<p>Given a <code>m x n</code> <code>grid</code> filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.</p>

<p><strong>Note:</strong> You can only move either down or right at any point in time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/05/minpath.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> grid = [[1,3,1],[1,5,1],[4,2,1]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Because the path 1 &rarr; 3 &rarr; 1 &rarr; 1 &rarr; 1 minimizes the sum.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,2,3],[4,5,6]]
<strong>Output:</strong> 12
</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;= 200</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 200</code></li>
</ul>

class Solution:
    def neighbors(self, grid, node) : 
        directions, nbrs = [(1, 0), (0, 1)], []
        for dx, dy in directions : 
            new_x, new_y = node[0] + dx, node[1] + dy 
            if 0 <= new_x < len(grid) and 0 <= new_y < len(grid[0]) :
                nbrs.append((new_x, new_y))
        return nbrs 

    def minPathSum(self, grid: List[List[int]]) -> int:
        visited = {} 
        for i in range(len(grid)) : 
            for j in range(len(grid[0])) : 
                visited[(i, j)] = False

        heap, start, end = [], (0, 0), (len(grid)-1, len(grid[0])-1)
        visited[start] = True 
        heappush(heap, (grid[0][0], start))
        while heap : 
            dist, node = heappop(heap)

            if node == end : 
                return dist 

            for nbr in self.neighbors(grid, node) : 
                if not visited[nbr] :   
                    heappush(heap, (dist + grid[nbr[0]][nbr[1]], nbr))
                    visited[nbr] = True 
22000