Size of all connected non-empty cells of a Matrix

Last Updated : 23 Nov, 2023

Given a binary matrix mat[][], the task is to find the size of all possible non-empty connected cells. An empty cell is denoted by 0 while a non-empty cell is denoted by 1.
Two cells are said to be connected if they are adjacent to each other horizontally or vertically, i.e. mat[i][j] = mat[i][j - 1] or mat[i][j] = mat[i][j + 1] or mat[i][j] = mat[i - 1][j] or mat[i][j] = mat[i + 1][j].

Examples:

Input: mat[][] = {{1, 1, 0, 0, 0}, {0, 1, 0, 0, 1}, {1, 0, 0, 1, 1}, {0, 0, 0, 0, 0}, {1, 0, 1, 0, 1}}
Output: 3 3 1 1 1 1
Explanation:
{mat[0][0], mat[0][1], mat[1][1]}, {mat[1][4], mat[2][3], mat[2][4]}}, {mat[2][0]}, {mat[4][0]}, {mat[4][2]}, {mat[4[4]} are the only possible connections.

1 1 0 0 0

0 1 0 0 1

1 0 0 1 1

0 0 0 0 0

1 0 1 0 1

Input: mat[][] = {{1, 1, 0, 0, 0}, {1, 1, 0, 1, 1}, {1, 0, 0, 1, 1}, {0, 0, 0, 0, 0}, {0, 0, 1, 1, 1}}
Output: 5 4 3

Approach:
The idea is to use BFS and Recursion on the matrix.
Follow the steps below:

Initialize a Queue Data Structure and insert a cell(mat[i][j] = 1).
Perform BFS on the inserted cell and traverse its adjacent cells.
Check for boundary conditions and check if the current element is 1, then flip it to 0.
Mark the cell visited and update the size of the connected non-empty cells.
Finally, print all the sizes of the connections obtained.

Below is the implementation of the above approach:

C++14

// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find size of all the
// islands from the given matrix
int BFS(vector<vector<int> >& matrix, int row, int col)
{
    int area = 0;

    // Initialize a queue for
    // the BFS traversal
    queue<pair<int, int> > Q;
    Q.push({ row, col });

    // Iterate until the
    // queue is empty
    while (!Q.empty()) {

        // Top element of queue
        auto it = Q.front();

        // Pop the element
        Q.pop();

        int r = it.first, c = it.second;

        // Check for boundaries
        if (r < 0 || c < 0 || r > 4 || c > 4)
            continue;

        // Check if current element is 0
        if (matrix[r][c] == 0)
            continue;

        // Check if current element is 1
        if (matrix[r][c] == 1) {

            // Mark the cell visited
            matrix[r][c] = 0;

            // Incrementing the size
            area++;
        }

        // Traverse all neighbors
        Q.push({ r + 1, c });
        Q.push({ r - 1, c });
        Q.push({ r, c + 1 });
        Q.push({ r, c - 1 });
    }

    // Return the answer
    return area;
}

// Function to print size of each connections
void sizeOfConnections(vector<vector<int> > matrix)
{

    // Stores the size of each
    // connected non-empty
    vector<int> result;

    for (int row = 0; row < 5; ++row) {
        for (int col = 0; col < 5; ++col) {

            // Check if the cell is
            // non-empty
            if (matrix[row][col] == 1) {

                // Function call
                int area = BFS(matrix, row, col);
                result.push_back(area);
            }
        }
    }

    // Print the answer
    for (int val : result)
        cout << val << " ";
}

// Driver Code
int main()
{

    vector<vector<int> > matrix = { { 1, 1, 0, 0, 0 },
                                    { 1, 1, 0, 1, 1 },
                                    { 1, 0, 0, 1, 1 },
                                    { 1, 0, 0, 0, 0 },
                                    { 0, 0, 1, 1, 1 } };

    sizeOfConnections(matrix);

    return 0;
}

Java

// Java program to implement 
// the above approach 
import java.util.*;
import java.lang.*;

class GFG{
    
static class pair
{
    int first, second;
    pair(int first, int second)
    {
        this.first = first;
        this.second = second;
    }
}

// Function to find size of all the
// islands from the given matrix
static int BFS(int[][] matrix,
               int row, int col)
{
    int area = 0;
    
