Normally mean of the matrix is the average of all elements present in the matrix. Consider a modified mean as the floor of the mean of the row-wise minimum and column-wise maximum. The row-wise minimum is the minimum element from each row of the given matrix and the column-wise maximum is the maximum element from each column. Given a matrix of order n*m, find the number of elements greater than the new mean obtained.
mean = floor ( (sum(row-wise Min) + sum (col-wise Max )) /
(row_no. + col_no.) )
Examples :
Input : mat[][] = {1, 5, 6,
2, 3, 0,
5, 2, 8}
Output : 4
Input : mat[][] = {1, 5,
5, 2}
Output : 2
Find the sum of all row-wise minimums and the sum of all column-wise maximums. Take the mean of this sum by dividing the sum value with (n+m) i.e., the total number of rows and columns. Now, as we have the mean of the row-wise minimum and column-wise maximum, iterate over the matrix to find the number of elements greater than the calculated mean
Below is the implementation of the above approach:
C++
// CPP program to count number of// elements greater than mean#include <bits/stdc++.h>using namespace std;// define constant for row and column#define n 4#define m 5// function to count elements // greater than meanint countElements(int mat[][m]){ // For each row find minimum // element and add to rowSum int rowSum = 0; for (int i = 0; i < n; i++) { int min = mat[i][0]; for (int j = 1; j < m; j++) if (mat[i][j] < min) min = mat[i][j]; rowSum += min; } // For each column find maximum // element and add to colSum int colSum = 0; for (int i = 0; i < m; i++) { int max = mat[0][i]; for (int j = 1; j < n; j++) if (max < mat[j][i]) max = mat[j][i]; colSum += max; } // Calculate mean of row-wise // minimum and column wise maximum int mean = (rowSum + colSum) / (m + n); // For whole matrix count // elements greater than mean int count = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mean < mat[i][j]) count++; return count;}// driver functionint main(){ int mat[n][m] = { 5, 4, 2, 8, 7, 1, 5, 8, 3, 4, 8, 5, 4, 6, 0, 2, 5, 8, 9, 4 }; cout << countElements(mat); return 0;} |
Java
// Java program to count// number of elements // greater than meanclass GFG { static int n = 4, m = 5; // function to count // elements greater // than mean static int countElements(int mat[][]) { // For each row find // minimum element // and add to rowSum int rowSum = 0; for (int i = 0; i < n; i++) { int min = mat[i][0]; for (int j = 1; j < m; j++) if (mat[i][j] < min) min = mat[i][j]; rowSum += min; } // For each column // find maximum // element and add // to colSum int colSum = 0; for (int i = 0; i < m; i++) { int max = mat[0][i]; for (int j = 1; j < n; j++) if (max < mat[j][i]) max = mat[j][i]; colSum += max; } // Calculate mean of // row-wise minimum // and column wise // maximum int mean = (rowSum + colSum) / (m + n); // For whole matrix // count elements // greater than mean int count = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mean < mat[i][j]) count++; return count; } // driver function public static void main(String[] args) { int mat[][] = {{ 5, 4, 2, 8, 7}, {1, 5, 8, 3, 4}, {8, 5, 4, 6, 0}, {2, 5, 8, 9, 4}}; System.out.println(countElements(mat)); }}// This article is contribute by Prerna Saini. |
Python3
# Python3 program to count# number of elements# greater than meann = 4;m = 5;# Function to count# elements greater# than meandef countElements(mat): # For each row find # minimum element # and add to rowSum rowSum = 0; for i in range(n): min = mat[i][0]; for j in range(1, m): if (mat[i][j] < min): min = mat[i][j]; rowSum += min; # For each column # find maximum # element and add # to colSum colSum = 0; for i in range(m): max = mat[0][i]; for j in range(1, n): if (max < mat[j][i]): max = mat[j][i]; colSum += max; # Calculate mean of # row-wise minimum # and column wise # maximum mean = ((rowSum + colSum) / (m + n)); # For whole matrix # count elements # greater than mean count = 0; for i in range(n): for j in range(m): if (mean < mat[i][j]): count += 1; return count;# Driver codeif __name__ == '__main__': mat = [[5, 4, 2, 8, 7], [1, 5, 8, 3, 4], [8, 5, 4, 6, 0], [2, 5, 8, 9, 4]]; print(countElements(mat));# This code is contributed by 29AjayKumar |
C#
