Unique cells in a binary matrix
Given a matrix of size n x m consisting of 0’s and 1’s.We need to find number of unique cells with value 1 such that corresponding entire row and entire column does not have another 1.Return the number of unique cells.
Examples:
Input : mat[][] = {0, 1, 0, 0
0, 0, 1, 0
1, 0, 0, 1}
Answer : 2
The two 1s that are unique
in their rows and columns
are highlighted.
Input : mat[][] = {
{0, 0, 0, 0, 0, 0, 1}
{0, 1, 0, 0, 0, 0, 0}
{0, 0, 0, 0, 0, 1, 0}
{1, 0, 0, 0, 0, 0, 0}
{0, 0, 1, 0, 0, 0, 1}
Output : 3
Method 1- Brute Force Approach
In this approach, we are going to check for each cell with value 1 whether the corresponding rows
satisfy our requirement. We will check in corresponding rows and columns of each cell with value 1.
C++
// C++ program to count unique cells in // a matrix #include <bits/stdc++.h> using namespace std; const int MAX = 100; // Returns true if mat[i][j] is unique bool isUnique(int mat[][MAX], int i, int j, int n, int m) { // checking in row calculating sumrow // will be moving column wise int sumrow = 0; for (int k = 0; k < m; k++) { sumrow += mat[i][k]; if (sumrow > 1) return false; } // checking in column calculating sumcol // will be moving row wise int sumcol = 0; for (int k = 0; k < n; k++) { sumcol += mat[k][j]; if (sumcol > 1) return false; } return true; } int countUnique(int mat[][MAX], int n, int m) { int uniquecount = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i][j] && isUnique(mat, i, j, n, m)) uniquecount++; return uniquecount; } // Driver code int main() { int mat[][MAX] = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}}; cout << countUnique(mat, 3, 4); return 0; } |
Java
// Efficient Java program to count unique // cells in a binary matrix class GFG { static final int MAX = 100; // Returns true if mat[i][j] is unique static boolean isUnique(int mat[][], int i, int j, int n, int m) { // checking in row calculating sumrow // will be moving column wise int sumrow = 0; for (int k = 0; k < m; k++) { sumrow += mat[i][k]; if (sumrow > 1) return false; } // checking in column calculating sumcol // will be moving row wise int sumcol = 0; for (int k = 0; k < n; k++) { sumcol += mat[k][j]; if (sumcol > 1) return false; } return true; } static int countUnique(int mat[][], int n, int m) { int uniquecount = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i][j]!=0 && isUnique(mat, i, j, n, m)) uniquecount++; return uniquecount; } // Driver code static public void main(String[] args) { int mat[][] = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}}; System.out.print(countUnique(mat, 3, 4)); } } // This code is contributed by Rajput-Ji |
Python3
# Python3 program to count unique cells in # a matrix MAX = 100 # Returns true if mat[i][j] is unique def isUnique(mat, i, j, n, m): # checking in row calculating sumrow # will be moving column wise sumrow = 0 for k in range(m): sumrow += mat[i][k] if (sumrow > 1): return False # checking in column calculating sumcol # will be moving row wise sumcol = 0 for k in range(n): sumcol += mat[k][j] if (sumcol > 1): return False return True def countUnique(mat, n, m): uniquecount = 0 for i in range(n): for j in range(m): if (mat[i][j] and isUnique(mat, i, j, n, m)): uniquecount += 1 return uniquecount # Driver code mat = [[0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 1]] print(countUnique(mat, 3, 4)) # This code is contributed by mohit kumar 29 |
C#
// Efficient C# program to count unique // cells in a binary matrix using System; public class GFG { static readonly int MAX = 100; // Returns true if mat[i][j] is unique static bool isUnique(int [,]mat, int i, int j, int n, int m) { // checking in row calculating sumrow // will be moving column wise int sumrow = 0; for (int k = 0; k < m; k++) { sumrow += mat[i,k]; if (sumrow > 1) return false; } // checking in column calculating sumcol // will be moving row wise int sumcol = 0; for (int k = 0; k < n; k++) { sumcol += mat[k,j]; if (sumcol > 1) return false; } return true; } static int countUnique(int [,]mat, int n, int m) { int uniquecount = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i,j]!=0 && isUnique(mat, i, j, n, m)) uniquecount++; return uniquecount; } // Driver code static public void Main() { int [,]mat = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}}; Console.Write(countUnique(mat, 3, 4)); } } // This code is contributed by Rajput-Ji |
