hash-algorithms" > 6.3.2 Design of hash algorithms< a class = "headerlink" href = "#632-design-of-hash-algorithms" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > The design of hash algorithms is a complex issue that requires consideration of many factors. However, for some less demanding scenarios, we can also design some simple hash algorithms.< / p >
< ul >
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< li > < strong > Additive hash< / strong > : Add up the ASCII codes of each character in the input and use the total sum as the hash value.< / li >
< li > < strong > Multiplicative hash< / strong > : Utilize the non-correlation of multiplication, multiplying each round by a constant, accumulating the ASCII codes of each character into the hash value.< / li >
< li > < strong > XOR hash< / strong > : Accumulate the hash value by XORing each element of the input data.< / li >
< li > < strong > Rotating hash< / strong > : Accumulate the ASCII code of each character into a hash value, performing a rotation operation on the hash value before each accumulation.< / li >
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< / ul >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:14" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_12" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_13" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_14" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Python< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Java< / label > < label for = "__tabbed_1_4" > C#< / label > < label for = "__tabbed_1_5" > Go< / label > < label for = "__tabbed_1_6" > Swift< / label > < label for = "__tabbed_1_7" > JS< / label > < label for = "__tabbed_1_8" > TS< / label > < label for = "__tabbed_1_9" > Dart< / label > < label for = "__tabbed_1_10" > Rust< / label > < label for = "__tabbed_1_11" > C< / label > < label for = "__tabbed_1_12" > Kotlin< / label > < label for = "__tabbed_1_13" > Ruby< / label > < label for = "__tabbed_1_14" > Zig< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > simple_hash.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > add_hash< / span > < span class = "p" > (< / span > < span class = "n" > key< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
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< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " Additive hash" " " < / span >
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< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "nb" > hash< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "n" > modulus< / span > < span class = "o" > =< / span > < span class = "mi" > 1000000007< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "k" > for< / span > < span class = "n" > c< / span > < span class = "ow" > in< / span > < span class = "n" > key< / span > < span class = "p" > :< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "nb" > hash< / span > < span class = "o" > +=< / span > < span class = "nb" > ord< / span > < span class = "p" > (< / span > < span class = "n" > c< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "k" > return< / span > < span class = "nb" > hash< / span > < span class = "o" > %< / span > < span class = "n" > modulus< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "k" > def< / span > < span class = "nf" > mul_hash< / span > < span class = "p" > (< / span > < span class = "n" > key< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
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< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " Multiplicative hash" " " < / span >
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< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "nb" > hash< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "n" > modulus< / span > < span class = "o" > =< / span > < span class = "mi" > 1000000007< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "k" > for< / span > < span class = "n" > c< / span > < span class = "ow" > in< / span > < span class = "n" > key< / span > < span class = "p" > :< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "nb" > hash< / span > < span class = "o" > =< / span > < span class = "mi" > 31< / span > < span class = "o" > *< / span > < span class = "nb" > hash< / span > < span class = "o" > +< / span > < span class = "nb" > ord< / span > < span class = "p" > (< / span > < span class = "n" > c< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "k" > return< / span > < span class = "nb" > hash< / span > < span class = "o" > %< / span > < span class = "n" > modulus< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "k" > def< / span > < span class = "nf" > xor_hash< / span > < span class = "p" > (< / span > < span class = "n" > key< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
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< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " XOR hash" " " < / span >
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< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "nb" > hash< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "n" > modulus< / span > < span class = "o" > =< / span > < span class = "mi" > 1000000007< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "k" > for< / span > < span class = "n" > c< / span > < span class = "ow" > in< / span > < span class = "n" > key< / span > < span class = "p" > :< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "nb" > hash< / span > < span class = "o" > ^=< / span > < span class = "nb" > ord< / span > < span class = "p" > (< / span > < span class = "n" > c< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "k" > return< / span > < span class = "nb" > hash< / span > < span class = "o" > %< / span > < span class = "n" > modulus< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "k" > def< / span > < span class = "nf" > rot_hash< / span > < span class = "p" > (< / span > < span class = "n" > key< / span > < span class = "p" > :< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span > < span class = "o" > -> < / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
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< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " Rotational hash" " " < / span >
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< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "nb" > hash< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "n" > modulus< / span > < span class = "o" > =< / span > < span class = "mi" > 1000000007< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "k" > for< / span > < span class = "n" > c< / span > < span class = "ow" > in< / span > < span class = "n" > key< / span > < span class = "p" > :< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "nb" > hash< / span > < span class = "o" > =< / span > < span class = "p" > (< / span > < span class = "nb" > hash< / span > < span class = "o" > < < < / span > < span class = "mi" > 4< / span > < span class = "p" > )< / span > < span class = "o" > ^< / span > < span class = "p" > (< / span > < span class = "nb" > hash< / span > < span class = "o" > > > < / span > < span class = "mi" > 28< / span > < span class = "p" > )< / span > < span class = "o" > ^< / span > < span class = "nb" > ord< / span > < span class = "p" > (< / span > < span class = "n" > c< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "k" > return< / span > < span class = "nb" > hash< / span > < span class = "o" > %< / span > < span class = "n" > modulus< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > simple_hash.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* Additive hash */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > addHash< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > unsigned< / span > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > c< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > hash< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "cm" > /* Multiplicative hash */< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > mulHash< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > unsigned< / span > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 31< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > c< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > hash< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "cm" > /* XOR hash */< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > xorHash< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > unsigned< / span > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > ^=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > c< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a >
