Add figures to replace_linear_by_hashing.md

codes/c/chapter_searching/CMakeLists.txt

@@ -1 +1 @@
-add_executable(leetcode_two_sum leetcode_two_sum.c)
+add_executable(two_sum two_sum.c)

codes/c/chapter_searching/two_sum.c

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.c
+ * File: two_sum.c
  * Created Time: 2023-01-19
  * Author: Reanon (793584285@qq.com)
  */
@@ -71,7 +71,7 @@ int *twoSumHashTable(int *nums, int numsSize, int target, int *returnSize) {
 int main() {
     // ======= Test Case =======
     int nums[] = {2, 7, 11, 15};
-    int target = 9;
+    int target = 13;
     // ====== Driver Code ======
     int returnSize;
     int *res = twoSumBruteForce(nums, sizeof(nums) / sizeof(int), target, &returnSize);

codes/cpp/chapter_searching/CMakeLists.txt

@@ -1,3 +1,3 @@
 add_executable(hashing_search hashing_search.cpp)
-add_executable(leetcode_two_sum leetcode_two_sum.cpp)
+add_executable(two_sum two_sum.cpp)
 add_executable(linear_search linear_search.cpp)

codes/cpp/chapter_searching/two_sum.cpp

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.cpp
+ * File: two_sum.cpp
  * Created Time: 2022-11-25
  * Author: Krahets (krahets@163.com)
  */
@@ -38,7 +38,7 @@ vector<int> twoSumHashTable(vector<int> &nums, int target) {
 int main() {
     // ======= Test Case =======
     vector<int> nums = {2, 7, 11, 15};
-    int target = 9;
+    int target = 13;
 
     // ====== Driver Code ======
     // 方法一

codes/csharp/chapter_searching/two_sum.cs

@@ -1,12 +1,12 @@
 /**
- * File: leetcode_two_sum.cs
+ * File: two_sum.cs
  * Created Time: 2022-12-23
  * Author: haptear (haptear@hotmail.com)
  */
 
 namespace hello_algo.chapter_searching;
 
-public class leetcode_two_sum {
+public class two_sum {
     /* 方法一：暴力枚举 */
     public static int[] twoSumBruteForce(int[] nums, int target) {
         int size = nums.Length;
@@ -39,7 +39,7 @@ public class leetcode_two_sum {
     public void Test() {
         // ======= Test Case =======
         int[] nums = { 2, 7, 11, 15 };
-        int target = 9;
+        int target = 13;
 
         // ====== Driver Code ======
         // 方法一

codes/dart/chapter_searching/two_sum.dart

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.dart
+ * File: two_sum.dart
  * Created Time: 2023-2-11
  * Author: Jefferson (JeffersonHuang77@gmail.com)
  */
@@ -34,7 +34,7 @@ List<int> twoSumHashTable(List<int> nums, int target) {
 int main() {
   // ======= Test Case =======
   List<int> nums = [2, 7, 11, 15];
-  int target = 9;
+  int target = 13;
 
   // ====== Driver Code ======
   // 方法一

codes/go/chapter_searching/two_sum.go

@@ -1,4 +1,4 @@
-// File: leetcode_two_sum.go
+// File: two_sum.go
 // Created Time: 2022-11-25
 // Author: reanon (793584285@qq.com)
 

codes/go/chapter_searching/two_sum_test.go

@@ -1,4 +1,4 @@
-// File: leetcode_two_sum_test.go
+// File: two_sum_test.go
 // Created Time: 2022-11-25
 // Author: reanon (793584285@qq.com)
 
@@ -12,7 +12,7 @@ import (
 func TestTwoSum(t *testing.T) {
 	// ======= Test Case =======
 	nums := []int{2, 7, 11, 15}
-	target := 9
+	target := 13
 
 	// ====== Driver Code ======
 	// 方法一：暴力解法

codes/java/chapter_searching/two_sum.java

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.java
+ * File: two_sum.java
  * Created Time: 2022-11-25
  * Author: Krahets (krahets@163.com)
  */
@@ -8,7 +8,7 @@ package chapter_searching;
 
 import java.util.*;
 
-public class leetcode_two_sum {
+public class two_sum {
     /* 方法一：暴力枚举 */
     static int[] twoSumBruteForce(int[] nums, int target) {
         int size = nums.length;
@@ -40,7 +40,7 @@ public class leetcode_two_sum {
     public static void main(String[] args) {
         // ======= Test Case =======
         int[] nums = { 2, 7, 11, 15 };
-        int target = 9;
+        int target = 13;
 
