<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:
        rows = len(grid)
        cols = len(grid[0])
        dp = [[0]*cols]*rows
        dp[-1][-1] = grid[-1][-1]
        print(dp)

        for ii in range(rows-1, -1, -1):
            for jj in range(cols-1, -1, -1):
                if ii < rows-1 and jj < cols - 1:
                    dp[ii][jj] = grid[ii][jj] + min(dp[ii+1][jj], dp[ii][jj+1])
                elif ii < rows-1:
                    dp[ii][jj] = grid[ii][jj] + dp[ii+1][jj]
                elif jj < cols - 1:
                    dp[ii][jj] = grid[ii][jj] + dp[ii][jj+1]
        
        print(dp)

        return dp[0][0]

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