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / a > < span class = "cm" > /* Rotational hash */< / span >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > rotHash< / span > < span class = "p" > (< / span > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "w" > < / span > < span class = "k" > const< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > unsigned< / span > < span class = "w" > < / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > ((< / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "mi" > 4< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ^< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "mi" > 28< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ^< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > c< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-37" name = "__codelineno-2-37" href = "#__codelineno-2-37" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-38" name = "__codelineno-2-38" href = "#__codelineno-2-38" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "n" > hash< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-2-39" name = "__codelineno-2-39" href = "#__codelineno-2-39" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > simple_hash.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* Additive hash */< / span >
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< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > addHash< / span > < span class = "p" > (< / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "kd" > final< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > .< / span > < span class = "na" > toCharArray< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a >
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< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "cm" > /* Multiplicative hash */< / span >
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< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > mulHash< / span > < span class = "p" > (< / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "kd" > final< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > .< / span > < span class = "na" > toCharArray< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "mi" > 31< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a >
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< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "cm" > /* XOR hash */< / span >
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< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > xorHash< / span > < span class = "p" > (< / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "kd" > final< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > .< / span > < span class = "na" > toCharArray< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > ^=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a >
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< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "cm" > /* Rotational hash */< / span >
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< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "nf" > rotHash< / span > < span class = "p" > (< / span > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / a > < span class = "w" > < / span > < span class = "kt" > long< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-34" name = "__codelineno-3-34" href = "#__codelineno-3-34" > < / a > < span class = "w" > < / span > < span class = "kd" > final< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 1000000007< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-35" name = "__codelineno-3-35" href = "#__codelineno-3-35" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > char< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "w" > < / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > key< / span > < span class = "p" > .< / span > < span class = "na" > toCharArray< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-36" name = "__codelineno-3-36" href = "#__codelineno-3-36" > < / a > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > ((< / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > < < < / span > < span class = "w" > < / span > < span class = "mi" > 4< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ^< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "mi" > 28< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > ^< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > c< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > %< / span > < span class = "w" > < / span > < span class = "n" > MODULUS< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-37" name = "__codelineno-3-37" href = "#__codelineno-3-37" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-38" name = "__codelineno-3-38" href = "#__codelineno-3-38" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-3-39" name = "__codelineno-3-39" href = "#__codelineno-3-39" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > simple_hash.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > simple_hash< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > AddHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > simple_hash< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > MulHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > simple_hash< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > XorHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > simple_hash< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > RotHash< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > simple_hash.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "p" > [< / span > < span class = "nx" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > addHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "p" > [< / span > < span class = "nx" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > mulHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "p" > [< / span > < span class = "nx" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > xorHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "p" > [< / span > < span class = "nx" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > rotHash< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > simple_hash.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > addHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > mulHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > xorHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > rotHash< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > simple_hash.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > addHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > mulHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > xorHash< / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > rotHash< / span > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
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< div class = "highlight" > < span class = "filename" > simple_hash.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > add_hash< / span > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > simple_hash.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > addHash< / span > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > simple_hash.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > < span class = "o" > [< / span > < span class = "n" > class< / span > < span class = "o" > ]< / span > < span class = "p" > {}< / span > < span class = "o" > -[< / span > < span class = "n" > func< / span > < span class = "o" > ]< / span > < span class = "p" > {< / span > < span class = "n" > addHash< / span > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > simple_hash.rb< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "o" > [< / span > < span class = "n" > class< / span > < span class = "o" > ]< / span > < span class = "p" > {}< / span > < span class = "o" > -[< / span > < span class = "n" > func< / span > < span class = "o" > ]< / span > < span class = "p" > {< / span > < span class = "n" > add_hash< / span > < span class = "p" > }< / span >
