<p>You are given an <code>m x n</code> binary grid <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water. An <strong>island</strong> is a maximal <strong>4-directionally</strong> (horizontal or vertical) connected group of <code>1</code>&#39;s.</p>

<p>The grid is said to be <strong>connected</strong> if we have <strong>exactly one island</strong>, otherwise is said <strong>disconnected</strong>.</p>

<p>In one day, we are allowed to change <strong>any </strong>single land cell <code>(1)</code> into a water cell <code>(0)</code>.</p>

<p>Return <em>the minimum number of days to disconnect the grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]

<strong>Output:</strong> 2
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land2.jpg" style="width: 404px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [[1,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Grid of full water is also disconnected ([[1,1]] -&gt; [[0,0]]), 0 islands.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

from pprint import pprint
import numpy as np
class Solution:
    DIRECTIONS = [[0,1], [1,0], [0,-1],[-1,0]]
    
    def is_unvisited_land(self, row, col) -> bool:
        return (0 <= row < self.rows
                and 0 <= col < self.cols
                and self.grid[row][col] == 1)

    def find_articulation_point(self, row, col):
        self.discovery_time[row][col] = self.time
        self.lowest_reachable_time[row][col] = self.time
        self.time += 1
        discovered_children_number = 0

        for d_row, d_col in self.DIRECTIONS:
            child_row = row + d_row
            child_col = col + d_col
            if not self.is_unvisited_land(child_row, child_col):
                continue
            if self.discovery_time[child_row][child_col] == -1:
                discovered_children_number += 1
                self.parent_cell[child_row][child_col] = row * self.cols + col
                self.find_articulation_point(child_row, child_col)

                self.lowest_reachable_time[row][col] = min(
                                                        self.lowest_reachable_time[row][col],
                                                        self.lowest_reachable_time[child_row][child_col])
                
                if (self.lowest_reachable_time[child_row][child_col] >= self.discovery_time[row][col]
                    and self.parent_cell[row][col] != -1):
                        self.has_AP = True

            elif child_row * self.cols + child_col != self.parent_cell[row][col] :
                self.lowest_reachable_time[row][col] = min(
                                                        self.lowest_reachable_time[row][col],
                                                        self.discovery_time[child_row][child_col])
        
        if (self.parent_cell[row][col] == -1
            and discovered_children_number > 1) :
            self.has_AP = True


    def minDays(self, grid: List[List[int]]) -> int:
        self.grid = grid
        self.rows, self.cols = len(grid), len(grid[0])
        self.time = 0
        self.has_AP = False
        self.discovery_time = [[-1] * self.cols for _ in range(self.rows)]
        self.lowest_reachable_time = [[-1] * self.cols for _ in range(self.rows)]
        self.parent_cell = [[-1] * self.cols for _ in range(self.rows)]

        count_land_cells = 0
        count_islands = 0

        for row in range(self.rows):
            for col in range(self.cols):
                if grid[row][col] == 1:
                    count_land_cells += 1
                    if self.discovery_time[row][col] == -1:
                        self.find_articulation_point(row, col)
                        count_islands += 1
        if count_islands == 0 or count_islands >= 2:
            return 0
        if count_land_cells == 1:
            return 1
        if self.has_AP:
            return 1

        return 2

      



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