// C# program to count number of // elements greater than meanusing System;class GFG { static int n = 4, m = 5; // function to count elements // greater than mean static int countElements(int [,]mat) { // For each row find minimum // element and add to rowSum int rowSum = 0; for (int i = 0; i < n; i++) { int min = mat[i,0]; for (int j = 1; j < m; j++) if (mat[i,j] < min) min = mat[i,j]; rowSum += min; } // For each column find maximum // element and add to colSum int colSum = 0; for (int i = 0; i < m; i++) { int max = mat[0,i]; for (int j = 1; j < n; j++) if (max < mat[j,i]) max = mat[j,i]; colSum += max; } // Calculate mean of row-wise minimum // and column wise maximum int mean = (rowSum + colSum) / (m + n); // For whole matrix count // elements greater than mean int count = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mean < mat[i,j]) count++; return count; } // Driver function public static void Main() { int [,]mat = {{5, 4, 2, 8, 7}, {1, 5, 8, 3, 4}, {8, 5, 4, 6, 0}, {2, 5, 8, 9, 4}}; Console.Write(countElements(mat)); }}// |
PHP
<?php// PHP program to count number of// elements greater than mean// define constant for // row and column$n = 4;$m = 5;// function to count elements // greater than meanfunction countElements($mat){ // For each row find minimum // element and add to rowSum $rowSum = 0; global $n, $m; for ($i = 0; $i < $n; $i++) { $min = $mat[$i][0]; for ($j = 1; $j < $m; $j++) if ($mat[$i][$j] < $min) $min = $mat[$i][$j]; $rowSum += $min; } // For each column find maximum // element and add to colSum $colSum = 0; for ($i = 0; $i < $m; $i++) { $max = $mat[0][$i]; for ($j = 1; $j < $n; $j++) if ($max < $mat[$j][$i]) $max = $mat[$j][$i]; $colSum += $max; } // Calculate mean of row-wise // minimum and column wise maximum $mean = ($rowSum + $colSum) / ($m + $n); // For whole matrix count // elements greater than mean $count = 0; for ($i = 0; $i < $n; $i++) for ($j = 0; $j < $m; $j++) if ($mean < $mat[$i][$j]) $count++; return $count;}// Driver Code$mat = array(array(5, 4, 2, 8, 7), array(1, 5, 8, 3, 4), array(8, 5, 4, 6, 0), array(2, 5, 8, 9, 4));echo countElements($mat);// This code is contribute by vt_m.?> |
Javascript
<script>// Javascript program to count number of// elements greater than mean// define constant for row and columnvar n = 4var m = 5// function to count elements // greater than meanfunction countElements(mat){ // For each row find minimum // element and add to rowSum var rowSum = 0; for (var i = 0; i < n; i++) { var min = mat[i][0]; for (var j = 1; j < m; j++) if (mat[i][j] < min) min = mat[i][j]; rowSum += min; } // For each column find maximum // element and add to colSum var colSum = 0; for (var i = 0; i < m; i++) { var max = mat[0][i]; for (var j = 1; j < n; j++) if (max < mat[j][i]) max = mat[j][i]; colSum += max; } // Calculate mean of row-wise // minimum and column wise maximum var mean = (rowSum + colSum) / (m + n); // For whole matrix count // elements greater than mean var count = 0; for (var i = 0; i < n; i++) for (var j = 0; j < m; j++) if (mean < mat[i][j]) count++; return count;}// driver functionvar mat = [ [5, 4, 2, 8, 7], [1, 5, 8, 3, 4], [8, 5, 4, 6, 0], [2, 5, 8, 9, 4 ]];document.write( countElements(mat));</script> |
Output
11
Time Complexity: O(n*m), where n is the number of rows and m is the number of columns.
Auxiliary Space: O(1)
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