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< p > It is observed that the last step of each hash algorithm is to take the modulus of the large prime number < span class = "arithmatex" > \(1000000007\)< / span > to ensure that the hash value is within an appropriate range. It is worth pondering why emphasis is placed on modulo a prime number, or what are the disadvantages of modulo a composite number? This is an interesting question.< / p >
< p > To conclude: < strong > Using a large prime number as the modulus can maximize the uniform distribution of hash values< / strong > . Since a prime number does not share common factors with other numbers, it can reduce the periodic patterns caused by the modulo operation, thus avoiding hash collisions.< / p >
< p > For example, suppose we choose the composite number < span class = "arithmatex" > \(9\)< / span > as the modulus, which can be divided by < span class = "arithmatex" > \(3\)< / span > , then all < code > key< / code > divisible by < span class = "arithmatex" > \(3\)< / span > will be mapped to hash values < span class = "arithmatex" > \(0\)< / span > , < span class = "arithmatex" > \(3\)< / span > , < span class = "arithmatex" > \(6\)< / span > .< / p >
< div class = "arithmatex" > \[
\begin{aligned}
\text{modulus} & = 9 \newline
\text{key} & = \{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots \} \newline
\text{hash} & = \{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\dots \}
\end{aligned}
\]< / div >
< p > If the input < code > key< / code > happens to have this kind of arithmetic sequence distribution, then the hash values will cluster, thereby exacerbating hash collisions. Now, suppose we replace < code > modulus< / code > with the prime number < span class = "arithmatex" > \(13\)< / span > , since there are no common factors between < code > key< / code > and < code > modulus< / code > , the uniformity of the output hash values will be significantly improved.< / p >
< div class = "arithmatex" > \[
\begin{aligned}
\text{modulus} & = 13 \newline
\text{key} & = \{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots \} \newline
\text{hash} & = \{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \dots \}
\end{aligned}
\]< / div >
< p > It is worth noting that if the < code > key< / code > is guaranteed to be randomly and uniformly distributed, then choosing a prime number or a composite number as the modulus can both produce uniformly distributed hash values. However, when the distribution of < code > key< / code > has some periodicity, modulo a composite number is more likely to result in clustering.< / p >
< p > In summary, we usually choose a prime number as the modulus, and this prime number should be large enough to eliminate periodic patterns as much as possible, enhancing the robustness of the hash algorithm.< / p >
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< h2 id = "633-common-hash-algorithms" > 6.3.3 Common hash algorithms< a class = "headerlink" href = "#633-common-hash-algorithms" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > It is not hard to see that the simple hash algorithms mentioned above are quite "fragile" and far from reaching the design goals of hash algorithms. For example, since addition and XOR obey the commutative law, additive hash and XOR hash cannot distinguish strings with the same content but in different order, which may exacerbate hash collisions and cause security issues.< / p >
< p > In practice, we usually use some standard hash algorithms, such as MD5, SHA-1, SHA-2, and SHA-3. They can map input data of any length to a fixed-length hash value.< / p >
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< p > Over the past century, hash algorithms have been in a continuous process of upgrading and optimization. Some researchers strive to improve the performance of hash algorithms, while others, including hackers, are dedicated to finding security issues in hash algorithms. Table 6-2 shows hash algorithms commonly used in practical applications.< / p >
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< ul >
< li > MD5 and SHA-1 have been successfully attacked multiple times and are thus abandoned in various security applications.< / li >
< li > SHA-2 series, especially SHA-256, is one of the most secure hash algorithms to date, with no successful attacks reported, hence commonly used in various security applications and protocols.< / li >
< li > SHA-3 has lower implementation costs and higher computational efficiency compared to SHA-2, but its current usage coverage is not as extensive as the SHA-2 series.< / li >
< / ul >
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< p align = "center" > Table 6-2 Common hash algorithms < / p >
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< div class = "center-table" >
< table >
< thead >
< tr >
< th > < / th >
< th > MD5< / th >
< th > SHA-1< / th >
< th > SHA-2< / th >
< th > SHA-3< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > Release Year< / td >
< td > 1992< / td >
< td > 1995< / td >
< td > 2002< / td >
< td > 2008< / td >
< / tr >
< tr >
< td > Output Length< / td >
< td > 128 bit< / td >
< td > 160 bit< / td >
< td > 256/512 bit< / td >
< td > 224/256/384/512 bit< / td >
< / tr >
< tr >
< td > Hash Collisions< / td >
< td > Frequent< / td >
< td > Frequent< / td >
< td > Rare< / td >
< td > Rare< / td >
< / tr >
< tr >
< td > Security Level< / td >
< td > Low, has been successfully attacked< / td >
< td > Low, has been successfully attacked< / td >
< td > High< / td >
< td > High< / td >
< / tr >
< tr >
< td > Applications< / td >
< td > Abandoned, still used for data integrity checks< / td >
< td > Abandoned< / td >
< td > Cryptocurrency transaction verification, digital signatures, etc.< / td >
< td > Can be used to replace SHA-2< / td >
< / tr >
< / tbody >
< / table >
< / div >
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< h1 id = "hash-values-in-data-structures" > Hash values in data structures< a class = "headerlink" href = "#hash-values-in-data-structures" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > We know that the keys in a hash table can be of various data types such as integers, decimals, or strings. Programming languages usually provide built-in hash algorithms for these data types to calculate the bucket indices in the hash table. Taking Python as an example, we can use the < code > hash()< / code > function to compute the hash values for various data types.< / p >
< ul >
< li > The hash values of integers and booleans are their own values.< / li >
< li > The calculation of hash values for floating-point numbers and strings is more complex, and interested readers are encouraged to study this on their own.< / li >
< li > The hash value of a tuple is a combination of the hash values of each of its elements, resulting in a single hash value.< / li >
< li > The hash value of an object is generated based on its memory address. By overriding the hash method of an object, hash values can be generated based on content.< / li >
< / ul >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > Be aware that the definition and methods of the built-in hash value calculation functions in different programming languages vary.< / p >
