python學習第9周：LeetCode 120. Triangle題解

#120
題目來源：
https://leetcode.com/problems/triangle


題目分析：
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.

 

 

題目思路：
這是一題動態規劃的題目，每一個點的最小值，依賴於它的上層點的最小值。
爲了實現O（n）的空間複雜度，可以用一個長度爲n的數組存儲到第i個點的最短路徑長度，然後每次從大往小更新數組。


代碼如下：

 

 

class Solution:
    def minimumTotal(self, triangle):
        """
        :type triangle: List[List[int]]
        :rtype: int
        """
        size = len(triangle);
        num = [0]*size;
        num[0] = triangle[0][0];
        for i in range(1,size):
            num[i] = num[i-1] + triangle[i][i];
            j = i - 1
            while j > 0:
                num[j] = min(num[j], num[j-1]) + triangle[i][j];
                j -= 1;
            num[0] = num[0] + triangle[i][0];
        minm = num[0];
        for i in range(1,size):
            minm = min(num[i], minm);
        return minm;