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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

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:

Time Complexity – O(n*m)
Auxiliary Space – O(n+m)

This article is contributed by Rahul Chawla.If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

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