< / div >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "2:13" > < input checked = "checked" id = "__tabbed_2_1" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_2" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_3" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_4" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_5" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_6" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_7" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_8" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_9" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_10" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_11" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_12" name = "__tabbed_2" type = "radio" / > < input id = "__tabbed_2_13" name = "__tabbed_2" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Python< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Java< / label > < label for = "__tabbed_2_4" > C#< / label > < label for = "__tabbed_2_5" > Go< / label > < label for = "__tabbed_2_6" > Swift< / label > < label for = "__tabbed_2_7" > JS< / label > < label for = "__tabbed_2_8" > TS< / label > < label for = "__tabbed_2_9" > Dart< / label > < label for = "__tabbed_2_10" > Rust< / label > < label for = "__tabbed_2_11" > C< / label > < label for = "__tabbed_2_12" > Kotlin< / label > < label for = "__tabbed_2_13" > Zig< / label > < / div >
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< div class = "tabbed-content" >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-15-1" name = "__codelineno-15-1" href = "#__codelineno-15-1" > < / a > < span class = "n" > num< / span > < span class = "o" > =< / span > < span class = "mi" > 3< / span >
< a id = "__codelineno-15-2" name = "__codelineno-15-2" href = "#__codelineno-15-2" > < / a > < span class = "n" > hash_num< / span > < span class = "o" > =< / span > < span class = "nb" > hash< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / a > < span class = "c1" > # Hash value of integer 3 is 3< / span >
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< a id = "__codelineno-15-4" name = "__codelineno-15-4" href = "#__codelineno-15-4" > < / a >
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< a id = "__codelineno-15-5" name = "__codelineno-15-5" href = "#__codelineno-15-5" > < / a > < span class = "n" > bol< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span >
< a id = "__codelineno-15-6" name = "__codelineno-15-6" href = "#__codelineno-15-6" > < / a > < span class = "n" > hash_bol< / span > < span class = "o" > =< / span > < span class = "nb" > hash< / span > < span class = "p" > (< / span > < span class = "n" > bol< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-7" name = "__codelineno-15-7" href = "#__codelineno-15-7" > < / a > < span class = "c1" > # Hash value of boolean True is 1< / span >
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< a id = "__codelineno-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / a >
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< a id = "__codelineno-15-9" name = "__codelineno-15-9" href = "#__codelineno-15-9" > < / a > < span class = "n" > dec< / span > < span class = "o" > =< / span > < span class = "mf" > 3.14159< / span >
< a id = "__codelineno-15-10" name = "__codelineno-15-10" href = "#__codelineno-15-10" > < / a > < span class = "n" > hash_dec< / span > < span class = "o" > =< / span > < span class = "nb" > hash< / span > < span class = "p" > (< / span > < span class = "n" > dec< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-11" name = "__codelineno-15-11" href = "#__codelineno-15-11" > < / a > < span class = "c1" > # Hash value of decimal 3.14159 is 326484311674566659< / span >
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< a id = "__codelineno-15-12" name = "__codelineno-15-12" href = "#__codelineno-15-12" > < / a >
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< a id = "__codelineno-15-13" name = "__codelineno-15-13" href = "#__codelineno-15-13" > < / a > < span class = "nb" > str< / span > < span class = "o" > =< / span > < span class = "s2" > " Hello 算法" < / span >
< a id = "__codelineno-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / a > < span class = "n" > hash_str< / span > < span class = "o" > =< / span > < span class = "nb" > hash< / span > < span class = "p" > (< / span > < span class = "nb" > str< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-15" name = "__codelineno-15-15" href = "#__codelineno-15-15" > < / a > < span class = "c1" > # Hash value of string " Hello 算法" is 4617003410720528961< / span >
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< a id = "__codelineno-15-16" name = "__codelineno-15-16" href = "#__codelineno-15-16" > < / a >
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< a id = "__codelineno-15-17" name = "__codelineno-15-17" href = "#__codelineno-15-17" > < / a > < span class = "n" > tup< / span > < span class = "o" > =< / span > < span class = "p" > (< / span > < span class = "mi" > 12836< / span > < span class = "p" > ,< / span > < span class = "s2" > " 小哈" < / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-18" name = "__codelineno-15-18" href = "#__codelineno-15-18" > < / a > < span class = "n" > hash_tup< / span > < span class = "o" > =< / span > < span class = "nb" > hash< / span > < span class = "p" > (< / span > < span class = "n" > tup< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-19" name = "__codelineno-15-19" href = "#__codelineno-15-19" > < / a > < span class = "c1" > # Hash value of tuple (12836, ' 小哈' ) is 1029005403108185979< / span >
< a id = "__codelineno-15-20" name = "__codelineno-15-20" href = "#__codelineno-15-20" > < / a >
< a id = "__codelineno-15-21" name = "__codelineno-15-21" href = "#__codelineno-15-21" > < / a > < span class = "n" > obj< / span > < span class = "o" > =< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-22" name = "__codelineno-15-22" href = "#__codelineno-15-22" > < / a > < span class = "n" > hash_obj< / span > < span class = "o" > =< / span > < span class = "nb" > hash< / span > < span class = "p" > (< / span > < span class = "n" > obj< / span > < span class = "p" > )< / span >
< a id = "__codelineno-15-23" name = "__codelineno-15-23" href = "#__codelineno-15-23" > < / a > < span class = "c1" > # Hash value of ListNode object at 0x1058fd810 is 274267521< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-16-1" name = "__codelineno-16-1" href = "#__codelineno-16-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-2" name = "__codelineno-16-2" href = "#__codelineno-16-2" > < / a > < span class = "kt" > size_t< / span > < span class = "w" > < / span > < span class = "n" > hashNum< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ()(< / span > < span class = "n" > num< / span > < span class = "p" > );< / span >
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< a id = "__codelineno-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / a > < span class = "c1" > // Hash value of integer 3 is 3< / span >
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< a id = "__codelineno-16-4" name = "__codelineno-16-4" href = "#__codelineno-16-4" > < / a >
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< a id = "__codelineno-16-5" name = "__codelineno-16-5" href = "#__codelineno-16-5" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-6" name = "__codelineno-16-6" href = "#__codelineno-16-6" > < / a > < span class = "kt" > size_t< / span > < span class = "w" > < / span > < span class = "n" > hashBol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "o" > < < / span > < span class = "kt" > bool< / span > < span class = "o" > > < / span > < span class = "p" > ()(< / span > < span class = "n" > bol< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-7" name = "__codelineno-16-7" href = "#__codelineno-16-7" > < / a > < span class = "c1" > // Hash value of boolean 1 is 1< / span >
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< a id = "__codelineno-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / a >
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< a id = "__codelineno-16-9" name = "__codelineno-16-9" href = "#__codelineno-16-9" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 3.14159< / span > < span class = "p" > ;< / span >
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< a id = "__codelineno-16-10" name = "__codelineno-16-10" href = "#__codelineno-16-10" > < / a > < span class = "kt" > size_t< / span > < span class = "w" > < / span > < span class = "n" > hashDec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "o" > < < / span > < span class = "kt" > double< / span > < span class = "o" > > < / span > < span class = "p" > ()(< / span > < span class = "n" > dec< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-11" name = "__codelineno-16-11" href = "#__codelineno-16-11" > < / a > < span class = "c1" > // Hash value of decimal 3.14159 is 4614256650576692846< / span >
