Number of elements greater than modified mean in matrix

Normally mean of matrix is the average of all elements present in matrix. Consider a modified mean as floor of mean of row-wise minimum and column-wise maximum. Row-wise minimum is the minimum element from each row of given matrix and column-wise maximum is the maximum element from each column. Given a matrix of order n*m, find the number of elements greater than 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 sum of all row-wise minimum and sum of all column-wise maximum. Take the mean of this sum by dividing the sum value with (n+m) i.e., total number of rows and columns. Now, as we have the mean of row-wise minimum and column-wise maximum, iterate over the matrix to find the number of elements greater than calculated mean.

Below is the implementation of above approach:

C++

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// 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 mean
int 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 function
int 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;
}

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Java

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// Java program to count
// number of elements 
// greater than mean
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(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.

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C#

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// C# program to count number of 
// elements greater than mean
using 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));
    }
}
  
// This article is contribute by nitin mittal.

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PHP

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<?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 mean
function 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.
?>

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Output:

11


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Improved By : nitin mittal, vt_m



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