74 lines
2.4 KiB
Markdown
74 lines
2.4 KiB
Markdown
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---
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title: Freecodecamp Algorithm Binary Search Guide
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localeTitle: Freecodecamp算法二进制搜索指南
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---
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二进制搜索是一种搜索算法，用于查找已排序数组中目标值的位置。
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## 例
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上图显示了当目标值为**4**时二进制搜索算法在排序数组上的工作情况。
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## 算法
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二进制搜索适用于已排序的数组。二进制搜索首先将数组的中间元素与目标值进行比较。如果目标值与中间元素匹配，则返回其在数组中的位置。如果目标值小于或大于中间元素，则搜索分别使用新的中间元素继续数组的下半部分或上半部分，从而消除另一半。
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二进制搜索算法的伪代码如下：
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```
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BinarySearch(A<a href='https://repl.it/CWZq/158' target='_blank' rel='nofollow'>0..N-1], value) {
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low = 0
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high = N - 1
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while (low <= high) {
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// invariants: value > A[i] for all i < low
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value < A[i] for all i > high
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mid = (low + high) / 2
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if (A[mid] > value)
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high = mid - 1
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else if (A[mid] < value)
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low = mid + 1
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else
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return mid
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}
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return not_found // value would be inserted at index "low"
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}
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```
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## 复杂
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* 最差案例表现： **O（log n）**
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* 最佳案例表现： **O（1）**
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* 平均案例表现： **O（log n）**
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* 最坏的案例空间复杂度： **O（1）**用于迭代; **O（log n）**用于递归。
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## C ++实现
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```
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int binarySearch(int arr[], int value, int left, int right) {
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int middle;
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while (left <= right) {
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middle = (left + right) / 2;
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if (arr[middle] == value)
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return middle;
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else if (arr[middle] > value)
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right = middle - 1;
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else
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left = middle + 1;
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}
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return -1;
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}
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```
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：rocket：\[运行代码## Python实现
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```
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def binary_search(l, value):
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low = 0
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high = len(l)-1
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while low <= high:
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mid = (low+high)//2
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if l<a href='https://forum.freecodecamp.com/images/emoji/emoji_one/rocket.png?v=3 ":rocket:"' target='_blank' rel='nofollow'>mid] > value: high = mid-1
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elif l[mid] < value: low = mid+1
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else: return mid
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return -1
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```
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 [运行代码](https://repl.it/CWZi/2)
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