<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 queue

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        # Breadth First Search
        
        m = len(grid)
        n = len(grid[0])
        
        def get_nodes(row, col):
            valid_nodes = []
            if row < m - 1:
                valid_nodes.append((row + 1, col))
            if col < n - 1:
                valid_nodes.append((row, col + 1))
            if len(valid_nodes) == 2 and grid[row + 1][col] > grid[row][col + 1]:
                valid_nodes[0], valid_nodes[1] = valid_nodes[1], valid_nodes[0]
            return valid_nodes

        pq = queue.PriorityQueue()
        visited = set()
        pq.put((grid[0][0], 0, 0))
        visited.add((0, 0))
        print(pq)
        while not pq.empty():
            distance, row, col = pq.get()
            # print("Location: " + str(row) + ", " + str(col) + " | Distance: " + str(distance))
            if row == m - 1 and col == n - 1:
                return distance
            for row_new, col_new in get_nodes(row, col):
                if (row_new, col_new )not in visited:
                    visited.add((row_new, col_new))
                    pq.put((distance + grid[row_new][col_new], row_new, col_new))
21800