# 162. Find Peak Element

## Problem Statement

<br>

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.

&#x20;

**Example 1:**

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

**Example 2:**

<pre><code><strong>Input: nums = [1,2,1,3,5,6,4]
</strong><strong>Output: 5
</strong><strong>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.
</strong></code></pre>

&#x20;

**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:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
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;
    }
};
```

{% endcode %}

### Approach 2:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
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;
    }
};
```

{% endcode %}

### Approach 3:

```
OPtimal
```

{% code title="C++" lineNumbers="true" %}

```cpp
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);
    }
};
```

{% endcode %}

### Approach 4:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

###


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