64. Minimum Path Sum.py

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

class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        # DP O(mn)
        if not grid or not grid[0]:
            return 0
        m, n = len(grid), len(grid[0])
        dp =  [[float('inf')] * n for _ in range(m)]
        dp[0][0] = grid[0][0]
        for i in range(1, m):
            dp[i][0] = grid[i][0] + dp[i - 1][0]
        for j in range(1, n):
            dp[0][j] = grid[0][j] + dp[0][j - 1]
        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
        return dp[m-1][n-1]