[Dichotomy] leetcode1095: Mountain array to find the target value (hard)

topic:

1095. Mountain array to find the target

answer:

• Three dichotomy looking mountains in the target array,
• The first two points: that the binary template Ⅱ, looking for peaks in the array, the array is divided into an array of arrays and the first half of the second half of the descending ascending
• Second half: half of the array in ascending order to continue to use the previous dichotomy template Ⅱ, to find a minimum value greater than or equal to x
• Third Division: If the first half did not find x, we need to use the template Ⅱ dichotomy of looking for the second half of descending array x

code show as below:

class Solution {
public:
    //思路：三次二分查找寻找目标值的最小下标
    int findInMountainArray(int target, MountainArray &mountainArr) {
        //注意使用闭区间，如果使用开区间，在[size-1,size)时mid取左中位数，mid+1会溢出，所以我们使用闭区间
        int left=0,right=mountainArr.length()-1;

        //第一次二分，寻找山脉的山峰
        while(left<right){
            //取左中位数，因为进入循环，数组一定至少有 2 个元素
            //因此，左中位数一定有右边元素，数组下标不会发生越界
            int mid=left+((right-left)>>1);
            //mid所指的值大于等于mid+1，那么山峰在数组的左边，我们应该向左边逼近
            if(mountainArr.get(mid)>=mountainArr.get(mid+1))right=mid;
            //mid所指的值小于mid+1，那么山峰在数组的右边，我们应该向右边逼近
            else left=mid+1;
        }
        //根据题意山峰一定存在，所以我们不用特判了
        int peak=left;

        //第二次二分，在前半部分升序数组中寻找target
        left=0,right=peak;
        while(left<right){
            int mid=left+((right-left)>>1);
            if(mountainArr.get(mid)>=target)right=mid;
            else left=mid+1;
        }
        //在左边找到target，直接返回下标，否则在右半部分寻找
        if(mountainArr.get(left)==target)return left;

        //第三次二分，在后半部分降序数组中寻找target
        left=peak+1,right=mountainArr.length()-1;
        while(left<right){
            int mid=left+((right-left)>>1);
            //注意这里为<=，因为mid比x小，mid右边的元素肯定比x大，那么我们应该向左逼近
            if(mountainArr.get(mid)<=target)right=mid;
            else left=mid+1;
        }
        //在右边找到target后，直接返回下标，否则返回-1
        if(mountainArr.get(left)==target)return left;
        return -1;
    }
};