二分查找

基本的二分搜索法

704.Binary Search

public int search(int[] nums, int target) {
    int low = 0;
    int high = nums.length - 1;
    // 停止条件 <= ：因为high=length-1, 使用的是闭区间
    // 结束情形：low > high
    while (low <= high) {
        int mid = low + (high - low) / 2;
        // 找到目标值, 可以终止
        if (nums[mid] == target) {
            return mid;
        }else if (nums[mid] > target) {
            // 当nums[mid] > target时，high=mid+1，因为mid已经搜索过，
            // 应该从搜索区间去除
            high = mid - 1;
        }else {
            // 同理
            low = mid + 1;
        }
    }
    return -1;
}

左右边界的二分搜索法

34.Find First and Last Position of Element in Sorted Array

public int[] searchRange(int[] nums, int target) {
    int[] res = new int[]{-1, -1};
    int low = 0;
    int high = nums.length - 1;

    if (nums.length == 0) {
        return res;
    }

    // 左边界
    while(low <= high) {
        int mid = low + (high - low) / 2;
        if (nums[mid] >= target) {
            high = mid - 1;
        } else {
            low = mid + 1;
        }
    }
    if (low >= nums.length || nums[low] != target) {
        return res;
    }else {
        res[0] = low;
    }

    // 右边界
    high = nums.length - 1;
    while(low <= high) {
        int mid = low + (high - low) / 2;
        if(nums[mid] <= target) {
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }
    res[1] = high;
    return res;
}

模板：

int left_bound(int[] nums, int target) {
    int left = 0, right = nums.length - 1;
    // 注意结束条件
    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) {
            // 别返回，锁定左侧边界
            right = mid - 1;
        }
    }
    // 重要：最后要检查 left 越界的情况
    if (left >= nums.length || nums[left] != target)
        return -1;
    return left;
}


int right_bound(int[] nums, int target) {
    int left = 0, right = nums.length - 1;
    // 注意结束条件
    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) {
            // 别返回，锁定右侧边界
            left = mid + 1;
        }
    }
    // 重要：最后要检查 right 越界的情况
    if (right < 0 || nums[right] != target)
        return -1;
    return right;
}

Cest la vie!