<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:
        # min sum up to current point
        # bottom up
        ROW = len(grid)
        COL = len(grid[0])
        res = [[0 for _ in range(COL + 1)] for _ in range(ROW + 1)]

        for i in range(ROW):
            res[i][COL] = float('inf')
        
        for j in range(COL):
            res[ROW][j] = float('inf')



        # def dfs(i, j, total):
        #     if i == ROW - 1 and j == COL - 1:
        #         return total + grid[i][j]
            
        #     if i >= ROW or j >= COL:
        #         return float('inf')
            
        #     total += grid[i][j]
        #     return min(dfs(i + 1, j, total), dfs(i, j + 1, total))
        res[ROW - 1][COL - 1] = grid[ROW - 1][COL - 1]
        for i in range(ROW - 1, -1, -1):
            for j in range(COL - 1, -1, -1):
                if i == ROW - 1 and j == COL - 1:
                    continue

                up = res[i + 1][j]
                left = res[i][j + 1]
                res[i][j] = grid[i][j] + min(up, left)
        print(res)
        return res[0][0]

19500