Description： Let’s call an array A a mountain if the following properties hold:

A.length >= 3
There exists some 0 < i < A.length - 1 such that A[0] < A[1] < ... A[i-1] < A[i] > A[i+1] > ... > A[A.length - 1]

Given an array that is definitely a mountain, return any i such that A[0] < A[1] < … A[i-1] < A[i] > A[i+1] > … > A[A.length - 1].

Example 1:

Input: [0,1,0]
Output: 1

Example 2:

Input: [0,2,1,0]
Output: 1

Note:

• 3 <= A.length <= 10000
• 0 <= A[i] <= 10^6
• A is a mountain, as defined above.

題意：給定一個一維陣列，要求找出位置i（0 < i < A.length - 1），另其滿足 A[0] < A[1] < … A[i-1] < A[i] > A[i+1] > … > A[A.length - 1]；

解法：對於位置i左邊和右邊的元素來說，是已經排好序的了，因此我們可以利用二分查詢法，定義left = 0, right = A.length - 1，mid = (left + right) /2 ；找到滿足A[mid] > A[mid - 1] && A[mid] > A[mid + 1]的那個位置；

Java

class Solution {
    public int peakIndexInMountainArray(int[] A) {
        int left = 0;
        int right = A.length - 1;
        while (left <= right) {
            int mid = (left + right) / 2;
            if (A[mid] > A[mid - 1] && A[mid] > A[mid + 1]) return mid;
            else if (A[mid] > A[mid - 1]) left = mid + 1;
            else right = mid - 1;
        }
        return -1;
    }
}