#1568

Hard

auto_awesomeArray plus Depth-First Search

LeetCode Problem Workspace

Minimum Number of Days to Disconnect Island

Find the minimum number of days to disconnect an island in a grid using depth-first search.

array depth first search breadth first search matrix strongly connected component

Problem Statement

You are given an m x n binary grid where 1 represents land and 0 represents water. An island is defined as a group of 1's connected horizontally or vertically. The grid is considered connected if there is exactly one island; otherwise, it is disconnected.

In one day, you are allowed to change any single land cell (1) to a water cell (0). Your task is to determine the minimum number of days required to disconnect the island. If the grid is already disconnected, return 0.

Examples

Example 1

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

Output: 2

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

Grid of full water is also disconnected ([[1,1]] -> [[0,0]]), 0 islands.

Constraints

m == grid.length
n == grid[i].length
1 <= m, n <= 30
grid[i][j] is either 0 or 1.

Solution Approach

Check if the Grid is Already Disconnected

Before attempting any modifications, first check if the grid is already disconnected. If the grid has no islands or multiple disconnected islands, then 0 days are required. This step is essential to avoid unnecessary changes and optimize the process.

Apply Depth-First Search (DFS) to Find Island

Use depth-first search (DFS) to explore the grid and locate the existing island. DFS will help you identify the connected components of land and mark cells that need to be altered in order to break the connectivity.

Modify the Grid to Disconnect the Island

To disconnect the island, determine the minimum number of land cells (1's) that need to be changed to water (0's) in order to separate the island. Changing any land cell strategically to water will isolate the components of the island. Track the number of changes required to achieve disconnection.

Complexity Analysis

Metric	Value
Time	O(m \cdot n)
Space	O(m \cdot n)

The time complexity of this solution is O(m * n) since we perform a DFS search through the grid, which involves visiting each cell at most once. The space complexity is O(m * n) due to the recursion stack used by DFS.

What Interviewers Usually Probe

Check if the candidate is able to identify the condition when the grid is already disconnected.
Look for the candidate's ability to explain depth-first search and its relevance to finding connected components in a grid.
Assess if the candidate considers the grid size and optimizes the approach accordingly.

Common Pitfalls or Variants

Common pitfalls

Overlooking the case when the grid is already disconnected and returning unnecessary steps.
Not properly handling edge cases such as small grid sizes or grids that are already water.
Failing to optimize the DFS or grid traversal to minimize the number of operations required.

Follow-up variants

Allowing modifications to diagonal connections in the grid instead of only vertical and horizontal connections.
Implementing the solution using a breadth-first search (BFS) instead of DFS.
Handling multiple islands and calculating the number of days to disconnect all of them.

FAQ

What is the primary algorithm used to solve the Minimum Number of Days to Disconnect Island problem?

The primary algorithm used is Depth-First Search (DFS) to identify connected components in the grid and then determine the minimum number of changes required to disconnect the island.

How do I handle the case where the grid is already disconnected?

If the grid is already disconnected, simply return 0, as no changes are necessary.

Can the problem be solved using Breadth-First Search (BFS) instead of DFS?

Yes, BFS can also be used for exploring the grid, but DFS is often preferred for this type of problem because it is simpler for handling recursion and grid traversal.

What are the time and space complexity of this problem?

The time complexity is O(m * n), and the space complexity is O(m * n), where m is the number of rows and n is the number of columns in the grid.

What is the minimum number of changes required to disconnect an island in a grid?

The minimum number of changes is the smallest number of land cells that must be changed to water to isolate the island, which can be determined using DFS.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def minDays(self, grid: List[List[int]]) -> int:
        if self.count(grid) != 1:
            return 0
        m, n = len(grid), len(grid[0])
        for i in range(m):
            for j in range(n):
                if grid[i][j] == 1:
                    grid[i][j] = 0
                    if self.count(grid) != 1:
                        return 1
                    grid[i][j] = 1
        return 2

    def count(self, grid):
        def dfs(i, j):
            grid[i][j] = 2
            for a, b in [[0, -1], [0, 1], [1, 0], [-1, 0]]:
                x, y = i + a, j + b
                if 0 <= x < m and 0 <= y < n and grid[x][y] == 1:
                    dfs(x, y)

        m, n = len(grid), len(grid[0])
        cnt = 0
        for i in range(m):
            for j in range(n):
                if grid[i][j] == 1:
                    dfs(i, j)
                    cnt += 1
        for i in range(m):
            for j in range(n):
                if grid[i][j] == 2:
                    grid[i][j] = 1
        return cnt

Continue Practicing

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