<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>

from collections import defaultdict
class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        dp = defaultdict(dict)
        def helper(r, c):
            if not (0 <= r < len(grid)) or not (0 <= c < len(grid[0])):
                return None
            if c in dp[r]:
                return dp[r][c]
            current = grid[r][c]
            if (r == len(grid) - 1) and (c == len(grid[0]) - 1):
                return current
            
            first = helper(r+1, c)
            second =  helper(r, c + 1)
            
            retval = float('inf')
            if first is not None:
                retval = current + first
            if second is not None:
                retval = min(retval, second + current)

            dp[r][c] = retval
            return  dp[r][c]
        return helper(0, 0)
20000