    // Initialize a queue for
    // the BFS traversal
    Queue<pair> Q = new LinkedList<>();
    Q.add(new pair(row, col));

    // Iterate until the
    // queue is empty
    while (!Q.isEmpty())
    {
        
        // Top element of queue
        pair it = Q.peek();

        // Pop the element
        Q.poll();

        int r = it.first, c = it.second;

        // Check for boundaries
        if (r < 0 || c < 0 ||
            r > 4 || c > 4)
            continue;

        // Check if current element is 0
        if (matrix[r][c] == 0)
            continue;

        // Check if current element is 1
        if (matrix[r][c] == 1) 
        {
            
            // Mark the cell visited
            matrix[r][c] = 0;

            // Incrementing the size
            area++;
        }

        // Traverse all neighbors
        Q.add(new pair(r + 1, c));
        Q.add(new pair(r - 1, c));
        Q.add(new pair(r, c + 1));
        Q.add(new pair(r, c - 1));
    }

    // Return the answer
    return area;
}

// Function to print size of each connections
static void sizeOfConnections(int[][] matrix)
{
    
    // Stores the size of each
    // connected non-empty
    ArrayList<Integer> result = new ArrayList<>();

    for(int row = 0; row < 5; ++row)
    {
        for(int col = 0; col < 5; ++col)
        {
            
            // Check if the cell is
            // non-empty
            if (matrix[row][col] == 1)
            {
                
                // Function call
                int area = BFS(matrix, row, col);
                result.add(area);
            }
        }
    }
    
    // Print the answer
    for(int val : result)
       System.out.print(val + " ");
}

// Driver code
public static void main (String[] args)
{
    int[][] matrix = { { 1, 1, 0, 0, 0 },
                    { 1, 1, 0, 1, 1 },
                    { 1, 0, 0, 1, 1 },
                    { 1, 0, 0, 0, 0 },
                    { 0, 0, 1, 1, 1 } };
                    
    sizeOfConnections(matrix);
}
}

// This code is contributed by offbeat

Python3

# Python3 program to implement
# the above approach
from collections import deque

# Function to find size of all the
# islands from the given matrix


def BFS(matrix, row, col):

    area = 0

    # Initialize a queue for
    # the BFS traversal
    Q = deque()
    Q.append([row, col])

    # Iterate until the
    # queue is empty
    while (len(Q) > 0):

        # Top element of queue
        it = Q.popleft()

        # Pop the element
        # Q.pop();
        r, c = it[0], it[1]

        # Check for boundaries
        if (r < 0 or c < 0 or r > 4 or c > 4):
            continue

        # Check if current element is 0
        if (matrix[r][c] == 0):
            continue

        # Check if current element is 1
        if (matrix[r][c] == 1):

            # Mark the cell visited
            matrix[r][c] = 0

            # Incrementing the size
            area += 1

        # Traverse all neighbors
        Q.append([r + 1, c])
        Q.append([r - 1, c])
        Q.append([r, c + 1])
        Q.append([r, c - 1])

    # Return the answer
    return area

# Function to prsize of each connections


def sizeOfConnections(matrix):

    # Stores the size of each
    # connected non-empty
    result = []

    for row in range(5):
        for col in range(5):

            # Check if the cell is
            # non-empty
            if (matrix[row][col] == 1):

                # Function call
                area = BFS(matrix, row, col)
                result.append(area)

    # Print the answer
    for val in result:
        print(val, end=" ")


# Driver Code
if __name__ == '__main__':

    matrix = [[1, 1, 0, 0, 0],
              [1, 1, 0, 1, 1],
              [1, 0, 0, 1, 1],
              [1, 0, 0, 0, 0],
              [0, 0, 1, 1, 1]]

    sizeOfConnections(matrix)

# This code is contributed by mohit kumar 29

// C# program to implement
// the above approach
using System;
using System.Collections;
using System.Collections.Generic;

class GFG {

    class pair {
        public int first, second;

        public pair(int first, int second)
        {
            this.first = first;
            this.second = second;
        }
    }

    // Function to find size of all the
    // islands from the given matrix
    static int BFS(int[, ] matrix, int row, int col)
    {
        int area = 0;

        // Initialize a queue for
        // the BFS traversal
        Queue<pair> Q = new Queue<pair>();
        Q.Enqueue(new pair(row, col));

