An item is said to be a peak element when it is greater than or equal with all four neighbor of that element. The neighbor elements are the top, bottom, left and right elements. For this problem, we will consider some bounds. The diagonal elements are not checked as neighbor elements. More than one peak element may present in a matrix, and the peak element is not necessarily the largest element in the matrix.
Input and Output
Input: A matrix of different numbers. 10 8 10 10 14 13 12 11 15 9 11 11 15 9 11 21 16 17 19 20 Output: The peak element of the matrix. Here the peak element is: 21
Algorithm
findMaxMid(rows, mid, max)
Input: Rows number of the matrix, mid row, a max element as an output argument.
Output: Update the max item and index of the max element.
Begin maxIndex := 0 for all rows r in the matrix, do if max < matrix[i, mid], then max = matrix[i, mid], maxIndex := r done return maxIndex End
findPeakElement(rows, columns, mid)
Input − Row and column of the matrix, and mid row place.
Output − Peak element in the matrix.
Begin maxMid := 0 maxMidIndex := findMaxMid(rows, mid, maxMid) if mid is first or last column, then return maxMid if maxMid>= item of previous and next row for mid column, then return maxMid if maxMid is less than its left element, then res := findPeakElement(rows, columns, mid – mid/2) return res if maxMid is less than its right element, then res := findPeakElement(rows, columns, mid + mid/2) return res End
Example
#include<iostream>
#define M 4
#define N 4
using namespace std;
intarr[M][N] = {
{10, 8, 10, 10},
{14, 13, 12, 11},
{15, 9, 11, 21},
{16, 17, 19, 20}
};
intfindMaxMid(int rows, int mid, int&max) {
intmaxIndex = 0;
for (int i = 0; i < rows; i++) { //find max element in the mid column
if (max <arr[i][mid]) {
max = arr[i][mid];
maxIndex = i;
}
}
return maxIndex;
}
intfindPeakElement(int rows, int columns, int mid) {
intmaxMid = 0;
intmaxMidIndex = findMaxMid(rows, mid, maxMid);
if (mid == 0 || mid == columns-1) //for first and last column, the maxMid is maximum
return maxMid;
// If maxMid is also peak
if (maxMid>= arr[maxMidIndex][mid-1] &&maxMid>= arr[maxMidIndex][mid+1])
return maxMid;
if (maxMid<arr[maxMidIndex][mid-1]) // If maxMid is less than its left element
return findPeakElement(rows, columns, mid - mid/2);
return findPeakElement(rows, columns, mid+mid/2);
}
int main() {
int row = 4, col = 4;
cout<< "The peak element is: "<<findPeakElement(row, col, col/2);
}Output
The peak element is: 21