Find the number of 'X' total shapes

Given a grid of size N * M consisting of O's and X's. The task is to find the number of 'X' total shapes.

Note: 'X' shape consists of one or more adjacents X's (diagonals not included).

Examples:

Input: grid = {{X, O, X}, {O, X, O}, {X, X, X}}
Output: 3
Explanation: The grid is:
X O X   |   X O X   |  X O X 
O X O  |   O X O   |  O X O
X X X   |   X X X    |  X X X
So, X with bold color are adjacent to each other vertically for horizontally (diagonals not included). So, there are 3 different groups in the given grid.

Input: grid = {{X, X}, {X, X}}
Output: 1
Explanation: The grid is: 
X X
X X
So, X with bold color are adjacent to each other vertically for horizontally (diagonals not included). So, there is only 1 group in the given grid.

Approach: To solve the problem follow the below idea:

The idea is to apply dfs from every cell having 'X' and not visited, mark all its adjacent cells visited if their value is X and increase the answer by one.

Follow the steps to solve this problem:

• Instead of using an extra vector vis of size n*m to keep track of what cell is visited and not, we can simply convert a visited cell having 'X' to 'O'
• Initialize variable ans with 0, it will keep count of connected components having only 'X'.
• Make a function dfs(x, y) to mark the whole connected component having only 'X' as visited by converting all 'X' to 'O'.
• Run 2 nested loops for iterating over the whole grid
  • Check if the current cell is having 'X', then run a dfs from it and convert all cells in its connected component as 'O' and
  • Increase the variable ans by 1.
• Return variable ans as the answer.

Below is the implementation of the above approach:

// C++ code to implement the approach

#include <bits/stdc++.h>
using namespace std;

// Function to run DFS
void dfs(vector<vector<char> >& grid, int x, int y)
{
    // Checking whether the cell is within
    // the matrix bounds
    if (x < 0 || y < 0 || x >= grid.size()
        || grid[x].size() <= y) {
        return;
    }

    // If grid value is X, we update the
    // grid value as 0 and call the
    // function recursively for
    // adjacent nodes.
    if (grid[x][y] == 'X') {
        grid[x][y] = 'O';
        dfs(grid, x + 1, y);
        dfs(grid, x, y + 1);
        dfs(grid, x - 1, y);
        dfs(grid, x, y - 1);
    }
}

// Function to find the number of
// 'X' total shapes.
int xShape(vector<vector<char> >& grid)
{
    int n = grid.size();
    int m = grid[0].size();
    int i, j, ans = 0;

    // Traversing all the cells of the matrix.
    for (i = 0; i < grid.size(); i++) {
        for (j = 0; j < grid[i].size(); j++) {

            // If grid value is X, we increment
            // the counter and call the
            // dfs function.
            if (grid[i][j] == 'X') {
                ans++;
                dfs(grid, i, j);
            }
        }
    }

    // Returning the count.
    return ans;
}

// Driver Code
int main()
{
    vector<vector<char> > grid = { { 'X', 'O', 'X' },
                                   { 'O', 'X', 'O' },
                                   { 'X', 'X', 'X' } };

    // Function Call
    cout << xShape(grid) << endl;

    return 0;
}

// Java code to implement the approach
import java.io.*;

class GFG {

  // Function to run DFS
  static void dfs(char[][] grid, int x, int y)
  {

    // Checking whether the cell is within
    // the matrix bounds
    if (x < 0 || y < 0 || x >= grid.length
        || grid[x].length <= y) {
      return;
    }

    // If grid value is X, we update the
    // grid value as 0 and call the
    // function recursively for
    // adjacent nodes.
    if (grid[x][y] == 'X') {
      grid[x][y] = 'O';
      dfs(grid, x + 1, y);
      dfs(grid, x, y + 1);
      dfs(grid, x - 1, y);
      dfs(grid, x, y - 1);
    }
  }

  // Function to find the number of
  // 'X' total shapes.
  static int xShape(char[][] grid)
  {
    int n = grid.length;
    int m = grid[0].length;
    int i, j, ans = 0;

    // Traversing all the cells of the matrix.
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++) {

        // If grid value is X, we increment
        // the counter and call the
        // dfs function.
        if (grid[i][j] == 'X') {
          ans++;
          dfs(grid, i, j);
        }
      }
    }

    // Returning the count.
    return ans;
  }

  public static void main(String[] args)
  {
    char[][] grid = { { 'X', 'O', 'X' },
                     { 'O', 'X', 'O' },
                     { 'X', 'X', 'X' } };

    // Function call
    System.out.println(xShape(grid));
  }
}

// This code is contributed by lokeshmvs21.

