Finding the existence of an enclosed space within a 2D M x N grid

The idea is:

• we start from every non-visited empty cell
• try to visit all connected empty cells
• if we can go to the boundary then this is not an enclosed area
• if no cell of the connected region is boundary cell then the region is enclosed by wall and we increment the count.

Here is sample implementation in c++ that count the number of enclosed area:

#include <string.h>
#include <cstdio>

// m is row_num, n is column_num
int m, n;
// grid
char grid[5005][5005];
// direction arrays
int R[] = {0, -1, 0, 1};
int C[] = {1, 0, -1, 0};
// check for weather we reach boundary or not
// and visit array
bool wentToBoundary, vis[5005][5005];

// DFS implementation of 2D grid
void dfs(int x, int y) {
    // visit the cell grid[x][y] as true
    vis[x][y] = true;

    // if the current cell is a boundary cell, then mark that
    // we reach to boundary from an inner cell
    if (x == 0 || x == m -1 || y == 0 || y == n - 1)
        wentToBoundary = true;

    // try to go in all 4 direction (right, up, left, down)
    // if the cell is not visited yet and contains ' '
    for (int i = 0; i < 4; i++) {
        int xx = x + R[i];
        int yy = y + C[i];
        
        if (xx >=0 && xx < m && yy >= 0 && yy < n) {
            if (!vis[xx][yy] && grid[xx][yy] == ' ')
                dfs(xx, yy);
        }
    }
}

int main() {
    // input the grid size;
    scanf("%d %d", &m, &n);
    getchar();

    // input the grid
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            scanf("%c", &grid[i][j]);
        }
        getchar();
    }

    // initialize
    int spaceEnclosedCount = 0;
    memset(vis, false, sizeof(vis));

    // iterate only for inner cells not the boundary cells
    for (int i = 1; i < m - 1; i++) {
        for (int j = 1; j < n - 1; j++) {
            if (!vis[i][j] && grid[i][j] == ' ') {
                wentToBoundary = false;
                dfs(i, j);

                if (!wentToBoundary) {
                    spaceEnclosedCount++;
                }
            }
        }
    }

    printf("number of area enclosed by spaces: %d\n", spaceEnclosedCount);

    return 0;
}