# Number of Closed Islands in C++

C++Server Side ProgrammingProgramming

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Suppose we have a 2D grid consists of 0s (as land) and 1s (as water). An island is a maximal 4- directionally connected group of 0s. A closed island is an island totally surrounded by 1s. We have to find the number of closed islands. So if the grid is like

 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0

So the output will be 2. There are two islands, that are completely surrounded by water.

To solve this, we will follow these steps −

• Define a variable flag

• Define a method called dfs, this will take the grid, i, j, n and m

• if i and j are not inside the range of the grid, then set flag := false and return
• if g[i,j] = 1 or g[i, j] = -1, then return

• if g[i, j] = 0, then g[i, j] = -1

• call dfs(g, i + 1, j, n, m), dfs(g, i, j+1, n, m), dfs(g, i - 1, j, n, m), dfs(g, i, j-1, n, m)

• The main method will be like −

• create a dp matrix of order n x m, and fill it with -1

• for i in range 0 to n – 1

• for j in range 0 to m – 1

• if g[i, j] = 0, then

• flag := true

• dfs(g, i, j, n, m)

• flag := true

• ans := ans + flag

• return ans

Let us see the following implementation to get better understanding −

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
vector < vector <int> > dp;
bool flag;
void dfs(vector<vector<int>>& g, int i, int j, int n, int m){
if(i>=n || j >=m || i<0 || j<0){
flag = false;
return ;
}
if(g[i][j] == 1 || g[i][j] == -1)return;
if(g[i][j] == 0)g[i][j] = -1;
dfs(g, i+1, j, n, m);
dfs(g, i, j+1, n, m);
dfs(g, i-1, j, n, m);
dfs(g,i, j-1, n, m);
}
int closedIsland(vector<vector<int>>& g) {
int ans = 0;
int n = g.size();
int m = g.size();
dp = vector < vector <int> > (n, vector <int> (m, -1));
for(int i = 0; i < n ; i++){
for(int j = 0; j < m; j++){
if(g[i][j] == 0){
flag = true;
dfs(g, i , j ,n ,m);
ans += flag;
}
}
}
return ans;
}
};
main(){
vector<vector<int>> v =
{{1,1,1,1,1,1,1,0},{1,0,0,0,0,1,1,0},{1,0,1,0,1,1,1,0},{1,0,0,0,0,1,0
,1},{1,1,1,1,1,1,1,0}};
Solution ob;
cout << (ob.closedIsland(v));
}

## Input

[[1,1,1,1,1,1,1,0],[1,0,0,0,0,1,1,0],[1,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,1],[1,1,1,1,1,1,1,0]]

## Output

2