[leetcode]Triangle @ Python

原题地址：https://oj.leetcode.com/problems/triangle/

题意：

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.

解题思路：使用动态规划（dp）。需要注意的是从后往前更新！

代码：

class Solution:
    # @param triangle, a list of lists of integers
    # @return an integer
    def minimumTotal(self, triangle):
        if len(triangle) == 0: return 0
        array = [0 for i in range(len(triangle))]
        array[0] = triangle[0][0]
        for i in range(1, len(triangle)):
            for j in range(len(triangle[i]) - 1, -1, -1):
                if j == len(triangle[i]) - 1:
                    array[j] = array[j-1] + triangle[i][j]
                elif j == 0:
                    array[j] = array[j] + triangle[i][j]
                else:
                    array[j] = min(array[j-1], array[j]) + triangle[i][j]
        return min(array)