         // ====== Driver Code ======
         // 方法一

codes/javascript/chapter_searching/two_sum.js

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.js
+ * File: two_sum.js
  * Created Time: 2022-12-15
  * Author: gyt95 (gytkwan@gmail.com)
  */
@@ -36,7 +36,7 @@ function twoSumHashTable(nums, target) {
 /* Driver Code */
 // 方法一
 const nums = [2, 7, 11, 15],
-    target = 9;
+    target = 13;
 
 let res = twoSumBruteForce(nums, target);
 console.log('方法一 res = ', res);

codes/python/chapter_searching/two_sum.py

@@ -1,5 +1,5 @@
 """
-File: leetcode_two_sum.py
+File: two_sum.py
 Created Time: 2022-11-25
 Author: Krahets (krahets@163.com)
 """
@@ -31,7 +31,7 @@ def two_sum_hash_table(nums: list[int], target: int) -> list[int]:
 if __name__ == "__main__":
     # ======= Test Case =======
     nums = [2, 7, 11, 15]
-    target = 9
+    target = 13
 
     # ====== Driver Code ======
     # 方法一

codes/rust/Cargo.toml

@@ -19,10 +19,10 @@ path = "chapter_computational_complexity/worst_best_time_complexity.rs"
 name = "space_complexity"
 path = "chapter_computational_complexity/space_complexity.rs"
 
-# Run Command: cargo run --bin leetcode_two_sum
+# Run Command: cargo run --bin two_sum
 [[bin]]
-name = "leetcode_two_sum"
-path = "chapter_computational_complexity/leetcode_two_sum.rs"
+name = "two_sum"
+path = "chapter_computational_complexity/two_sum.rs"
 
 # Run Command: cargo run --bin array
 [[bin]]

codes/rust/chapter_searching/two_sum.rs

@@ -1,5 +1,5 @@
 /*
- * File: leetcode_two_sum.rs
+ * File: two_sum.rs
  * Created Time: 2023-01-14
  * Author: xBLACICEx (xBLACKICEx@outlook.com), sjinzh (sjinzh@gmail.com)
  */
@@ -39,7 +39,7 @@ pub fn two_sum_hash_table(nums: &Vec<i32>, target: i32) -> Option<Vec<i32>> {
 fn main() {
     // ======= Test Case =======
     let nums = vec![ 2, 7, 11, 15 ];
-    let target = 9;
+    let target = 13;
 
     // ====== Driver Code ======
     // 方法一

codes/swift/Package.swift

@@ -43,7 +43,7 @@ let package = Package(
         .executable(name: "graph_bfs", targets: ["graph_bfs"]),
         .executable(name: "graph_dfs", targets: ["graph_dfs"]),
         // chapter_searching
-        .executable(name: "leetcode_two_sum", targets: ["leetcode_two_sum"]),
+        .executable(name: "two_sum", targets: ["two_sum"]),
         .executable(name: "linear_search", targets: ["linear_search"]),
         .executable(name: "hashing_search", targets: ["hashing_search"]),
         // chapter_sorting
@@ -104,7 +104,7 @@ let package = Package(
         .executableTarget(name: "graph_bfs", dependencies: ["utils", "graph_adjacency_list_target"], path: "chapter_graph", sources: ["graph_bfs.swift"]),
         .executableTarget(name: "graph_dfs", dependencies: ["utils", "graph_adjacency_list_target"], path: "chapter_graph", sources: ["graph_dfs.swift"]),
         // chapter_searching
-        .executableTarget(name: "leetcode_two_sum", path: "chapter_searching", sources: ["leetcode_two_sum.swift"]),
+        .executableTarget(name: "two_sum", path: "chapter_searching", sources: ["two_sum.swift"]),
         .executableTarget(name: "linear_search", dependencies: ["utils"], path: "chapter_searching", sources: ["linear_search.swift"]),
         .executableTarget(name: "hashing_search", dependencies: ["utils"], path: "chapter_searching", sources: ["hashing_search.swift"]),
         // chapter_sorting

codes/swift/chapter_searching/two_sum.swift

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.swift
+ * File: two_sum.swift
  * Created Time: 2023-01-03
  * Author: nuomi1 (nuomi1@qq.com)
  */
@@ -37,7 +37,7 @@ enum LeetcodeTwoSum {
     static func main() {
         // ======= Test Case =======
         let nums = [2, 7, 11, 15]
-        let target = 9
+        let target = 13
         // ====== Driver Code ======
         // 方法一
         var res = twoSumBruteForce(nums: nums, target: target)

codes/typescript/chapter_searching/two_sum.ts

@@ -1,5 +1,5 @@
 /**
- * File: leetcode_two_sum.ts
+ * File: two_sum.ts
  * Created Time: 2022-12-15
  * Author: gyt95 (gytkwan@gmail.com)
  */
@@ -37,7 +37,7 @@ function twoSumHashTable(nums: number[], target: number): number[] {
 /* Driver Code */
 // 方法一
 const nums = [2, 7, 11, 15],
-    target = 9;
+    target = 13;
 
 let res = twoSumBruteForce(nums, target);
 console.log('方法一 res = ', res);

codes/zig/build.zig

@@ -52,18 +52,18 @@ pub fn build(b: *std.build.Builder) void {
         run_step_space_complexity.dependOn(&run_cmd_space_complexity.step);
 
