[LeetCode]题解（python）：120 Triangle

题目来源

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https://leetcode.com/problems/triangle/

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.

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题意分析

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Input:一个三角矩阵

Output:最短路径

Conditions:使用O(n)空间

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题目思路

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首先初始化一个n大小的array，然后，初始化array为0，array[0]就是triangle的第一行的值，然后遍历剩余行，不断更新array，注意要从后往前遍历，否则会覆盖前面值。

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AC代码（Python）

class Solution(object):
    def minimumTotal(self, triangle):
        """
        :type triangle: List[List[int]]
        :rtype: int
        """
        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)