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Find number of transformation to make two Matrix Equal in C++
In this problem, we are given two matrices mat1[][] and mat2[][] of the same size. Our task is to find the number of transformations to make two Matrices Equal.
The transformation one matrices are −
Select any matrix of the two matrices.
Select a row or column from the matrices
Add 1 to all elements of the selected row or column.
Let’s take an example to understand the problem,
Input
mat1[][] = {{1 2} {2 1}} mat1[][] = {{2 3} {4 3}}
Output
3
Explanation
1 2 => 2 2 => 2 3 => 2 3 2 1 => 3 1 => 3 2 => 4 3
Solution Approach
A simple solution to the problem is by finding whether transformation is possible or not. For this, we need to check −
if( mat[i][j] - mat[i][0] - mat[0][j] + mat[0][0] != 0 )
Then no solution exists.
Now, if transformation is possible, we will count transformations for rows and columns.
Program to illustrate the working of our solution,
Example
#include <bits/stdc++.h> using namespace std; const int MAX = 100; int countTransformationReq(int mat1[][MAX], int mat2[][MAX], int m, int n) { for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) mat1[i][j] -= mat2[i][j]; for (int i = 1; i < n; i++) for (int j = 1; j < m; j++) if (mat1[i][j] - mat1[i][0] - mat1[0][j] + mat1[0][0] != 0) return -1; int trxCount = 0; for (int i = 0; i < n; i++) trxCount += abs(mat1[i][0]); for (int j = 0; j < m; j++) trxCount += abs(mat1[0][j] - mat1[0][0]); return (trxCount); } int main() { int mat1[MAX][MAX] = { {1, 2}, {2, 1}}; int mat2[MAX][MAX] = { {2, 3}, {4, 3}}; cout<<"The number of transformation to make the teo maxtrces equal are "<<countTransformationReq(mat1, mat2, 2, 2) ; return 0; }
Output
The number of transformation to make the teo maxtrces equal are 3
Efficient approach
A more effective solution to the problem is by using the handshake formula.
We will create a temp[] array to count the occurrence of 0 and 1 in the modulo of the array. And then return the count value.
Program to illustrate the working of our solution,
Example
#include<iostream> using namespace std; int countEvenSumSubArray(int arr[], int n){ int temp[2] = {1, 0}; int count = 0, sum = 0; for (int i=0; i<=n-1; i++){ sum = ( (sum + arr[i]) % 2 + 2) % 2; temp[sum]++; } count += (temp[0]*(temp[0]-1)/2); count += (temp[1]*(temp[1]-1)/2); return (count); } int main(){ int arr[] = {2, 1, 4, 2}; int n = sizeof (arr) / sizeof (arr[0]); cout<<"The count of Subarrays with even sum is "<<countEvenSumSubArray(arr, n); return (0); }
Output
The count of Subarrays with even sum is 4
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