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< a id = "__codelineno-16-12" name = "__codelineno-16-12" href = "#__codelineno-16-12" > < / a >
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< a id = "__codelineno-16-13" name = "__codelineno-16-13" href = "#__codelineno-16-13" > < / a > < span class = "n" > string< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Hello 算法" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / a > < span class = "kt" > size_t< / span > < span class = "w" > < / span > < span class = "n" > hashStr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "o" > < < / span > < span class = "n" > string< / span > < span class = "o" > > < / span > < span class = "p" > ()(< / span > < span class = "n" > str< / span > < span class = "p" > );< / span >
< a id = "__codelineno-16-15" name = "__codelineno-16-15" href = "#__codelineno-16-15" > < / a > < span class = "c1" > // Hash value of string " Hello 算法" is 15466937326284535026< / span >
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< a id = "__codelineno-16-16" name = "__codelineno-16-16" href = "#__codelineno-16-16" > < / a >
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< a id = "__codelineno-16-17" name = "__codelineno-16-17" href = "#__codelineno-16-17" > < / a > < span class = "c1" > // In C++, built-in std::hash() only provides hash values for basic data types< / span >
< a id = "__codelineno-16-18" name = "__codelineno-16-18" href = "#__codelineno-16-18" > < / a > < span class = "c1" > // Hash values for arrays and objects need to be implemented separately< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-17-1" name = "__codelineno-17-1" href = "#__codelineno-17-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-2" name = "__codelineno-17-2" href = "#__codelineno-17-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashNum< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Integer< / span > < span class = "p" > .< / span > < span class = "na" > hashCode< / span > < span class = "p" > (< / span > < span class = "n" > num< / span > < span class = "p" > );< / span >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "c1" > // Hash value of integer 3 is 3< / span >
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< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / a >
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< a id = "__codelineno-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "kt" > boolean< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashBol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Boolean< / span > < span class = "p" > .< / span > < span class = "na" > hashCode< / span > < span class = "p" > (< / span > < span class = "n" > bol< / span > < span class = "p" > );< / span >
< a id = "__codelineno-17-7" name = "__codelineno-17-7" href = "#__codelineno-17-7" > < / a > < span class = "c1" > // Hash value of boolean true is 1231< / span >
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< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a >
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< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 3.14159< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashDec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Double< / span > < span class = "p" > .< / span > < span class = "na" > hashCode< / span > < span class = "p" > (< / span > < span class = "n" > dec< / span > < span class = "p" > );< / span >
< a id = "__codelineno-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / a > < span class = "c1" > // Hash value of decimal 3.14159 is -1340954729< / span >
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< a id = "__codelineno-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / a >
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< a id = "__codelineno-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / a > < span class = "n" > String< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Hello 算法" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-17-14" name = "__codelineno-17-14" href = "#__codelineno-17-14" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashStr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "p" > .< / span > < span class = "na" > hashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-17-15" name = "__codelineno-17-15" href = "#__codelineno-17-15" > < / a > < span class = "c1" > // Hash value of string " Hello 算法" is -727081396< / span >
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< a id = "__codelineno-17-16" name = "__codelineno-17-16" href = "#__codelineno-17-16" > < / a >
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< a id = "__codelineno-17-17" name = "__codelineno-17-17" href = "#__codelineno-17-17" > < / a > < span class = "n" > Object< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "mi" > 12836< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " 小哈" < / span > < span class = "w" > < / span > < span class = "p" > };< / span >
< a id = "__codelineno-17-18" name = "__codelineno-17-18" href = "#__codelineno-17-18" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashTup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Arrays< / span > < span class = "p" > .< / span > < span class = "na" > hashCode< / span > < span class = "p" > (< / span > < span class = "n" > arr< / span > < span class = "p" > );< / span >
< a id = "__codelineno-17-19" name = "__codelineno-17-19" href = "#__codelineno-17-19" > < / a > < span class = "c1" > // Hash value of array [12836, 小哈] is 1151158< / span >
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< a id = "__codelineno-17-20" name = "__codelineno-17-20" href = "#__codelineno-17-20" > < / a >
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< a id = "__codelineno-17-21" name = "__codelineno-17-21" href = "#__codelineno-17-21" > < / a > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "n" > obj< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-17-22" name = "__codelineno-17-22" href = "#__codelineno-17-22" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashObj< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > obj< / span > < span class = "p" > .< / span > < span class = "na" > hashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-17-23" name = "__codelineno-17-23" href = "#__codelineno-17-23" > < / a > < span class = "c1" > // Hash value of ListNode object utils.ListNode@7dc5e7b4 is 2110121908< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > built_in_hash.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-18-1" name = "__codelineno-18-1" href = "#__codelineno-18-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashNum< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "p" > .< / span > < span class = "n" > GetHashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "c1" > // Hash value of integer 3 is 3;< / span >
< a id = "__codelineno-18-4" name = "__codelineno-18-4" href = "#__codelineno-18-4" > < / a >
< a id = "__codelineno-18-5" name = "__codelineno-18-5" href = "#__codelineno-18-5" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashBol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "p" > .< / span > < span class = "n" > GetHashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / a > < span class = "c1" > // Hash value of boolean true is 1;< / span >
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / a >
