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

Given a 2-D matrix mat[][] the task is to 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```

Approach: For every cell that hasn’t been visited before performing 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`

## Javascript

 ``

Output:

`4`

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

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