<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:
        h,w = len(grid),len(grid[0])
        dp = [[-1 for i in range(w)] for _ in range(h)]
        old_row = [9999999 for _ in range(w)]
        
        for y in range(h):
            new_row = [0 for _ in range(w)]
            for x in range(w):
                if y == 0 and x == 0:
                    new_row[0] = grid[0][0]
                    continue
                upper_val = old_row[x]
                if x == 0:
                    left_val = 99999
                else:
                    left_val = new_row[x-1]
                print(left_val)
                new_row[x] = min(upper_val,left_val) + grid[y][x]
            old_row = new_row[:]

        return new_row[-1]
17600