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

Given a 2-D matrix mat[][] the task is count the number of connected components in the matrix. A connected component is formed by all equal elements that share some common side with at least one other element of the same component.

Examples:

```Input: mat[][] = {"bbba",
"baaa"}
Output: 2
The two connected components are:
bbb
b

AND

a
aaa

Input: mat[][] = {"aabba",
"aabba",
"aaaca"}
Output: 4
```

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

Approach: For every cell that hasn’t been visited before perform DFS. DFS will cover all the connected cells (up, left, right and down) with same value. So the answer would be the total times DFS is run.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define maxRow 500 ` `#define maxCol 500 ` ` `  `bool` `visited[maxRow][maxCol] = { 0 }; ` ` `  `// Function that return true if mat[row][col] ` `// is valid and hasn't been visited ` `bool` `isSafe(string M[], ``int` `row, ``int` `col, ``char` `c,  ` `                                    ``int` `n, ``int` `l) ` `{ ` `    ``// If row and column are valid and element  ` `    ``// is matched and hasn't been visited then  ` `    ``// the cell is safe ` `    ``return` `(row >= 0 && row < n) ` `           ``&& (col >= 0 && col < l) ` `           ``&& (M[row][col] == c && !visited[row][col]); ` `} ` ` `  `// Function for depth first search ` `void` `DFS(string M[], ``int` `row, ``int` `col, ``char` `c,  ` `                                 ``int` `n, ``int` `l) ` `{ ` `    ``// These arrays are used to get row and column ` `    ``// numbers of 4 neighbours of a given cell ` `    ``int` `rowNbr[] = { -1, 1, 0, 0 }; ` `    ``int` `colNbr[] = { 0, 0, 1, -1 }; ` ` `  `    ``// Mark this cell as visited ` `    ``visited[row][col] = ``true``; ` ` `  `    ``// Recur for all connected neighbours ` `    ``for` `(``int` `k = 0; k < 4; ++k) ` `        ``if` `(isSafe(M, row + rowNbr[k], ` `                  ``col + colNbr[k], c, n, l)) ` ` `  `            ``DFS(M, row + rowNbr[k],  ` `                ``col + colNbr[k], c, n, l); ` `} ` ` `  `// Function to return the number of ` `// connectewd components in the matrix ` `int` `connectedComponents(string M[], ``int` `n) ` `{ ` `    ``int` `connectedComp = 0; ` `    ``int` `l = M.length(); ` ` `  `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``for` `(``int` `j = 0; j < l; j++) { ` `            ``if` `(!visited[i][j]) { ` `                ``char` `c = M[i][j]; ` `                ``DFS(M, i, j, c, n, l); ` `                ``connectedComp++; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `connectedComp; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string M[] = {``"aabba"``, ``"aabba"``, ``"aaaca"``}; ` `    ``int` `n = ``sizeof``(M)/``sizeof``(M); ` ` `  `    ``cout << connectedComponents(M, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG  ` `{ ` `static` `final` `int` `maxRow = ``500``; ` `static` `final` `int` `maxCol = ``500``; ` ` `  `static` `boolean` `visited[][] = ``new` `boolean``[maxRow][maxCol]; ` ` `  `// Function that return true if mat[row][col] ` `// is valid and hasn't been visited ` `static` `boolean` `isSafe(String M[], ``int` `row, ``int` `col,  ` `                                  ``char` `c, ``int` `n, ``int` `l)  ` `{ ` `    ``// If row and column are valid and element  ` `    ``// is matched and hasn't been visited then  ` `    ``// the cell is safe ` `    ``return` `(row >= ``0` `&& row < n) &&  ` `           ``(col >= ``0` `&& col < l) && ` `           ``(M[row].charAt(col) == c && ` `           ``!visited[row][col]); ` `} ` ` `  `// Function for depth first search ` `static` `void` `DFS(String M[], ``int` `row, ``int` `col,  ` `                        ``char` `c, ``int` `n, ``int` `l)  ` `{ ` `    ``// These arrays are used to get row and column ` `    ``// numbers of 4 neighbours of a given cell ` `    ``int` `rowNbr[] = {-``1``, ``1``, ``0``, ``0``}; ` `    ``int` `colNbr[] = {``0``, ``0``, ``1``, -``1``}; ` ` `  `    ``// Mark this cell as visited ` `    ``visited[row][col] = ``true``; ` ` `  `    ``// Recur for all connected neighbours ` `    ``for` `(``int` `k = ``0``; k < ``4``; ++k) ` `    ``{ ` `        ``if` `(isSafe(M, row + rowNbr[k], ` `                      ``col + colNbr[k], c, n, l))  ` `        ``{ ` `            ``DFS(M, row + rowNbr[k], ` `                   ``col + colNbr[k], c, n, l); ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the number of ` `// connectewd components in the matrix ` `static` `int` `connectedComponents(String M[], ``int` `n)  ` `{ ` `    ``int` `connectedComp = ``0``; ` `    ``int` `l = M[``0``].length(); ` ` `  `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` `        ``for` `(``int` `j = ``0``; j < l; j++)  ` `        ``{ ` `            ``if` `(!visited[i][j]) ` `            ``{ ` `                ``char` `c = M[i].charAt(j); ` `                ``DFS(M, i, j, c, n, l); ` `                ``connectedComp++; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `connectedComp; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``String M[] = {``"aabba"``, ``"aabba"``, ``"aaaca"``}; ` `    ``int` `n = M.length; ` `    ``System.out.println(connectedComponents(M, n)); ` `} ` `} ` ` `  `// This code contributed by PrinciRaj1992  `

