"""
64. Minimum Path Sum
Difficulty: Medium
https://leetcode.com/problems/minimum-path-sum/

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Given a m x n grid filled with non-negative numbers, find a path from
top left to bottom right, which minimizes the sum of all numbers along
its path.

Note: You can only move either down or right at any point in time.



Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1
minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12



Constraints:

        • m == grid.length

        • n == grid[i].length

        • 1 <= m, n <= 200

        • 0 <= grid[i][j] <= 200
"""


class Solution:
    def minPathSum(self, grid: list[list[int]]) -> int:
        if not grid or not grid[0]:
            return 0

        m = len(grid)
        n = len(grid[0])
        dp = [[0 for _ in range(n)] for _ in range(m)]

        for c in range(n):
            dp[0][c] = dp[0][c - 1] + grid[0][c] if c else grid[0][c]

        for r in range(m):
            dp[r][0] = dp[r - 1][0] + grid[r][0] if r else grid[r][0]

        for r in range(1, m):
            for c in range(1, n):
                dp[r][c] = min(dp[r - 1][c], dp[r][c - 1]) + grid[r][c]

        return dp[-1][-1]