162. Find Peak Element

Problem Statement

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

Given a 0-indexed integer array nums, find a peak element, and return its index. If the array contains multiple peaks, return the index to any of the peaks.

You may imagine that nums[-1] = nums[n] = -∞. In other words, an element is always considered to be strictly greater than a neighbor that is outside the array.

You must write an algorithm that runs in O(log n) time.

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: 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.

Constraints:

1 <= nums.length <= 1000
-231 <= nums[i] <= 231 - 1
nums[i] != nums[i + 1] for all valid i.

Intuition

Approach:

There is increasing curve, Then peak, Then decreasing

We find at each step if we are at increasing or decreasing 
And move like that

Links

https://leetcode.com/problems/find-peak-element/description/

Video Links

https://www.youtube.com/watch?v=cXxmbemS6XM&ab_channel=takeUforward

Approach 1:

C++

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

        return 0;
    }
};

Approach 2:

C++

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

        return nums.size()-1;
    }
};

Approach 3:

OPtimal

C++

class Solution {
public:
    int find_ans(vector<int>& arr, int low, int high){
        while(low<=high){
            int mid = low+(high-low)/2;
            if(arr[mid-1] < arr[mid] and arr[mid] > arr[mid+1])
                return mid;
            else if(arr[mid-1] < arr[mid])
                low = mid+1;
            else
                high=mid-1;
        }
        return -1;
    }

    int findPeakElement(vector<int>& nums) {
        int n = nums.size();
        if(n == 1 or nums[0] > nums[1])
            return 0;

        if(nums[n-1] > nums[n-2])
            return n-1;

        return find_ans(nums,1, n-2);
    }
};

Approach 4:

C++