Question

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:

1. 3 <= A.length <= 10000
2. 0 <= A[i] <= 10^6
3. A is a mountain, as defined above.

Difficulty:Easy

Category:Binary-Search

Analyze

这是一道 easy 题目， 可以通过线扫描，找到最大的顶点数值， 也可以通过Binary Search 的方式在 log n 的时间内找到。

Solution

Solution 1: Line Scan

Time Complexity: O(n), Space Complexity: O(1)

class Solution {
 public:
  int peakIndexInMountainArray(vector<int>& A) {
    for (int i = 1; i < A.size(); ++i)
      if (A[i] < A[i - 1]) return i - 1;
    return 0;
  }
};

Solution 2: Binary Search

Time complexity: O(log n), Space Complexity: O(1)

class Solution {
 public:
  int peakIndexInMountainArray(vector<int>& A) {
    // Binary Search
    int left = 0, right = A.size();
    while (left < right) {
      int mid = left + (right - left) / 2;
      if (A[mid] > A[mid + 1]) right = mid; // For the left part
      else left = mid + 1;
    }
    return left;
  }
};