        // Iterate until the
        // queue is empty
        while (Q.Count != 0) {

            // Top element of queue
            pair it = Q.Peek();

            // Pop the element
            Q.Dequeue();

            int r = it.first, c = it.second;

            // Check for boundaries
            if (r < 0 || c < 0 || r > 4 || c > 4)
                continue;

            // Check if current element is 0
            if (matrix[r, c] == 0)
                continue;

            // Check if current element is 1
            if (matrix[r, c] == 1) {

                // Mark the cell visited
                matrix[r, c] = 0;

                // Incrementing the size
                area++;
            }

            // Traverse all neighbors
            Q.Enqueue(new pair(r + 1, c));
            Q.Enqueue(new pair(r - 1, c));
            Q.Enqueue(new pair(r, c + 1));
            Q.Enqueue(new pair(r, c - 1));
        }

        // Return the answer
        return area;
    }

    // Function to print size of each connections
    static void sizeOfConnections(int[, ] matrix)
    {

        // Stores the size of each
        // connected non-empty
        ArrayList result = new ArrayList();

        for (int row = 0; row < 5; ++row) {
            for (int col = 0; col < 5; ++col) {

                // Check if the cell is
                // non-empty
                if (matrix[row, col] == 1) {

                    // Function call
                    int area = BFS(matrix, row, col);
                    result.Add(area);
                }
            }
        }

        // Print the answer
        foreach(int val in result) Console.Write(val + " ");
    }

    // Driver code
    public static void Main(string[] args)
    {
        int[, ] matrix = { { 1, 1, 0, 0, 0 },
                           { 1, 1, 0, 1, 1 },
                           { 1, 0, 0, 1, 1 },
                           { 1, 0, 0, 0, 0 },
                           { 0, 0, 1, 1, 1 } };

        sizeOfConnections(matrix);
    }
}

// This code is contributed by grand_master

JavaScript

<script>

// Javascript program to implement
// the above approach

class pair 
{
    constructor(first, second)
    {
        this.first = first;
        this.second = second;
    }
}

// Function to find size of all the
// islands from the given matrix
function BFS(matrix, row, col)
{
    var area = 0;

    // Initialize a queue for
    // the BFS traversal
    var Q = [];
    Q.push(new pair(row, col));

    // Iterate until the
    // queue is empty
    while (Q.length != 0) 
    {
        
        // Top element of queue
        var it = Q[0];

        // Pop the element
        Q.shift();

        var r = it.first, c = it.second;

        // Check for boundaries
        if (r < 0 || c < 0 || r > 4 || c > 4)
            continue;

        // Check if current element is 0
        if (matrix[r][ c] == 0)
            continue;

        // Check if current element is 1
        if (matrix[r][c] == 1) 
        {
            
            // Mark the cell visited
            matrix[r][c] = 0;
            
            // Incrementing the size
            area++;
        }

        // Traverse all neighbors
        Q.push(new pair(r + 1, c));
        Q.push(new pair(r - 1, c));
        Q.push(new pair(r, c + 1));
        Q.push(new pair(r, c - 1));
    }

    // Return the answer
    return area;
}

// Function to print size of each connections
function sizeOfConnections(matrix)
{
    
    // Stores the size of each
    // connected non-empty
    var result = [];

    for(var row = 0; row < 5; ++row)
    {
        for(var col = 0; col < 5; ++col) 
        {
            
            // Check if the cell is
            // non-empty
            if (matrix[row][col] == 1) 
            {
                
                // Function call
                var area = BFS(matrix, row, col);
                result.push(area);
            }
        }
    }

    // Print the answer
    for(var val of result) 
        document.write(val + " ");
}

// Driver code
var matrix = [ [ 1, 1, 0, 0, 0 ],
                [ 1, 1, 0, 1, 1 ],
                [ 1, 0, 0, 1, 1 ],
                [ 1, 0, 0, 0, 0 ],
                [ 0, 0, 1, 1, 1 ] ];
sizeOfConnections(matrix);


</script>

Output

6 4 3

Time Complexity: O(row * col)
Auxiliary Space: O(row * col)

Number of connected components in a 2-D matrix of strings

chirags_30

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Size of all connected non-empty cells of a Matrix

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