<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 minPathSum(self, grid: List[List[int]]) -> int:
        r = len(grid)
        c = len(grid[0])
        res = [[inf for _ in range(c)] for _ in range(r)]

        h = [(grid[0][0], 0, 0)]
        visited = set()

        while h:
            v, x, y = heapq.heappop(h)
            if (x, y) not in visited:

                visited.add((x,y))
                res[x][y] = min(res[x][y], v)

                if x < r - 1:
                    if res[x + 1][y] > v + grid[x + 1][y]:
                        res[x + 1][y] = v + grid[x + 1][y]
                        heapq.heappush(h, (v + grid[x + 1][y], x + 1, y))
                if y < c - 1:
                    if res[x][y + 1] > v + grid[x][y + 1]:
                        res[x][y + 1] = v + grid[x][y + 1]
                        heapq.heappush(h, (v + grid[x][y + 1], x, y + 1))

        return res[- 1][- 1]


        
        
23800