# python code

# Function to run DFS
def dfs(grid, x, y):
    # Checking whether the cell is within
    # the matrix bounds
    if x < 0 or y < 0 or x >= len(grid) or len(grid[x]) <= y:
        return

    # If grid value is X, we update the
    # grid value as 0 and call the
    # function recursively for
    # adjacent nodes.
    if grid[x][y] == 'X':
        grid[x][y] = 'O'
        dfs(grid, x + 1, y)
        dfs(grid, x, y + 1)
        dfs(grid, x - 1, y)
        dfs(grid, x, y - 1)

# Function to find the number of
# 'X' total shapes.


def xShape(grid):
    n = len(grid)
    m = len(grid[0])
    ans = 0

    # Traversing all the cells of the matrix.
    for i in range(len(grid)):
        for j in range(len(grid[i])):

            # If grid value is X, we increment
            # the counter and call the
            # dfs function.
            if grid[i][j] == 'X':
                ans += 1
                dfs(grid, i, j)

    # Returning the count.
    return ans

# Driver Code
grid = [
    ['X', 'O', 'X'],
    ['O', 'X', 'O'],
    ['X', 'X', 'X']
]

# Function Call
print(xShape(grid))

# This code is contributed by ksam24000

// C# code to implement the approach
using System;
public class GFG {

  // Function to run DFS
  static void dfs(char[, ] grid, int x, int y)
  {

    // Checking whether the cell is within
    // the matrix bounds
    if (x < 0 || y < 0 || x >= grid.GetLength(0)
        || grid.GetLength(1) <= y) {
      return;
    }

    // If grid value is X, we update the
    // grid value as 0 and call the
    // function recursively for
    // adjacent nodes.
    if (grid[x, y] == 'X') {
      grid[x, y] = 'O';
      dfs(grid, x + 1, y);
      dfs(grid, x, y + 1);
      dfs(grid, x - 1, y);
      dfs(grid, x, y - 1);
    }
  }

  // Function to find the number of
  // 'X' total shapes.
  static int xShape(char[, ] grid)
  {
    int n = grid.GetLength(0);
    int m = grid.GetLength(1);
    int i, j, ans = 0;

    // Traversing all the cells of the matrix.
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++) {

        // If grid value is X, we increment
        // the counter and call the
        // dfs function.
        if (grid[i, j] == 'X') {
          ans++;
          dfs(grid, i, j);
        }
      }
    }

    // Returning the count.
    return ans;
  }

  static public void Main()
  {

    // Code
    char[, ] grid = { { 'X', 'O', 'X' },
                     { 'O', 'X', 'O' },
                     { 'X', 'X', 'X' } };

    // Function call
    Console.WriteLine(xShape(grid));
  }
}

// This code is contributed by lokesh.

    // JavaScript code for the above approach

    // Function to run DFS
    function dfs(grid, x, y) {
      // Checking whether the cell is within
      // the matrix bounds
      if (x < 0 || y < 0 || x >= grid.length
        || grid[x].length <= y) {
        return;
      }

      // If grid value is X, we update the
      // grid value as 0 and call the
      // function recursively for
      // adjacent nodes.
      if (grid[x][y] == 'X') {
        grid[x][y] = 'O';
        dfs(grid, x + 1, y);
        dfs(grid, x, y + 1);
        dfs(grid, x - 1, y);
        dfs(grid, x, y - 1);
      }
    }

    // Function to find the number of
    // 'X' total shapes.
    function xShape(grid) {
      let n = grid.length;
      let m = grid[0].length;
      let i, j, ans = 0;

      // Traversing all the cells of the matrix.
      for (i = 0; i < grid.length; i++) {
        for (j = 0; j < grid[i].length; j++) {

          // If grid value is X, we increment
          // the counter and call the
          // dfs function.
          if (grid[i][j] == 'X') {
            ans++;
            dfs(grid, i, j);
          }
        }
      }

      // Returning the count.
      return ans;
    }

    // Driver Code

    let grid = [['X', 'O', 'X'],
    ['O', 'X', 'O'],
    ['X', 'X', 'X']];

    // Function Call
    console.log(xShape(grid));

 // This code is contributed by Potta Lokesh.

3

Time Complexity: O(N * M), as the vector grid is having N * M cells, and each cell is visited at a max of one time.
Auxiliary Space: O(1) If the recursion stack is considered the time complexity is O(N * M)

Related Articles:

• Introduction to Matrix or Grid - Data Structures and Algorithms Tutorials
• Depth First Search or DFS for a Graph