<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>

import heapq
from typing import List

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        # SSSP, Dijkstra Algorithm 
        m, n = len(grid), len(grid[0])
        visited = [[False for _ in range(n)] for _ in range(m)]
        queue = [[grid[0][0], 0, 0]] 
        # positions = [[0,1], [1,0], [0,-1], [-1,0]]
        positions = [[0,1], [1,0]]
        
        while queue: 
            cost, x, y = heapq.heappop(queue)
            
            if x == m - 1 and y == n - 1: 
                return cost
            
            if visited[x][y]:
                continue
            
            visited[x][y] = True 
            
            for offsetX, offsetY in positions: 
                nextX = x + offsetX 
                nextY = y + offsetY 
                
                if 0 <= nextX < m and 0 <= nextY < n and not visited[nextX][nextY]: 
                    heapq.heappush(queue, [cost + grid[nextX][nextY], nextX, nextY])
        
        return -1  

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