[Leetcode]Minimum Path Sum

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.

和Unique Path类似，同样是用动态规划~递推式是dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j]~代码如下~

class Solution:
    # @param grid, a list of lists of integers
    # @return an integer
    def minPathSum(self, grid):
        if grid is None or len(grid) == 0 or len(grid[0]) == 0: return 0
        lenRow, lenCol = len(grid), len(grid[0])
        dp = [[0] * lenCol for i in xrange(lenRow)]
        dp[0][0] = grid[0][0]
        for i in xrange(1, lenRow):
            dp[i][0] = dp[i - 1][0] + grid[i][0]
        for j in xrange(1, lenCol):
            dp[0][j] = dp[0][j - 1] + grid[0][j]
        for i in xrange(1, lenRow):
            for j in xrange(1, lenCol):
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j]
        return dp[lenRow - 1][lenCol - 1]

还有一种一维的动态规划解法，可以参考http://blog.youkuaiyun.com/linhuanmars/article/details/22257673