< a id = "__codelineno-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 3.14159< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-10" name = "__codelineno-18-10" href = "#__codelineno-18-10" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashDec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > < span class = "p" > .< / span > < span class = "n" > GetHashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-11" name = "__codelineno-18-11" href = "#__codelineno-18-11" > < / a > < span class = "c1" > // Hash value of decimal 3.14159 is -1340954729;< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "kt" > string< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Hello 算法" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashStr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "p" > .< / span > < span class = "n" > GetHashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / a > < span class = "c1" > // Hash value of string " Hello 算法" is -586107568;< / span >
< a id = "__codelineno-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / a > < span class = "kt" > object< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "m" > 12836< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s" > " 小哈" < / span > < span class = "p" > ];< / span >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashTup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "p" > .< / span > < span class = "n" > GetHashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-19" name = "__codelineno-18-19" href = "#__codelineno-18-19" > < / a > < span class = "c1" > // Hash value of array [12836, 小哈] is 42931033;< / span >
< a id = "__codelineno-18-20" name = "__codelineno-18-20" href = "#__codelineno-18-20" > < / a >
< a id = "__codelineno-18-21" name = "__codelineno-18-21" href = "#__codelineno-18-21" > < / a > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "n" > obj< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-18-22" name = "__codelineno-18-22" href = "#__codelineno-18-22" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashObj< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > obj< / span > < span class = "p" > .< / span > < span class = "n" > GetHashCode< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-18-23" name = "__codelineno-18-23" href = "#__codelineno-18-23" > < / a > < span class = "c1" > // Hash value of ListNode object 0 is 39053774;< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-19-1" name = "__codelineno-19-1" href = "#__codelineno-19-1" > < / a > < span class = "c1" > // Go does not provide built-in hash code functions< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-20-1" name = "__codelineno-20-1" href = "#__codelineno-20-1" > < / a > < span class = "kd" > let< / span > < span class = "nv" > num< / span > < span class = "p" > =< / span > < span class = "mi" > 3< / span >
< a id = "__codelineno-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / a > < span class = "kd" > let< / span > < span class = "nv" > hashNum< / span > < span class = "p" > =< / span > < span class = "n" > num< / span > < span class = "p" > .< / span > < span class = "n" > hashValue< / span >
< a id = "__codelineno-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / a > < span class = "c1" > // Hash value of integer 3 is 9047044699613009734< / span >
< a id = "__codelineno-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / a >
< a id = "__codelineno-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "kd" > let< / span > < span class = "nv" > bol< / span > < span class = "p" > =< / span > < span class = "kc" > true< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / a > < span class = "kd" > let< / span > < span class = "nv" > hashBol< / span > < span class = "p" > =< / span > < span class = "n" > bol< / span > < span class = "p" > .< / span > < span class = "n" > hashValue< / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / a > < span class = "c1" > // Hash value of boolean true is -4431640247352757451< / span >
< a id = "__codelineno-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / a > < span class = "kd" > let< / span > < span class = "nv" > dec< / span > < span class = "p" > =< / span > < span class = "mf" > 3.14159< / span >
< a id = "__codelineno-20-10" name = "__codelineno-20-10" href = "#__codelineno-20-10" > < / a > < span class = "kd" > let< / span > < span class = "nv" > hashDec< / span > < span class = "p" > =< / span > < span class = "n" > dec< / span > < span class = "p" > .< / span > < span class = "n" > hashValue< / span >
< a id = "__codelineno-20-11" name = "__codelineno-20-11" href = "#__codelineno-20-11" > < / a > < span class = "c1" > // Hash value of decimal 3.14159 is -2465384235396674631< / span >
< a id = "__codelineno-20-12" name = "__codelineno-20-12" href = "#__codelineno-20-12" > < / a >
< a id = "__codelineno-20-13" name = "__codelineno-20-13" href = "#__codelineno-20-13" > < / a > < span class = "kd" > let< / span > < span class = "nv" > str< / span > < span class = "p" > =< / span > < span class = "s" > " Hello 算法" < / span >
< a id = "__codelineno-20-14" name = "__codelineno-20-14" href = "#__codelineno-20-14" > < / a > < span class = "kd" > let< / span > < span class = "nv" > hashStr< / span > < span class = "p" > =< / span > < span class = "n" > str< / span > < span class = "p" > .< / span > < span class = "n" > hashValue< / span >
< a id = "__codelineno-20-15" name = "__codelineno-20-15" href = "#__codelineno-20-15" > < / a > < span class = "c1" > // Hash value of string " Hello 算法" is -7850626797806988787< / span >
< a id = "__codelineno-20-16" name = "__codelineno-20-16" href = "#__codelineno-20-16" > < / a >
< a id = "__codelineno-20-17" name = "__codelineno-20-17" href = "#__codelineno-20-17" > < / a > < span class = "kd" > let< / span > < span class = "nv" > arr< / span > < span class = "p" > =< / span > < span class = "p" > [< / span > < span class = "n" > AnyHashable< / span > < span class = "p" > (< / span > < span class = "mi" > 12836< / span > < span class = "p" > ),< / span > < span class = "n" > AnyHashable< / span > < span class = "p" > (< / span > < span class = "s" > " 小哈" < / span > < span class = "p" > )]< / span >
< a id = "__codelineno-20-18" name = "__codelineno-20-18" href = "#__codelineno-20-18" > < / a > < span class = "kd" > let< / span > < span class = "nv" > hashTup< / span > < span class = "p" > =< / span > < span class = "n" > arr< / span > < span class = "p" > .< / span > < span class = "n" > hashValue< / span >
< a id = "__codelineno-20-19" name = "__codelineno-20-19" href = "#__codelineno-20-19" > < / a > < span class = "c1" > // Hash value of array [AnyHashable(12836), AnyHashable(" 小哈" )] is -2308633508154532996< / span >
< a id = "__codelineno-20-20" name = "__codelineno-20-20" href = "#__codelineno-20-20" > < / a >
< a id = "__codelineno-20-21" name = "__codelineno-20-21" href = "#__codelineno-20-21" > < / a > < span class = "kd" > let< / span > < span class = "nv" > obj< / span > < span class = "p" > =< / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "n" > x< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-20-22" name = "__codelineno-20-22" href = "#__codelineno-20-22" > < / a > < span class = "kd" > let< / span > < span class = "nv" > hashObj< / span > < span class = "p" > =< / span > < span class = "n" > obj< / span > < span class = "p" > .< / span > < span class = "n" > hashValue< / span >
< a id = "__codelineno-20-23" name = "__codelineno-20-23" href = "#__codelineno-20-23" > < / a > < span class = "c1" > // Hash value of ListNode object utils.ListNode is -2434780518035996159< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-21-1" name = "__codelineno-21-1" href = "#__codelineno-21-1" > < / a > < span class = "c1" > // JavaScript does not provide built-in hash code functions< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-22-1" name = "__codelineno-22-1" href = "#__codelineno-22-1" > < / a > < span class = "c1" > // TypeScript does not provide built-in hash code functions< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "kt" > num< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashNum< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kt" > num< / span > < span class = "p" > .< / span > < span class = "n" > hashCode< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / a > < span class = "c1" > // Hash value of integer 3 is 34803< / span >
< a id = "__codelineno-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / a >