     // Section: "Space Time Tradeoff"
-        // Source File: "chapter_computational_complexity/leetcode_two_sum.zig"
-        // Run Command: zig build run_leetcode_two_sum
-        const exe_leetcode_two_sum = b.addExecutable("leetcode_two_sum", "chapter_computational_complexity/leetcode_two_sum.zig");
-        exe_leetcode_two_sum.addPackagePath("include", "include/include.zig");
-        exe_leetcode_two_sum.setTarget(target);
-        exe_leetcode_two_sum.setBuildMode(mode);
-        exe_leetcode_two_sum.install();
-        const run_cmd_leetcode_two_sum = exe_leetcode_two_sum.run();
-        run_cmd_leetcode_two_sum.step.dependOn(b.getInstallStep());
-        if (b.args) |args| run_cmd_leetcode_two_sum.addArgs(args);
-        const run_step_leetcode_two_sum = b.step("run_leetcode_two_sum", "Run leetcode_two_sum");
-        run_step_leetcode_two_sum.dependOn(&run_cmd_leetcode_two_sum.step);
+        // Source File: "chapter_computational_complexity/two_sum.zig"
+        // Run Command: zig build run_two_sum
+        const exe_two_sum = b.addExecutable("two_sum", "chapter_computational_complexity/two_sum.zig");
+        exe_two_sum.addPackagePath("include", "include/include.zig");
+        exe_two_sum.setTarget(target);
+        exe_two_sum.setBuildMode(mode);
+        exe_two_sum.install();
+        const run_cmd_two_sum = exe_two_sum.run();
+        run_cmd_two_sum.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_two_sum.addArgs(args);
+        const run_step_two_sum = b.step("run_two_sum", "Run two_sum");
+        run_step_two_sum.dependOn(&run_cmd_two_sum.step);
 
     // Section: "Array"
         // Source File: "chapter_array_and_linkedlist/array.zig"

codes/zig/chapter_searching/two_sum.zig

@@ -1,4 +1,4 @@
-// File: leetcode_two_sum.zig
+// File: two_sum.zig
 // Created Time: 2023-01-07
 // Author: sjinzh (sjinzh@gmail.com)
 

docs/chapter_searching/replace_linear_by_hashing.md

@@ -1,78 +1,74 @@
 # 哈希优化策略
 
-在算法题中，**我们时常通过将线性查找替换为哈希查找来降低算法的时间复杂度**。以 LeetCode 全站第一题 [两数之和](https://leetcode.cn/problems/two-sum/) 为例。
+在算法题中，**我们常通过将线性查找替换为哈希查找来降低算法的时间复杂度**。我们借助一个算法题来加深理解。
 
 !!! question "两数之和"
 
-    给定一个整数数组 `nums` 和一个整数目标值 `target` ，请你在该数组中找出“和”为目标值 `target` 的那两个整数，并返回它们的数组下标。
-
-    你可以假设每种输入只会对应一个答案。但是，数组中同一个元素在答案里不能重复出现。
-
-    你可以按任意顺序返回答案。
+    给定一个整数数组 `nums` 和一个整数目标值 `target` ，请在数组中搜索“和”为目标值 `target` 的两个整数，并返回他们在数组中的索引。注意，数组中同一个元素在答案里不能重复出现。返回任意一个解即可。
 
 ## 线性查找：以时间换空间
 
 考虑直接遍历所有可能的组合。开启一个两层循环，在每轮中判断两个整数的和是否为 `target` ，若是，则返回它们的索引。
 
-（图）
+![线性查找求解两数之和](replace_linear_by_hashing.assets/two_sum_brute_force.png)
 
 === "Java"
 
-    ```java title="leetcode_two_sum.java"
-    [class]{leetcode_two_sum}-[func]{twoSumBruteForce}
+    ```java title="two_sum.java"
+    [class]{two_sum}-[func]{twoSumBruteForce}
     ```
 
