1568. Minimum Number of Days to Disconnect Island

1568. Minimum Number of Days to Disconnect Island (Medium)

Given a 2D grid consisting of 1s (land) and 0s (water).  An island is a maximal 4-directionally (horizontal or vertical) connected group of 1s.

The grid is said to be connected if we have exactly one island, otherwise is said disconnected.

In one day, we are allowed to change any single land cell (1) into a water cell (0).

Return the minimum number of days to disconnect the grid.

 

Example 1:

Input: grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]
Output: 2
Explanation: We need at least 2 days to get a disconnected grid.
Change land grid[1][1] and grid[0][2] to water and get 2 disconnected island.

Example 2:

Input: grid = [[1,1]]
Output: 2
Explanation: Grid of full water is also disconnected ([[1,1]] -> [[0,0]]), 0 islands.

Example 3:

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

Example 4:

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

Example 5:

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

 

Constraints:

• 1 <= grid.length, grid[i].length <= 30
• grid[i][j] is 0 or 1.

Related Topics:
Greedy

Solution 1.

You need at most two days to separate out a 1 at the corner with all other 1s. So the answer is one of 0, 1, 2.

If the graph is already disconnected, return 0.

For each 1, see if removing it can disconnect the graph. If yes, then return 1.

Otherwise return 2.

// OJ: https://leetcode.com/problems/minimum-number-of-days-to-disconnect-island/
// Author: github.com/lzl124631x
// Time: O((MN)^2)
// Space: O(MN)
class Solution {
    int M, N, dirs[4][2] = {{0,1},{0,-1},{1,0},{-1,0}};
    void dfs(vector<vector<int>> &G, int i, int j,vector<vector<int>> &seen) {
        seen[i][j] = true;
        for (auto &[dx, dy] : dirs) {
            int x = dx + i, y = dy + j;
            if (x < 0 || x >= M || y < 0 || y >= N || G[x][y] != 1 || seen[x][y]) continue;
            dfs(G, x, y, seen);
        }
    }
    bool disconnected(vector<vector<int>> &G) {
        vector<vector<int>> seen(M, vector<int>(N, false));
        int cnt = 0;
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                if (G[i][j] != 1 || seen[i][j]) continue;
                if (++cnt > 1) return true;
                dfs(G, i, j, seen);
            }
        }
        return cnt == 0;
    }
public:
    int minDays(vector<vector<int>>& G) {
        M = G.size(), N = G[0].size();
        if (disconnected(G)) return 0;
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                if (G[i][j] != 1) continue;
                G[i][j] = 0;
                if (disconnected(G)) return 1;
                G[i][j] = 1;
            }
        }
        return 2;
    }
};