普通的二分查找

先引入一個最簡單的二分查找吧

int binarySearch(int* nums, int numsSize, int target){int left = 0, right = numsSize-1;while(left <= right){int mid = left + (right - left)/2;if(nums[mid] == target){return mid;}else if(nums[mid] > target){right = mid - 1;}else left = mid + 1;}return -1; }

很明顯，這么寫法將每次執(zhí)行的區(qū)間劃分為
[left .....mid -1] (mid) [mid+1....right]

那換個寫法呢（結(jié)果都是正確的）？

int binarySearch_2(int* nums, int numsSize, int target){int left = 0, right = numsSize;while(left < right){int mid = left + (right - left)/2;if(nums[mid] == target){return mid;}else if(nums[mid] > target){right = mid;}else left = mid + 1;}return -1; }

這個寫法將區(qū)間分為了左閉右開型，不同于上面的左右兩邊都是閉區(qū)間
[left....mid) (mid) [mid+1....right)

以上兩個寫法的while條件，一個是left <= right，一個則是left < right

說明第一種while循環(huán)的結(jié)束條件為left > right，第二種結(jié)束條件為left == right

其原因就是因為左閉右閉的區(qū)間[i, i]是包含元素nums[i]的，而左閉右開的區(qū)間[i, i) 相當于空集。

搞清楚while循環(huán)結(jié)束時的具體情況，對我們分析邊界值非常重要。

當數(shù)組中存在多個目標值時，這種方法返回的是位于中間位置那個目標值的下標，但是如果我們想獲得目標值第一次出現(xiàn)時的下標應(yīng)該怎么辦呢?

獲取左側(cè)邊界的二分查找

int binarySearch_3(int *nums, int numsSize, int target){int left = 0, right = numsSize - 1;while(left <= right){int mid = left + (right - left)/2;if(nums[mid] == target){right = mid - 1;}else if(nums[mid] > target){right = mid - 1;}else left = mid + 1;}return nums[left] == target? left : -1; }

此算法while循環(huán)的結(jié)束條件為left > right，或者說是left = right + 1，如果nums[left] == target則說明我們最終找到了目標值，而且此時的left是該目標值第一次出現(xiàn)的位置。這種也可以換成子區(qū)間左閉右開的寫法

int binarySearch_4(int *nums, int numsSize, int target){int left = 0, right = numsSize;while(left < right){int mid = left + (right - left)/2;if(nums[mid] == target){right = mid;}else if(nums[mid] > target){right = mid;}else left = mid + 1;}return nums[left] == target? left : -1; }

獲取右側(cè)邊界的二分查找

原理同上，兩種寫法

int binarySearch_5(int *nums, int numsSize, int target){int left = 0, right = numsSize-1;while(left <= right){int mid = left + (right - left)/2;if(nums[mid] == target){left = mid + 1;}else if(nums[mid] > target){right = mid - 1;}else left = mid + 1;}return nums[right] == target? right : -1; } int binarySearch_6(int *nums, int numsSize, int target){int left = 0, right = numsSize;while(left < right){int mid = left + (right - left)/2;if(nums[mid] == target){left = mid + 1;}else if(nums[mid] > target){right = mid;}else left = mid + 1;}return nums[right-1] == target? right-1 : -1; } int main(){int nums[6] = {1,2,2,2,3,5};printf("binarySearch_1: %d\n", binarySearch_1(nums, 6, 2));printf("binarySearch_2: %d\n", binarySearch_2(nums, 6, 2));printf("binarySearch_3: %d\n", binarySearch_3(nums, 6, 2));printf("binarySearch_4: %d\n", binarySearch_4(nums, 6, 2));printf("binarySearch_5: %d\n", binarySearch_5(nums, 6, 2));printf("binarySearch_6: %d\n", binarySearch_6(nums, 6, 2));return 0; }

“茴香豆”的“茴”字有四種寫法，可這二分法有六種寫法，孔乙己，得虧你生的早啊。

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