<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:
        res = float("inf")
        total = 0
        dir = [(1,0), (0,1)]
        minH = [(grid[0][0], 0, 0)]
        visit =set()
        ROWS = len(grid)
        COLS = len(grid[0])
        while minH:
            curr_sum, r ,c = heapq.heappop(minH)
            if (r,c) in visit:
                continue
            
            visit.add((r,c))

            if (r==ROWS-1 and c == COLS-1):
                return curr_sum

            for dr,dc in dir:
                row = r+dr
                col = c+dc
                if (row<0 or row>=ROWS or col<0 or col>=COLS or (row,col) in visit):
                    continue
                
                heapq.heappush(minH, [curr_sum+grid[row][col], row, col] )
            
        return -1




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