Related Articles

# Size of all connected non-empty cells of a Matrix

• Last Updated : 05 Aug, 2021

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.

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 ``using` `namespace` `std;` `// Function to find size of all the``// islands from the given matrix``int` `BFS(vector >& mat,``        ``int` `row, ``int` `col)``{``    ``int` `area = 0;` `    ``// Initialize a queue for``    ``// the BFS traversal``    ``queue > 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` `(mat[r] == 0)``            ``continue``;` `        ``// Check if current element is 1``        ``if` `(mat[r] == 1) {` `            ``// Mark the cell visited``            ``mat[r] = 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 > mat)``{` `    ``// 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` `(mat[row][col] == 1) {` `                ``// Function call``                ``int` `area = BFS(mat, row, col);``                ``result.push_back(area);``            ``}``        ``}``    ``}` `    ``// Print the answer``    ``for` `(``int` `val : result)``        ``cout << val << ``" "``;``}` `// Driver Code``int` `main()``{` `    ``vector > mat``        ``= { { 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(mat);` `    ``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``[][] mat,``               ``int` `row, ``int` `col)``{``    ``int` `area = ``0``;``    ` `    ``// Initialize a queue for``    ``// the BFS traversal``    ``Queue 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` `(mat[r] == ``0``)``            ``continue``;` `        ``// Check if current element is 1``        ``if` `(mat[r] == ``1``)``        ``{``            ` `            ``// Mark the cell visited``            ``mat[r] = ``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``[][] mat)``{``    ` `    ``// 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` `(mat[row][col] == ``1``)``            ``{``                ` `                ``// Function call``                ``int` `area = BFS(mat, 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``[][] mat = { { ``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(mat);``}``}` `// 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(mat, 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` `(mat[r] ``=``=` `0``):``            ``continue` `        ``# Check if current element is 1``        ``if` `(mat[r] ``=``=` `1``):` `            ``# Mark the cell visited``            ``mat[r] ``=` `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(mat):``    ` `    ``# 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` `(mat[row][col] ``=``=` `1``):``                ` `                ``# Function call``                ``area ``=` `BFS(mat, row, col);``                ``result.append(area)` `    ``# Print the answer``    ``for` `val ``in` `result:``        ``print``(val, end ``=` `" "``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:` `    ``mat ``=` `[ [ ``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(mat)` `# This code is contributed by mohit kumar 29`

## C#

 `// 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``[, ] mat, ``int` `row, ``int` `col)``{``    ``int` `area = 0;` `    ``// Initialize a queue for``    ``// the BFS traversal``    ``Queue Q = ``new` `Queue();``    ``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` `(mat[r, c] == 0)``            ``continue``;` `        ``// Check if current element is 1``        ``if` `(mat[r, c] == 1)``        ``{``            ` `            ``// Mark the cell visited``            ``mat[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``[,] mat)``{``    ` `    ``// 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` `(mat[row, col] == 1)``            ``{``                ` `                ``// Function call``                ``int` `area = BFS(mat, 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``[, ] mat = { { 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(mat);``}``}` `// This code is contributed by grand_master`

## Javascript

 ``
Output:
`6 4 3`

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

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up