An element is a peak element if it is greater than or equal to its four neighbors, left, right, top and bottom. For example neighbors for A[i][j] are A[i-1][j], A[i+1][j], A[i][j-1] and A[i][j+1]. For corner elements, missing neighbors are considered of negative infinite value.

Examples:

Input : 10 20 15 21 30 14 7 16 32 Output : 30 30 is a peak element because all its neighbors are smaller or equal to it. 32 can also be picked as a peak. Input : 10 7 11 17 Output : 17

Below are some facts about this problem:

1: A Diagonal adjacent is not considered as neighbor.

2: A peak element is not necessarily the maximal element.

3: More than one such elements can exist.

4: There is always a peak element. We can see this property by creating some matrices using pen and paper.

**Method 1: (Brute Force)**

Iterate through all the elements of Matrix and check if it is greater/equal to all its neighbors. If yes, return the element.

Time Complexity: O(rows * columns)

Auxiliary Space: O(1)

**Method 2 : (Efficient)**

This problem is mainly an extension of Find a peak element in 1D array. We apply similar Binary Search based solution here.

- Consider mid column and find maximum element in it.
- Let index of mid column be ‘mid’, value of maximum element in mid column be ‘max’ and maximum element be at ‘mat[max_index][mid]’.
- If max >= A[index][mid-1] & max >= A[index][pick+1], max is a peak, return max.
- If max < mat[max_index][mid-1], recur for left half of matrix.
- If max < mat[max_index][mid+1], recur for right half of matrix.

Below is the C++ implementation of above algorithm:

`// Finding peak element in a 2D Array. ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `const` `int` `MAX = 100; ` ` ` `// Function to find the maximum in column 'mid' ` `// 'rows' is number of rows. ` `int` `findMax(` `int` `arr[][MAX], ` `int` `rows, ` `int` `mid, ` `int` `&max) ` `{ ` ` ` `int` `max_index = 0; ` ` ` `for` `(` `int` `i = 0; i < rows; i++) ` ` ` `{ ` ` ` `if` `(max < arr[i][mid]) ` ` ` `{ ` ` ` `// Saving global maximum and its index ` ` ` `// to check its neighbours ` ` ` `max = arr[i][mid]; ` ` ` `max_index = i; ` ` ` `} ` ` ` `} ` ` ` `return` `max_index; ` `} ` ` ` `// Function to find a peak element ` `int` `findPeakRec(` `int` `arr[][MAX], ` `int` `rows, ` `int` `columns, ` ` ` `int` `mid) ` `{ ` ` ` `// Evaluating maximum of mid column. Note max is ` ` ` `// passed by reference. ` ` ` `int` `max = 0; ` ` ` `int` `max_index = findMax(arr, rows, mid, max); ` ` ` ` ` `// If we are on the first or last column, ` ` ` `// max is a peak ` ` ` `if` `(mid == 0 || mid == columns-1) ` ` ` `return` `max; ` ` ` ` ` `// If mid column maximum is also peak ` ` ` `if` `(max >= arr[max_index][mid-1] && ` ` ` `max >= arr[max_index][mid+1]) ` ` ` `return` `max; ` ` ` ` ` `// If max is less than its left ` ` ` `if` `(max < arr[max_index][mid-1]) ` ` ` `return` `findPeakRec(arr, rows, columns, mid - mid/2); ` ` ` ` ` `// If max is less than its left ` ` ` `// if (max < arr[max_index][mid+1]) ` ` ` `return` `findPeakRec(arr, rows, columns, mid+mid/2); ` `} ` ` ` `// A wrapper over findPeakRec() ` `int` `findPeak(` `int` `arr[][MAX], ` `int` `rows, ` `int` `columns) ` `{ ` ` ` `return` `findPeakRec(arr, rows, columns, columns/2); ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `arr[][MAX] = {{ 10, 8, 10, 10 }, ` ` ` `{ 14, 13, 12, 11 }, ` ` ` `{ 15, 9, 11, 21 }, ` ` ` `{ 16, 17, 19, 20 } }; ` ` ` ` ` `// Number of Columns ` ` ` `int` `rows = 4, columns = 4; ` ` ` `cout << findPeak(arr, rows, columns); ` ` ` `return` `0; ` `} ` |

Output: 21

Time Complexity : O(rows * log(columns)). We recur for half number of columns. In every recursive call we linearly search for maximum in current mid column.

Auxiliary Space : O(columns/2) for Recursion Call Stack

This article is contributed by **Rohit Thapliyal**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Shuffle 2n integers in format {a1, b1, a2, b2, a3, b3, ......, an, bn} without using extra space
- Find distinct elements common to all rows of a matrix
- Collect all coins in minimum number of steps
- Search element in a sorted matrix
- Quickhull Algorithm for Convex Hull
- Place k elements such that minimum distance is maximized
- Allocate minimum number of pages
- Find frequency of each element in a limited range array in less than O(n) time
- Find a peak element
- Merge Sort
- Divide and Conquer Algorithm | Introduction
- Find the row with maximum number of 1s
- Find the maximum element in an array which is first increasing and then decreasing
- Program to count number of set bits in an (big) array
- Search in a row wise and column wise sorted matrix