 === "C++"
 
-    ```cpp title="leetcode_two_sum.cpp"
+    ```cpp title="two_sum.cpp"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
 === "Python"
 
-    ```python title="leetcode_two_sum.py"
+    ```python title="two_sum.py"
     [class]{}-[func]{two_sum_brute_force}
     ```
 
 === "Go"
 
-    ```go title="leetcode_two_sum.go"
+    ```go title="two_sum.go"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
 === "JavaScript"
 
-    ```javascript title="leetcode_two_sum.js"
+    ```javascript title="two_sum.js"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
 === "TypeScript"
 
-    ```typescript title="leetcode_two_sum.ts"
+    ```typescript title="two_sum.ts"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
 === "C"
 
-    ```c title="leetcode_two_sum.c"
+    ```c title="two_sum.c"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
 === "C#"
 
-    ```csharp title="leetcode_two_sum.cs"
-    [class]{leetcode_two_sum}-[func]{twoSumBruteForce}
+    ```csharp title="two_sum.cs"
+    [class]{two_sum}-[func]{twoSumBruteForce}
     ```
 
 === "Swift"
 
-    ```swift title="leetcode_two_sum.swift"
+    ```swift title="two_sum.swift"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
 === "Zig"
 
-    ```zig title="leetcode_two_sum.zig"
+    ```zig title="two_sum.zig"
     [class]{}-[func]{twoSumBruteForce}
     ```
 
@@ -80,52 +76,61 @@
 
 ## 哈希查找：以空间换时间
 
-考虑借助一个哈希表，将数组元素和元素索引构建为键值对。循环遍历数组中的每个元素 `num` 并执行：
+考虑借助一个哈希表，键值对分别为数组元素和元素索引。循环遍历数组，每轮执行：
 
-1. 判断数字 `target - num` 是否在哈希表中，若是则直接返回该两个元素的索引；
-2. 将元素 `num` 和其索引添加进哈希表；
+1. 判断数字 `target - nums[i]` 是否在哈希表中，若是则直接返回这两个元素的索引；
+2. 将键值对 `num[i]` 和索引 `i` 添加进哈希表；
 
-（图）
+=== "<1>"
+    ![two_sum_hashtable_step1](replace_linear_by_hashing.assets/two_sum_hashtable_step1.png)
+
+=== "<2>"
+    ![two_sum_hashtable_step2](replace_linear_by_hashing.assets/two_sum_hashtable_step2.png)
+
+=== "<3>"
+    ![two_sum_hashtable_step3](replace_linear_by_hashing.assets/two_sum_hashtable_step3.png)
+
+实现代码如下所示，仅需单层循环即可。
 
 === "Java"
 
-    ```java title="leetcode_two_sum.java"
-    [class]{leetcode_two_sum}-[func]{twoSumHashTable}
+    ```java title="two_sum.java"
+    [class]{two_sum}-[func]{twoSumHashTable}
     ```
 
 === "C++"
 
-    ```cpp title="leetcode_two_sum.cpp"
+    ```cpp title="two_sum.cpp"
     [class]{}-[func]{twoSumHashTable}
     ```
 
 === "Python"
 
-    ```python title="leetcode_two_sum.py"
+    ```python title="two_sum.py"
     [class]{}-[func]{two_sum_hash_table}
     ```
 
 === "Go"
 
-    ```go title="leetcode_two_sum.go"
+    ```go title="two_sum.go"
     [class]{}-[func]{twoSumHashTable}
     ```
 
 === "JavaScript"
 
-    ```javascript title="leetcode_two_sum.js"
+    ```javascript title="two_sum.js"
     [class]{}-[func]{twoSumHashTable}
     ```
 
 === "TypeScript"
 
-    ```typescript title="leetcode_two_sum.ts"
+    ```typescript title="two_sum.ts"
     [class]{}-[func]{twoSumHashTable}
     ```
 
 === "C"
 
-    ```c title="leetcode_two_sum.c"
+    ```c title="two_sum.c"
     [class]{hashTable}-[func]{}
 
     [class]{}-[func]{twoSumHashTable}
@@ -133,19 +138,19 @@
 
 === "C#"
 
-    ```csharp title="leetcode_two_sum.cs"
-    [class]{leetcode_two_sum}-[func]{twoSumHashTable}
+    ```csharp title="two_sum.cs"
+    [class]{two_sum}-[func]{twoSumHashTable}
     ```
 
 === "Swift"
 
-    ```swift title="leetcode_two_sum.swift"
+    ```swift title="two_sum.swift"
     [class]{}-[func]{twoSumHashTable}
     ```
 
 === "Zig"
 
-    ```zig title="leetcode_two_sum.zig"
+    ```zig title="two_sum.zig"
     [class]{}-[func]{twoSumHashTable}
     ```