Formatted question description: https://leetcode.ca/all/1254.html

1254. Number of Closed Islands (Medium)

Given a 2D grid consists of 0s (land) and 1s (water).  An island is a maximal 4-directionally connected group of 0s and a closed island is an island totally (all left, top, right, bottom) surrounded by 1s.

Return the number of closed islands.

 

Example 1:

Input: grid = [[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
Explanation:
Islands in gray are closed because they are completely surrounded by water (group of 1s).

Example 2:

Input: grid = [[0,0,1,0,0],[0,1,0,1,0],[0,1,1,1,0]]
Output: 1

Example 3:

Input: grid = [[1,1,1,1,1,1,1],
               [1,0,0,0,0,0,1],
               [1,0,1,1,1,0,1],
               [1,0,1,0,1,0,1],
               [1,0,1,1,1,0,1],
               [1,0,0,0,0,0,1],
               [1,1,1,1,1,1,1]]
Output: 2

 

Constraints:

• 1 <= grid.length, grid[0].length <= 100
• 0 <= grid[i][j] <=1

Related Topics: Depth-first Search

Solution 1. DFS

// OJ: https://leetcode.com/problems/number-of-closed-islands/

// Time: O(MN)
// Space: O(1)
class Solution {
    int dirs[4][2] = { {0,1},{0,-1},{-1,0},{1,0} }, M, N;
    bool dfs(vector<vector<int>> &G, int x, int y, int id) {
        G[x][y] = id;
        bool ans = true;
        for (auto &[dx, dy] : dirs) {
            int a = x + dx, b = y + dy;
            bool oob = a < 0 || b < 0 || a >= M || b >= N;
            ans = ans && !oob;
            if (oob || G[a][b] != 0) continue;
            ans = dfs(G, a, b, id) && ans;
        }
        return ans;
    }
public:
    int closedIsland(vector<vector<int>>& G) {
        int id = 2, ans = 0;
        M = G.size(), N = G[0].size();
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                if (G[i][j] != 0) continue;
                if (dfs(G, i, j, id++)) ++ans;
            }
        }
        return ans;
    }
};

Java

class Solution {
    final int WATER = -1;
    final int WHITE = 0;
    final int GRAY = 1;
    final int BLACK = 2;

    public int closedIsland(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0)
            return 0;
        int rows = grid.length, columns = grid[0].length;
        int insideRows = rows - 1, insideColumns = columns - 1;
        int[][] colors = new int[rows][columns];
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < columns; j++)
                colors[i][j] = grid[i][j] == 1 ? WATER : WHITE;
        }
        for (int i = 0; i < rows; i++) {
            if (colors[i][0] == WHITE)
                breadthFirstSearch(grid, colors, i, 0);
            if (colors[i][columns - 1] == WHITE)
                breadthFirstSearch(grid, colors, i, columns - 1);
        }
        for (int i = 1; i < insideColumns; i++) {
            if (colors[0][i] == WHITE)
                breadthFirstSearch(grid, colors, 0, i);
            if (colors[rows - 1][i] == WHITE)
                breadthFirstSearch(grid, colors, rows - 1, i);
        }
        int islandCount = 0;
        for (int i = 1; i < insideRows; i++) {
            for (int j = 1; j < insideColumns; j++) {
                if (colors[i][j] == WHITE) {
                    breadthFirstSearch(grid, colors, i, j);
                    islandCount++;
                }
            }
        }
        return islandCount;
    }

    public void breadthFirstSearch(int[][] grid, int[][] colors, int row, int column) {
        int rows = grid.length, columns = grid[0].length;
        int[][] directions = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
        Queue<int[]> queue = new LinkedList<int[]>();
        colors[row][column] = GRAY;
        queue.offer(new int[]{row, column});
        while (!queue.isEmpty()) {
            int[] cell = queue.poll();
            int curRow = cell[0], curColumn = cell[1];
            for (int[] direction : directions) {
                int newRow = curRow + direction[0], newColumn = curColumn + direction[1];
                if (newRow >= 0 && newRow < rows && newColumn >= 0 && newColumn < columns && colors[newRow][newColumn] == WHITE) {
                    colors[newRow][newColumn] = GRAY;
                    queue.offer(new int[]{newRow, newColumn});
                }
            }
            colors[curRow][curColumn] = BLACK;
        }
    }
}

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