162. Find Peak Element

• Difficulty: Medium

• Topics: Array, Binary Search

• Similar Questions:

  • Peak Index in a Mountain Array

Problem:

A peak element is an element that is greater than its neighbors.

Given an input array nums, where nums[i] ≠ nums[i+1], find a peak element and return its index.

The array may contain multiple peaks, in that case return the index to any one of the peaks is fine.

You may imagine that nums[-1] = nums[n] = -∞.

Example 1:

Input: nums = [1,2,3,1]
Output: 2
Explanation: 3 is a peak element and your function should return the index number 2.

Example 2:

Input: nums = [1,2,1,3,5,6,4]
Output: 1 or 5 
Explanation: Your function can return either index number 1 where the peak element is 2, 
             or index number 5 where the peak element is 6.

Note:

Your solution should be in logarithmic complexity.

Solutions:

class Solution {
public:
    int findPeakElement(vector<int>& nums) { // this problem does not eliminate the scenario [1]
        int left = 0;
        int right = nums.size() - 1;
        while (left + 1 < right) {
            int mid = left + (right - left)/2;
            if (nums[mid] > nums[mid-1] && nums[mid] > nums[mid + 1])   return mid;
            if (nums[mid] < nums[mid - 1]) right = mid;
            else left = mid;
        }

        if (left == 0) {
            if (nums.size() > left + 1 && nums[left + 1] < nums[left])   return left;
            else return right;
        } else {
            if (nums.size() > left + 1 && left -1 >= 0 && nums[left] > nums[left - 1] && nums[left] > nums[left + 1]) return left;
            else return right;
        }
    }
};