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Revisit the English version (#1885)

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Yudong Jin
2026-04-10 23:03:03 +08:00
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en/docs/chapter_divide_and_conquer/binary_search_recur.md
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We have already learned that search algorithms are divided into two major categories.
- **Brute-force search**: Implemented by traversing the data structure, with a time complexity of $O(n)$.
- **Adaptive search**: Utilizes unique data organization forms or prior information, with time complexity reaching $O(\log n)$ or even $O(1)$.
- **Adaptive search**: Leverages specific data organization or prior information, with time complexity reaching $O(\log n)$ or even $O(1)$.
In fact, **search algorithms with time complexity of $O(\log n)$ are typically implemented based on the divide and conquer strategy**, such as binary search and trees.
@@ -24,7 +24,7 @@ In previous sections, binary search was implemented based on iteration. Now we i
!!! question
Given a sorted array `nums` of length $n$, where all elements are unique, find the element `target`.
Given a sorted array `nums` of length $n$, where all elements are unique, find `target`.
From a divide and conquer perspective, we denote the subproblem corresponding to the search interval $[i, j]$ as $f(i, j)$.
@@ -32,7 +32,7 @@ Starting from the original problem $f(0, n-1)$, perform binary search through th
1. Calculate the midpoint $m$ of the search interval $[i, j]$, and use it to eliminate half of the search interval.
2. Recursively solve the subproblem reduced by half in size, which could be $f(i, m-1)$ or $f(m+1, j)$.
3. Repeat steps `1.` and `2.` until `target` is found or the interval is empty and return.
3. Repeat steps `1.` and `2.` until `target` is found, or return when the interval is empty.
The figure below shows the divide and conquer process of binary search for element $6$ in an array.