## Python3

 `# Python3 implementation of the approach  ` `import` `numpy as np ` ` `  `maxRow ``=` `500` `maxCol ``=` `500` ` `  `visited ``=` `np.zeros((maxCol, maxRow)) ` ` `  `# Function that return true if mat[row][col]  ` `# is valid and hasn't been visited  ` `def` `isSafe(M, row, col, c, n, l) : ` `                                         `  `    ``# If row and column are valid and element  ` `    ``# is matched and hasn't been visited then  ` `    ``# the cell is safe  ` `    ``return` `((row >``=` `0` `and` `row < n) ``and`  `            ``(col >``=` `0` `and` `col < l) ``and`  `            ``(M[row][col] ``=``=` `c ``and` `not`  `             ``visited[row][col]));  ` ` `  `# Function for depth first search  ` `def` `DFS(M, row, col, c, n, l) :  ` ` `  `    ``# These arrays are used to get row  ` `    ``# and column numbers of 4 neighbours  ` `    ``# of a given cell  ` `    ``rowNbr ``=` `[ ``-``1``, ``1``, ``0``, ``0` `];  ` `    ``colNbr ``=` `[ ``0``, ``0``, ``1``, ``-``1` `];  ` ` `  `    ``# Mark this cell as visited  ` `    ``visited[row][col] ``=` `True``;  ` ` `  `    ``# Recur for all connected neighbours  ` `    ``for` `k ``in` `range``(``4``) : ` `        ``if` `(isSafe(M, row ``+` `rowNbr[k],  ` `                   ``col ``+` `colNbr[k], c, n, l)) : ` ` `  `            ``DFS(M, row ``+` `rowNbr[k],  ` `                ``col ``+` `colNbr[k], c, n, l);  ` ` `  `# Function to return the number of  ` `# connectewd components in the matrix  ` `def` `connectedComponents(M, n) : ` ` `  `    ``connectedComp ``=` `0``;  ` `    ``l ``=` `len``(M[``0``]);  ` ` `  `    ``for` `i ``in` `range``(n) : ` `        ``for` `j ``in` `range``(l) : ` `            ``if` `(``not` `visited[i][j]) :  ` `                ``c ``=` `M[i][j];  ` `                ``DFS(M, i, j, c, n, l);  ` `                ``connectedComp ``+``=` `1``;  ` `         `  `    ``return` `connectedComp;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``M ``=` `[``"aabba"``, ``"aabba"``, ``"aaaca"``];  ` `    ``n ``=` `len``(M) ` ` `  `    ``print``(connectedComponents(M, n));  ` ` `  `# This code is contributed by Ryuga `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `static` `readonly` `int` `maxRow = 500; ` `static` `readonly` `int` `maxCol = 500; ` ` `  `static` `bool` `[,]visited = ``new` `bool``[maxRow,maxCol]; ` ` `  `// Function that return true if mat[row,col] ` `// is valid and hasn't been visited ` `static` `bool` `isSafe(String []M, ``int` `row, ``int` `col,  ` `                                ``char` `c, ``int` `n, ``int` `l)  ` `{ ` `    ``// If row and column are valid and element  ` `    ``// is matched and hasn't been visited then  ` `    ``// the cell is safe ` `    ``return` `(row >= 0 && row < n) &&  ` `        ``(col >= 0 && col < l) && ` `        ``(M[row][col] == c && ` `        ``!visited[row,col]); ` `} ` ` `  `// Function for depth first search ` `static` `void` `DFS(String []M, ``int` `row, ``int` `col,  ` `                        ``char` `c, ``int` `n, ``int` `l)  ` `{ ` `    ``// These arrays are used to get row and column ` `    ``// numbers of 4 neighbours of a given cell ` `    ``int` `[]rowNbr = {-1, 1, 0, 0}; ` `    ``int` `[]colNbr = {0, 0, 1, -1}; ` ` `  `    ``// Mark this cell as visited ` `    ``visited[row,col] = ``true``; ` ` `  `    ``// Recur for all connected neighbours ` `    ``for` `(``int` `k = 0; k < 4; ++k) ` `    ``{ ` `        ``if` `(isSafe(M, row + rowNbr[k], ` `                    ``col + colNbr[k], c, n, l))  ` `        ``{ ` `            ``DFS(M, row + rowNbr[k], ` `                ``col + colNbr[k], c, n, l); ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the number of ` `// connectewd components in the matrix ` `static` `int` `connectedComponents(String []M, ``int` `n)  ` `{ ` `    ``int` `connectedComp = 0; ` `    ``int` `l = M.Length; ` ` `  `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` `        ``for` `(``int` `j = 0; j < l; j++)  ` `        ``{ ` `            ``if` `(!visited[i,j]) ` `            ``{ ` `                ``char` `c = M[i][j]; ` `                ``DFS(M, i, j, c, n, l); ` `                ``connectedComp++; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `connectedComp; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``String []M = {``"aabba"``, ``"aabba"``, ``"aaaca"``}; ` `    ``int` `n = M.Length; ` `    ``Console.WriteLine(connectedComponents(M, n)); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```4
``` My Personal Notes arrow_drop_up 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.