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fix minor gramma and expression issues

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Thomas Qiu 2024-12-04 18:51:18 +11:00
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en/docs/chapter_searching/binary_search.md
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# Binary search
<u>Binary search</u> is an efficient search algorithm based on the divide-and-conquer strategy. By taking advantage of the orderliness of elements inside the sorted array, it reduces the search interval by half each round until the target element is found or the search interval is empty.
<u>Binary search</u> is an efficient search algorithm that uses a divide-and-conquer strategy. It takes advantage of the sorted order of elements in an array by reducing the search interval by half in each iteration, continuing until either the target element is found or the search interval becomes empty.
!!! question
Given an array `nums` of length $n$, where elements arranged in ascending order without duplicates. Please find and return the index of element `target` in this array. If the array does not contain the element, return $-1$. An example is shown in the figure below.
Given an array `nums` of length $n$, where elements are arranged in ascending order without duplicates. Please find and return the index of element `target` in this array. If the array does not contain the element, return $-1$. An example is shown in the figure below.
![Binary search example data](binary_search.assets/binary_search_example.png)
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- Binary search can only be applied to sorted data. Unsorted data must be sorted before applying binary search, which may not be worthwhile as sorting algorithm typically has a time complexity of $O(n \log n)$. Such cost is even higher than linear search, not to mention binary search itself. For scenarios with frequent insertion, the cost of remaining the array in order is pretty high as the time complexity of inserting new elements into specific positions is $O(n)$.
- Binary search may use array only. Binary search requires non-continuous (jumping) element access, which is inefficient in linked list. As a result, linked list or data structures based on linked list may not be suitable for this algorithm.
- Linear search performs better in small dataset. In linear search, only 1 decision operation is required for each iteration; whereas in binary search, it involves 1 addition, 1 division, 1 to 3 decision operations, 1 addition (subtraction), totaling 4 to 6 operations. Therefore, if data size $n$ is small, linear search is faster than binary search.
- Linear search performs better on small dataset. In linear search, only 1 decision operation is required for each iteration; whereas in binary search, it involves 1 addition, 1 division, 1 to 3 decision operations, 1 addition (subtraction), totaling 4 to 6 operations. Therefore, if data size $n$ is small, linear search is faster than binary search.