Number of square matrices with all 1s

Given an N*M matrix containing only 0s and 1s, the task is to count the number of square submatrices containing all 1s.

Examples:

Input: arr[][] = {{0, 1, 1, 1},
{1, 1, 1, 1},
{0, 1, 1, 1}}
Output: 15
Explanation:
There are 10 squares of side length 1.
There are 4 squares of side length 2.
There is 1 square of side length 3.
Total number of squares = 10 + 4 + 1 = 15.



Input: arr[][] = {{1, 0, 1},
{1, 1, 0},
{1, 1, 0}}
Output: 7

Approach: This problem can be solved using Dynamic Programming.

  1. Let the array arr[i][j] store the number of square matrices ending at (i, j)
  2. The recurrence relation to find the number of squares ending at (i, j) can be given by:
    • If arr[i][j] is 1:
      • arr[i][j] = min( min(arr[i-1][j], arr[i][j-1]), arr[i-1][j-1]) + 1
    • Else if arr[i][j] is 0:
      • arr[i][j] = 0
  3. Calculate the sum of the array which is equal to the number of square submatrices with all 1s.

Below is the implementation of the above approach:

CPP

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to return the number of
// square submatrices with all 1s
#include <bits/stdc++.h>
using namespace std;
  
#define n 3
#define m 3
  
// Function to return the number of
// square submatrices with all 1s
int countSquareMatrices(int a[][m],
                        int N, int M)
{
    // Initialize count variable
    int count = 0;
  
    for (int i = 1; i < N; i++) {
        for (int j = 1; j < M; j++) {
            // If a[i][j] is equal to 0
            if (a[i][j] == 0)
                continue;
  
            // Calculate number of
            // square submatrices
            // ending at (i, j)
            a[i][j] = min(min(a[i - 1][j],
                              a[i][j - 1]),
                          a[i - 1][j - 1])
                      + 1;
        }
    }
  
    // Calculate the sum of the array
    for (int i = 0; i < N; i++)
        for (int j = 0; j < M; j++)
            count += a[i][j];
  
    return count;
}
  
// Driver code
int main()
{
    int arr[][m] = { { 1, 0, 1 },
                     { 1, 1, 0 },
                     { 1, 1, 0 } };
  
    cout << countSquareMatrices(arr, n, m);
  
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java program to return the number of  


// square submatrices with all 1s 


class GFG  


{ 


      


    final static int n = 3;  


    final static int m = 3;  


      


    // Function to return the number of  


    // square submatrices with all 1s  


    static int countSquareMatrices(int a[][], int N, int M)  


    {  


        // Initialize count variable  


        int count = 0;  


      


        for (int i = 1; i < N; i++) 


        {  


            for (int j = 1; j < M; j++)  


            {  


                // If a[i][j] is equal to 0  


                if (a[i][j] == 0)  


                    continue;  


      


                // Calculate number of  


                // square submatrices  


                // ending at (i, j)  


                a[i][j] = Math.min(Math.min(a[i - 1][j], a[i][j - 1]),  


                            a[i - 1][j - 1]) + 1;  


            }  


        }  


      


        // Calculate the sum of the array  


        for (int i = 0; i < N; i++)  


            for (int j = 0; j < M; j++)  


                count += a[i][j];  


      


        return count;  


    }  


      


    // Driver code  


    public static void main (String[] args) 


    {  


        int arr[][] = { { 1, 0, 1 },  


                        { 1, 1, 0 },  


                        { 1, 1, 0 } };  


      


        System.out.println(countSquareMatrices(arr, n, m));  


    }  


} 


  


// This code is contributed by AnkitRai01 



















                        chevron_right







                        filter_none









Python














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Python3 program to return the number of 


# square submatrices with all 1s 


n = 3


m = 3


  


# Function to return the number of 


# square submatrices with all 1s 


def countSquareMatrices(a, N, M): 


      


    # Initialize count variable 


    count = 0


  


    for i in range(1, N): 


        for j in range(1, M): 


              


            # If a[i][j] is equal to 0 


            if (a[i][j] == 0): 


                continue


  


            # Calculate number of 


            # square submatrices 


            # ending at (i, j) 


            a[i][j] = min([a[i - 1][j],  


                      a[i][j - 1], a[i - 1][j - 1]])+1


  


    # Calculate the sum of the array 


    for i in range(N): 


        for j in range(M): 


            count += a[i][j] 


  


    return count 


  


# Driver code 


  


arr = [ [ 1, 0, 1], 


    [ 1, 1, 0 ], 


    [ 1, 1, 0 ] ] 


  


print(countSquareMatrices(arr, n, m)) 


  


# This code is contributed by mohit kumar 29 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# program to return the number of  


// square submatrices with all 1s 


using System; 


  


class GFG  


{ 


      


    static int n = 3;  


    static int m = 3;  


      


    // Function to return the number of  


    // square submatrices with all 1s  


    static int countSquareMatrices(int [,]a, int N, int M)  


    {  


        // Initialize count variable  


        int count = 0;  


      


        for (int i = 1; i < N; i++) 


        {  


            for (int j = 1; j < M; j++)  


            {  


                // If a[i][j] is equal to 0  


                if (a[i, j] == 0)  


                    continue;  


      


                // Calculate number of  


                // square submatrices  


                // ending at (i, j)  


                a[i, j] = Math.Min(Math.Min(a[i - 1, j], a[i, j - 1]),  


                            a[i - 1, j - 1]) + 1;  


            }  


        }  


      


        // Calculate the sum of the array  


        for (int i = 0; i < N; i++)  


            for (int j = 0; j < M; j++)  


                count += a[i, j];  


      


        return count;  


    }  


      


    // Driver code  


    public static void Main() 


    {  


        int [,]arr = { { 1, 0, 1 },  


                        { 1, 1, 0 },  


                        { 1, 1, 0 } };  


      


        Console.WriteLine(countSquareMatrices(arr, n, m));  


    }  


} 


  


// This code is contributed by AnkitRai01 



















                        chevron_right







                        filter_none










Output :


7


Time Complexity: O(N*M)





    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
rupesh_rao
Check out this Author's contributed articles.
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.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.


Improved By :  mohit kumar 29, AnkitRai01