<p>You are given a <strong>0-indexed</strong> 2D integer array <code>grid</code> of size <code>m x n</code>. Each cell has one of two values:</p>

<ul>
	<li><code>0</code> represents an <strong>empty</strong> cell,</li>
	<li><code>1</code> represents an <strong>obstacle</strong> that may be removed.</li>
</ul>

<p>You can move up, down, left, or right from and to an empty cell.</p>

<p>Return <em>the <strong>minimum</strong> number of <strong>obstacles</strong> to <strong>remove</strong> so you can move from the upper left corner </em><code>(0, 0)</code><em> to the lower right corner </em><code>(m - 1, n - 1)</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/04/06/example1drawio-1.png" style="width: 605px; height: 246px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1],[1,1,0],[1,1,0]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can remove the obstacles at (0, 1) and (0, 2) to create a path from (0, 0) to (2, 2).
It can be shown that we need to remove at least 2 obstacles, so we return 2.
Note that there may be other ways to remove 2 obstacles to create a path.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/04/06/example1drawio.png" style="width: 405px; height: 246px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,0,0,0],[0,1,0,1,0],[0,0,0,1,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> We can move from (0, 0) to (2, 4) without removing any obstacles, so we return 0.
</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;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> <strong>or</strong> <code>1</code>.</li>
	<li><code>grid[0][0] == grid[m - 1][n - 1] == 0</code></li>
</ul>

from queue import PriorityQueue
from collections import deque
class Solution:
    def minimumObstacles(self, grid: List[List[int]]) -> int:
        
        m = len(grid)
        n = len(grid[0])
        
        dist = [[float("inf")] * n for _ in range(m)]
        dist[0][0] = 0
        
#         q = PriorityQueue()
#         q.put((0, 0, 0))
        
#         while not q.empty():
#             curr_dist, x, y = q.get()
#             if x == m-1 and y == n-1: return curr_dist
            
#             for a, b in [(0,1), (0,-1), (1,0), (-1,0)]:
#                 new_x, new_y = x+a, y+b
#                 if 0 <= new_x < m and 0 <= new_y < n and curr_dist + grid[new_x][new_y] < dist[new_x][new_y]:
#                     dist[new_x][new_y] = curr_dist + grid[new_x][new_y]
#                     q.put((dist[new_x][new_y], new_x, new_y))

        q = deque([(0,0)])
        while q:
            x, y = q.popleft()
            if x == m-1 and y == n-1: return dist[x][y]
            
            for a, b in [(0,1), (0,-1), (1,0), (-1,0)]:
                new_x, new_y = a+x, b+y
                if 0 <= new_x < m and 0 <= new_y < n:
                    new_dist = dist[x][y] + grid[new_x][new_y]
                    if new_dist < dist[new_x][new_y]:
                        dist[new_x][new_y] = new_dist
                    
                        if grid[new_x][new_y] == 0:
                            q.appendleft((new_x, new_y))
                        else:
                            q.append((new_x, new_y))

        # return dist[-1][-1]
        
        
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