# Minimum operations of given type to make all elements of a matrix equal in C++

C++Server Side ProgrammingProgramming

## Problem statement

Given an integer K and a matrix of M x N, the task is to find the minimum number of operations required to make all the elements of the matrix equal. In a single operation, K can be added to or subtracted from any element of the matrix.

## Example

If input matrix is:
{
{2, 4},
{20, 40}
} and K = 2 then total 27 operations required as follows;
Matrix = 2 + (K * 9) = 20 = 9 operations
Matrix = 4 + (k * 8) = 20 = 8 operations
Matrix = 20 + (k * 10) = 40 = 10 operations

## Algorithm

1. Since we are only allowed to add or subtract K from any element, we can easily infer that mod of all the elements with K should be equal. If it’s not, then return -1
2. sort all the elements of the matrix in non-deceasing order and find the median of the sorted elements
3. The minimum number of steps would occur if we convert all the elements equal to the median

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
int getMinOperations(int n, int m, int k, vector<vector<int> >& matrix) {
vector<int> arr(n * m, 0);
int mod = matrix % k;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
arr[i * m + j] = matrix[i][j];
if (matrix[i][j] % k != mod) {
return -1;
}
}
}
sort(arr.begin(), arr.end());
int median = arr[(n * m) / 2];
int minOperations = 0;
for (int i = 0; i < n * m; ++i)
minOperations += abs(arr[i] - median) / k;
if ((n * m) % 2 == 0) {
int newMedian = arr[(n * m) / 2];
int newMinOperations = 0;
for (int i = 0; i < n * m; ++i)
newMinOperations += abs(arr[i] - newMedian) / k;
minOperations = min(minOperations, newMinOperations);
}
return minOperations;
}
int main() {
vector<vector<int> > matrix = {
{ 2, 4},
{ 20, 40},
};
int n = matrix.size();
int m = matrix.size();
int k = 2;
cout << "Minimum required operations = " <<
getMinOperations(n, m, k, matrix) << endl;
return 0;
}

When you compile and execute above program. It generates following output

## Output

Minimum required operations = 27