# C++ Program to Find Peak Element of an Array using Binary Search

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C++ Program to find the peak element of an array using Binary Search approach.

Problem Description

1. Using binary search approach one of the peaks in the array can be found.
2. It returns the first peak found as a result.
3. The time complexity of the algorithm is O(log(n)).

Problem Solution

1. Implement the binary search to find a peak in the array.
2. If the middle element is more than its both neighbors, then it is the peak.
3. Otherwise, split the array and check the same.
4. Exit.

Program/Source Code

C++ program to find the peak element of an array using Binary Search approach.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

```#include<iostream>

using namespace std;

// A function implementing Binary search approach to find a peak.
int PeakSearch(int a[], int start, int end)
{
int i, mid;
// Assigning middle of the array.
mid = (end+start+1)/2;
// If mid is at boundary index of the array sub-part, and higher than its only neighbor the mid is the peak of array.
if((a[mid] > a[mid+1] && mid == start)||(a[mid] > a[mid-1] && mid == end))
{
return a[mid];
}
// If mid is higher than its neighbors then it is the peak element.
else if(a[mid] > a[mid-1] && a[mid] > a[mid+1])
{
return a[mid];
}
// If right neighbor is higher then right subpart must have a peak.
else if(a[mid] <= a[mid+1])
{
return PeakSearch(a, mid+1, end);
}
// If left neighbor is higher then left subpart must have a peak.
else if(a[mid] <= a[mid-1])
{
return PeakSearch(a, start,mid-1);
}
}

int main()
{
int n, i, peak;
cout<<"\nEnter the number of data element: ";
cin>>n;

int arr[n];
// Take data input.
for(i = 0; i < n; i++)
{
cout<<"Enter element "<<i+1<<": ";
cin>>arr[i];
}

// Get the peak of the array.
peak = PeakSearch(arr, 0, n-1);

// Print the result.
cout<<"\nThe peak element of the given array is: "<<peak;

return 0;
}```
Program Explanation

1. Assign the data to the array.
2. Call PeakSearch() function with ‘arr’ the array of data, start and end index in the argument list.
3. Assign the mid of subpart of the array.
4. Check if mid is at the boundary index and value at mid is higher than its neighbor then return mid as peak.
5. Otherwise, check if the value at mid is greater than both of its neighbors then return mid as peak.
6. Otherwise, check if the value at the right of mid is greater than mid then send second sub-part of the array into PeakSearch().
7. Otherwise, check if the value at the left of mid is greater than mid then send first sub-part of the array into PeakSearch().
8. Return to main and display the peak value.
9. exit.

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Runtime Test Cases
```
Enter the number of data element: 20
Enter element 1: 3
Enter element 2: 9
Enter element 3: 16
Enter element 4: 45
Enter element 5: 91
Enter element 6: 156
Enter element 7: 984
Enter element 8: 784
Enter element 9: 653
Enter element 10: 641
Enter element 11: 599
Enter element 12: 481
Enter element 13: 411
Enter element 14: 321
Enter element 15: 222
Enter element 16: 198
Enter element 17: 47
Enter element 18: 43
Enter element 19: 22
Enter element 20: 1

The peak element of the given array is: 984```

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