<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 heapq import heappush, heappop

class Solution:
    def is_valid(self, x, y, grid):
        return 0 <= x < len(grid) and 0 <= y < len(grid[0])

    def minimumObstacles(self, grid: List[List[int]]) -> int:
        distanceFromOrigin = [[sys.maxsize for _ in range(len(grid[0]))] for _ in range(len(grid))]
        distanceFromOrigin[0][0] = 0
        q = []
        heappush(q, (0, 0, 0)) # current dist, x, y
        dirs = [[-1, 0], [1, 0], [0, 1], [0, -1]]

        while q:
            currentDist, x, y = heappop(q)
            if x == len(grid) - 1 and y == len(grid[0]) - 1:
                return currentDist
            if currentDist > distanceFromOrigin[x][y]:
                continue

            for x_dir, y_dir in dirs:
                new_x, new_y = x + x_dir, y + y_dir
                if not self.is_valid(new_x, new_y, grid):
                    continue

                if grid[new_x][new_y] and distanceFromOrigin[new_x][new_y] > currentDist + 1:
                    distanceFromOrigin[new_x][new_y] = currentDist + 1
                    heappush(q, (currentDist + 1, new_x, new_y))
                
                if grid[new_x][new_y] == 0 and distanceFromOrigin[new_x][new_y] > currentDist:
                    distanceFromOrigin[new_x][new_y] = currentDist
                    heappush(q, (currentDist, new_x, new_y))
        return distanceFromOrigin[len(grid) - 1][len(grid[0]) - 1]


            
        
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