二分查找 解题通用模板

 /**
     * 范围查询规律
     * 初始化:
     *   int left = 0;
     *   int right = nums.length - 1;
     * 循环条件
     *   left <= right
     * 右边取值
     *   right = mid - 1
     * 左边取值
     *   left = mid + 1
     * 查询条件
     *   >= target值, 则 nums[mid] >= target时, 都减right = mid - 1
     *   >  target值, 则 nums[mid] >  target时, 都减right = mid - 1
     *   <= target值, 则 nums[mid] <= target时, 都加left = mid + 1
     *   <  target值, 则 nums[mid] <  target时, 都加left = mid + 1
     * 结果
     *   求大于(含等于), 返回left
     *   求小于(含等于), 返回right
     * 核心思想: 要找某个值, 则查找时遇到该值时, 当前指针(例如right指针)要错过它, 让另外一个指针(left指针)跨过他(体现在left <= right中的=号), 则找到了
     */

例1：

答案：

class Solution {
     public int[] searchRange(int[] nums, int target) {
        //寻找左边界(这里寻找第一个 >= target的索引)
        int leftIndex = search(nums, target);
        if (leftIndex >= nums.length || nums[leftIndex] != target){
            return new int[]{-1, -1};
        }
        //寻找右边界(这里寻找第一个 >= target+1的索引)
        int rightIndex = search(nums, target + 1);
        return new int[]{leftIndex, rightIndex - 1};
    }

    /**
     * 寻找第一个>=目标值的索引, 找不到则返回数组长度
     */
    private int search(int[] nums, int target) {
        int left = 0;
        int right = nums.length - 1;
        while (left <= right){
            int mid = (right - left) / 2 + left;
            if (nums[mid] >= target){
                right = mid - 1;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}

例2：

代码：

class Solution {
    public int searchInsert(int[] nums, int target) {
        int index=getOne(nums,target);
        if(index==nums.length){
            return index;
        }
        if(nums[index]==target){
            return index;
        }
        return index;
    }

    //寻找第一个>=target的数的下标
    public int getOne(int[] nums, int target){
        int left=0;
        int right=nums.length-1;
        while(left<=right){
            int mid=(right-left)/2+left;
            if(nums[mid]>=target){
                right=mid-1;
            }else{
                left=mid+1;
            }
        }
        return left;
    }
}

class Solution {
    public int mySqrt(int target) {
        if(target==0 || target==1){
            return target;
        }
        
        return getNum(target);
    }
    //找<=target的最大整数、
    public int getNum(int target){
        int left=0;
        int right=target-1;
        // int ans;
        while(left<=right){
            int mid=(right-left)/2+left;
            if((long)mid*(long)mid<=target){
                left=mid+1;
            }else{
                right=mid-1;
            }
        }
        return right;
    }
}