二分查找基础

​ 本⽂探究了⼏个最常⽤的⼆分查找场景：寻找⼀个数、寻找左侧边界、寻找右侧边界。

寻找⼀个数

这个场景是最简单的，可能也是最熟悉的，即搜索⼀个数，如果存在，返回其索引，否则返回 -1。

int BinarySearch(vector<int>& nums, int target) {
    int left = 0;
    int right = nums.size() - 1; 

    while(left <= right) {
        // left + (right-left)/2 为防⽌溢出
        int mid = left + (right-left)/2;  
        if(nums[mid] == target)
            return mid;
        else if(nums[mid] < target)
            left = mid + 1;
        else if(nums[mid] > target)
            right = mid - 1;
    }
    return -1;
}

func BinarySearch(nums []int, target int) int {
    left := 0
    right := len(nums) - 1

    for left <= right {
        // left + (right-left)/2 为防⽌溢出
        mid := left + (right-left)/2
        if nums[mid] == target {
            return mid
        } else if nums[mid] < target {
            left = mid + 1
        } else if nums[mid] > target {
            right = mid - 1
        }
    }
    return -1
}

寻找左侧边界

int left_bound(vector<int>& nums, int target) {
    int left = 0;
    int right = nums.size()-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 if(nums[mid] == target) {
            // 收缩右边界，锁定左边界
            right = mid - 1;
        }
    } 
    // 最后要检查 left 越界的情况
    if(left>=nums.size() || nums[left]!=target){
        return -1;
    }
    return left;
}

func left_bound(nums []int, target int) int {
    left := 0
    right := len(nums) - 1
    for left <= right {
        mid := left + (right-left)/2
        if nums[mid] < target {
            left = mid + 1
        } else if nums[mid] > target {
            right = mid - 1
        } else if nums[mid] == target {
            // 收缩右边界，锁定左边界
            right = mid - 1
        }
    }
    // 最后要检查 left 越界的情况
    if left >= len(nums) || nums[left] != target {
        return -1
    }
    return left
}

寻找右侧边界

int right_bound(vector<int>& nums, int target) {
    int left = 0;
    int right = nums.size()-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 if(nums[mid] == target) {
            // 收缩左边界，锁定右边界
            left = mid + 1;
        }
    }
    // 最后要检查 right 越界的情况
    if(right<0 || nums[right]!=target)
        return -1;
    return right;
}

func right_bound(nums []int, target int) int {
    left := 0
    right := len(nums) - 1
    for left <= right {
        mid := left + (right-left)/2
        if nums[mid] < target {
            left = mid + 1
        } else if nums[mid] > target {
            right = mid - 1
        } else if nums[mid] == target {
            // 收缩左边界，锁定右边界
            left = mid + 1
        }
    }
    // 最后要检查 right 越界的情况
    if right < 0 || nums[right] != target {
        return -1
    }
    return right
}