< a id = "__codelineno-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a > < span class = "kt" > bool< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashBol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "p" > .< / span > < span class = "n" > hashCode< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / a > < span class = "c1" > // Hash value of boolean true is 1231< / span >
< a id = "__codelineno-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / a >
< a id = "__codelineno-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / a > < span class = "kt" > double< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "m" > 3.14159< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-10" name = "__codelineno-23-10" href = "#__codelineno-23-10" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashDec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > < span class = "p" > .< / span > < span class = "n" > hashCode< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-11" name = "__codelineno-23-11" href = "#__codelineno-23-11" > < / a > < span class = "c1" > // Hash value of decimal 3.14159 is 2570631074981783< / span >
< a id = "__codelineno-23-12" name = "__codelineno-23-12" href = "#__codelineno-23-12" > < / a >
< a id = "__codelineno-23-13" name = "__codelineno-23-13" href = "#__codelineno-23-13" > < / a > < span class = "kt" > String< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s2" > " Hello 算法" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-14" name = "__codelineno-23-14" href = "#__codelineno-23-14" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashStr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > str< / span > < span class = "p" > .< / span > < span class = "n" > hashCode< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-15" name = "__codelineno-23-15" href = "#__codelineno-23-15" > < / a > < span class = "c1" > // Hash value of string " Hello 算法" is 468167534< / span >
< a id = "__codelineno-23-16" name = "__codelineno-23-16" href = "#__codelineno-23-16" > < / a >
< a id = "__codelineno-23-17" name = "__codelineno-23-17" href = "#__codelineno-23-17" > < / a > < span class = "n" > List< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > [< / span > < span class = "m" > 12836< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "s2" > " 小哈" < / span > < span class = "p" > ];< / span >
< a id = "__codelineno-23-18" name = "__codelineno-23-18" href = "#__codelineno-23-18" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashArr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "p" > .< / span > < span class = "n" > hashCode< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-19" name = "__codelineno-23-19" href = "#__codelineno-23-19" > < / a > < span class = "c1" > // Hash value of array [12836, 小哈] is 976512528< / span >
< a id = "__codelineno-23-20" name = "__codelineno-23-20" href = "#__codelineno-23-20" > < / a >
< a id = "__codelineno-23-21" name = "__codelineno-23-21" href = "#__codelineno-23-21" > < / a > < span class = "n" > ListNode< / span > < span class = "w" > < / span > < span class = "n" > obj< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > );< / span >
< a id = "__codelineno-23-22" name = "__codelineno-23-22" href = "#__codelineno-23-22" > < / a > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > hashObj< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > obj< / span > < span class = "p" > .< / span > < span class = "n" > hashCode< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-23-23" name = "__codelineno-23-23" href = "#__codelineno-23-23" > < / a > < span class = "c1" > // Hash value of ListNode object Instance of ' ListNode' is 1033450432< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / a > < span class = "k" > use< / span > < span class = "w" > < / span > < span class = "n" > std< / span > ::< span class = "n" > collections< / span > ::< span class = "n" > hash_map< / span > ::< span class = "n" > DefaultHasher< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / a > < span class = "k" > use< / span > < span class = "w" > < / span > < span class = "n" > std< / span > ::< span class = "n" > hash< / span > ::< span class = "p" > {< / span > < span class = "n" > Hash< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > Hasher< / span > < span class = "p" > };< / span >
< a id = "__codelineno-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / a >
< a id = "__codelineno-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > num< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mi" > 3< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > num_hasher< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > DefaultHasher< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / a > < span class = "n" > num< / span > < span class = "p" > .< / span > < span class = "n" > hash< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > num_hasher< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > hash_num< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > num_hasher< / span > < span class = "p" > .< / span > < span class = "n" > finish< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "c1" > // Hash value of integer 3 is 568126464209439262< / span >
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a >
< a id = "__codelineno-24-10" name = "__codelineno-24-10" href = "#__codelineno-24-10" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > bol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "kc" > true< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-11" name = "__codelineno-24-11" href = "#__codelineno-24-11" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > bol_hasher< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > DefaultHasher< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-12" name = "__codelineno-24-12" href = "#__codelineno-24-12" > < / a > < span class = "n" > bol< / span > < span class = "p" > .< / span > < span class = "n" > hash< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > bol_hasher< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-13" name = "__codelineno-24-13" href = "#__codelineno-24-13" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > hash_bol< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > bol_hasher< / span > < span class = "p" > .< / span > < span class = "n" > finish< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-14" name = "__codelineno-24-14" href = "#__codelineno-24-14" > < / a > < span class = "c1" > // Hash value of boolean true is 4952851536318644461< / span >
< a id = "__codelineno-24-15" name = "__codelineno-24-15" href = "#__codelineno-24-15" > < / a >
< a id = "__codelineno-24-16" name = "__codelineno-24-16" href = "#__codelineno-24-16" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > dec< / span > : < span class = "kt" > f32< / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "mf" > 3.14159< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-17" name = "__codelineno-24-17" href = "#__codelineno-24-17" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > dec_hasher< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > DefaultHasher< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-18" name = "__codelineno-24-18" href = "#__codelineno-24-18" > < / a > < span class = "n" > dec< / span > < span class = "p" > .< / span > < span class = "n" > to_bits< / span > < span class = "p" > ().< / span > < span class = "n" > hash< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > dec_hasher< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-19" name = "__codelineno-24-19" href = "#__codelineno-24-19" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > hash_dec< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > dec_hasher< / span > < span class = "p" > .< / span > < span class = "n" > finish< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-20" name = "__codelineno-24-20" href = "#__codelineno-24-20" > < / a > < span class = "c1" > // Hash value of decimal 3.14159 is 2566941990314602357< / span >
< a id = "__codelineno-24-21" name = "__codelineno-24-21" href = "#__codelineno-24-21" > < / a >
< a id = "__codelineno-24-22" name = "__codelineno-24-22" href = "#__codelineno-24-22" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "kt" > str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "s" > " Hello 算法" < / span > < span class = "p" > ;< / span >