PHP
<?php // PHP program to count // unique cells in a matrix $MAX = 100; // Returns true if // mat[i][j] is unique function isUnique($mat, $i, $j, $n, $m) { global $MAX; // checking in row calculating // sumrow will be moving column wise $sumrow = 0; for ($k = 0; $k < $m; $k++) { $sumrow += $mat[$i][$k]; if ($sumrow > 1) return false; } // checking in column // calculating sumcol // will be moving row wise $sumcol = 0; for ($k = 0; $k < $n; $k++) { $sumcol += $mat[$k][$j]; if ($sumcol > 1) return false; } return true; } function countUnique($mat, $n, $m) { $uniquecount = 0; for ($i = 0; $i < $n; $i++) for ($j = 0; $j < $m; $j++) if ($mat[$i][$j] && isUnique($mat, $i, $j, $n, $m)) $uniquecount++; return $uniquecount; } // Driver code $mat = array(array(0, 1, 0, 0), array(0, 0, 1, 0), array(1, 0, 0, 1)); echo countUnique($mat, 3, 4); // This code is contributed by ajit ?> |
Output:
2
Time Complexity: O((n*m)*(n+m))
This goes to order of cubic due to check condition for every corresponding row and column
Method 2- O(n*m) Approach
In this approach, we are going to use extra space for rowsum array and colsum array and then check for each cell with value 1 whether the corresponding rowsum array and colsum array values are 1.
C++
// Efficient C++ program to count unique // cells in a binary matrix #include <bits/stdc++.h> using namespace std; const int MAX = 100; int countUnique(int mat[][MAX], int n, int m) { int rowsum[n], colsum[m]; memset(colsum, 0, sizeof(colsum)); memset(rowsum, 0, sizeof(rowsum)); // Count number of 1s in each row // and in each column for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i][j]) { rowsum[i]++; colsum[j]++; } // Using above count arrays, find // cells int uniquecount = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i][j] && rowsum[i] == 1 && colsum[j] == 1) uniquecount++; return uniquecount; } // Driver code int main() { int mat[][MAX] = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}}; cout << countUnique(mat, 3, 4); return 0; } |
Java
// Efficient Java program to count unique // cells in a binary matrix class GFG { static int MAX = 100; static int countUnique(int mat[][], int n, int m) { int []rowsum = new int[n]; int []colsum = new int[m]; // Count number of 1s in each row // and in each column for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i][j] != 0) { rowsum[i]++; colsum[j]++; } // Using above count arrays, find // cells int uniquecount = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i][j] != 0 && rowsum[i] == 1 && colsum[j] == 1) uniquecount++; return uniquecount; } // Driver code public static void main(String[] args) { int mat[][] = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}}; System.out.print(countUnique(mat, 3, 4)); } } // This code is contributed by Rajput-Ji |
Python3
# Efficient Python3 program to count unique # cells in a binary matrix MAX = 100; def countUnique(mat, n, m): rowsum = [0] * n; colsum = [0] * m; # Count number of 1s in each row # and in each column for i in range(n): for j in range(m): if (mat[i][j] != 0): rowsum[i] += 1; colsum[j] += 1; # Using above count arrays, # find cells uniquecount = 0; for i in range(n): for j in range(m): if (mat[i][j] != 0 and rowsum[i] == 1 and colsum[j] == 1): uniquecount += 1; return uniquecount; # Driver code if __name__ == '__main__': mat = [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 0, 1 ]; print(countUnique(mat, 3, 4)); # This code is contributed by 29AjayKumar |
C#
// Efficient C# program to count unique // cells in a binary matrix using System; class GFG { static int MAX = 100; static int countUnique(int [,]mat, int n, int m) { int []rowsum = new int[n]; int []colsum = new int[m]; // Count number of 1s in each row // and in each column for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i, j] != 0) { rowsum[i]++; colsum[j]++; } // Using above count arrays, find // cells int uniquecount = 0; for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (mat[i, j] != 0 && rowsum[i] == 1 && colsum[j] == 1) uniquecount++; return uniquecount; } // Driver code public static void Main(String[] args) { int [,]mat = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}}; Console.Write(countUnique(mat, 3, 4)); } } // This code is contributed by Rajput-Ji |
Output:
2
Time Complexity – O(n*m)
Auxiliary Space – O(n+m)
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