Leetcode #120 Triangle

题目:

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle 
[ 
[2], 
[3,4], 
[6,5,7], 
[4,1,8,3] 
] 
The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note: 
Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

分析:

动态规划，求一个三角形二维数组从顶到低端的最小路径和。直接用triangle数组完成动态转移方程：triangle[i][j] += min(triangle[i+1][j],triangle[i+1][j+1]),从低向顶遍历。

代码:

class Solution(object):
    def minimumTotal(self, triangle):
        """
        :type triangle: List[List[int]]
        :rtype: int
        """
        n = len(triangle)
        for i in range(n-2,-1,-1):
            for j in range(i+1):
                triangle[i][j] += min(triangle[i+1][j],triangle[i+1][j+1])
        
        return triangle[0][0]