< a id = "__codelineno-24-23" name = "__codelineno-24-23" href = "#__codelineno-24-23" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > str_hasher< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > DefaultHasher< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-24" name = "__codelineno-24-24" href = "#__codelineno-24-24" > < / a > < span class = "kt" > str< / span > < span class = "p" > .< / span > < span class = "n" > hash< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > str_hasher< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-25" name = "__codelineno-24-25" href = "#__codelineno-24-25" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > hash_str< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > str_hasher< / span > < span class = "p" > .< / span > < span class = "n" > finish< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-26" name = "__codelineno-24-26" href = "#__codelineno-24-26" > < / a > < span class = "c1" > // Hash value of string " Hello 算法" is 16092673739211250988< / span >
< a id = "__codelineno-24-27" name = "__codelineno-24-27" href = "#__codelineno-24-27" > < / a >
< a id = "__codelineno-24-28" name = "__codelineno-24-28" href = "#__codelineno-24-28" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > arr< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "mi" > 12836< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "s" > " 小哈" < / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-29" name = "__codelineno-24-29" href = "#__codelineno-24-29" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > tup_hasher< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > DefaultHasher< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-30" name = "__codelineno-24-30" href = "#__codelineno-24-30" > < / a > < span class = "n" > arr< / span > < span class = "p" > .< / span > < span class = "n" > hash< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > tup_hasher< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-31" name = "__codelineno-24-31" href = "#__codelineno-24-31" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > hash_tup< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tup_hasher< / span > < span class = "p" > .< / span > < span class = "n" > finish< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-32" name = "__codelineno-24-32" href = "#__codelineno-24-32" > < / a > < span class = "c1" > // Hash value of tuple (12836, " 小哈" ) is 1885128010422702749< / span >
< a id = "__codelineno-24-33" name = "__codelineno-24-33" href = "#__codelineno-24-33" > < / a >
< a id = "__codelineno-24-34" name = "__codelineno-24-34" href = "#__codelineno-24-34" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > node< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > ListNode< / span > ::< span class = "n" > new< / span > < span class = "p" > (< / span > < span class = "mi" > 42< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-35" name = "__codelineno-24-35" href = "#__codelineno-24-35" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > hasher< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > DefaultHasher< / span > ::< span class = "n" > new< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-36" name = "__codelineno-24-36" href = "#__codelineno-24-36" > < / a > < span class = "n" > node< / span > < span class = "p" > .< / span > < span class = "n" > borrow< / span > < span class = "p" > ().< / span > < span class = "n" > val< / span > < span class = "p" > .< / span > < span class = "n" > hash< / span > < span class = "p" > (< / span > < span class = "o" > & < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > hasher< / span > < span class = "p" > );< / span >
< a id = "__codelineno-24-37" name = "__codelineno-24-37" href = "#__codelineno-24-37" > < / a > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "n" > hash< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > hasher< / span > < span class = "p" > .< / span > < span class = "n" > finish< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-24-38" name = "__codelineno-24-38" href = "#__codelineno-24-38" > < / a > < span class = "c1" > // Hash value of ListNode object RefCell { value: ListNode { val: 42, next: None } } is 15387811073369036852< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-25-1" name = "__codelineno-25-1" href = "#__codelineno-25-1" > < / a > < span class = "c1" > // C does not provide built-in hash code functions< / span >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-26-1" name = "__codelineno-26-1" href = "#__codelineno-26-1" > < / a >
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< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
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< div class = "highlight" > < span class = "filename" > built_in_hash.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-27-1" name = "__codelineno-27-1" href = "#__codelineno-27-1" > < / a >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > Code Visualization< / summary >
< p > < div style = "height: 549px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=class%20ListNode%3A%0A%20%20%20%20%22%22%22%E9%93%BE%E8%A1%A8%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.next%3A%20ListNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%90%8E%E7%BB%A7%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20num%20%3D%203%0A%20%20%20%20hash_num%20%3D%20hash%28num%29%0A%20%20%20%20%23%20%E6%95%B4%E6%95%B0%203%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%203%0A%0A%20%20%20%20bol%20%3D%20True%0A%20%20%20%20hash_bol%20%3D%20hash%28bol%29%0A%20%20%20%20%23%20%E5%B8%83%E5%B0%94%E9%87%8F%20True%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%201%0A%0A%20%20%20%20dec%20%3D%203.14159%0A%20%20%20%20hash_dec%20%3D%20hash%28dec%29%0A%20%20%20%20%23%20%E5%B0%8F%E6%95%B0%203.14159%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20326484311674566659%0A%0A%20%20%20%20str%20%3D%20%22Hello%20%E7%AE%97%E6%B3%95%22%0A%20%20%20%20hash_str%20%3D%20hash%28str%29%0A%20%20%20%20%23%20%E5%AD%97%E7%AC%A6%E4%B8%B2%E2%80%9CHello%20%E7%AE%97%E6%B3%95%E2%80%9D%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%204617003410720528961%0A%0A%20%20%20%20tup%20%3D%20%2812836,%20%22%E5%B0%8F%E5%93%88%22%29%0A%20%20%20%20hash_tup%20%3D%20hash%28tup%29%0A%20%20%20%20%23%20%E5%85%83%E7%BB%84%20%2812836,%20'%E5%B0%8F%E5%93%88'%29%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%201029005403108185979%0A%0A%20%20%20%20obj%20%3D%20ListNode%280%29%0A%20%20%20%20hash_obj%20%3D%20hash%28obj%29%0A%20%20%20%20%23%20%E8%8A%82%E7%82%B9%E5%AF%B9%E8%B1%A1%20%3CListNode%20object%20at%200x1058fd810%3E%20%E7%9A%84%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20274267521&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=19&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" > < / iframe > < / div >
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< / details >
< p > In many programming languages, < strong > only immutable objects can serve as the < code > key< / code > in a hash table< / strong > . If we use a list (dynamic array) as a < code > key< / code > , when the contents of the list change, its hash value also changes, and we would no longer be able to find the original < code > value< / code > in the hash table.< / p >
< p > Although the member variables of a custom object (such as a linked list node) are mutable, it is hashable. < strong > This is because the hash value of an object is usually generated based on its memory address< / strong > , and even if the contents of the object change, the memory address remains the same, so the hash value remains unchanged.< / p >
< p > You might have noticed that the hash values output in different consoles are different. < strong > This is because the Python interpreter adds a random salt to the string hash function each time it starts up< / strong > . This approach effectively prevents HashDoS attacks and enhances the security of the hash algorithm.< / p >
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