LeetCode #120 Triangle

【问题描述】

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

Forexample, 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 youare able to do this using only O(n) extra space, where n is the total number ofrows in the triangle.

【解决思路】

采用自下而上的规划思路：

用一个同等大小的二位数组roads（不建议对直接修改原数组）记录到达每个节点的最短路径。

从倒数第二行遍历至第一行（下标为 0，0），最后一行的初始值等于原数组最后一行的值。

每次遍历中，roads[i][j] = min(roads[i+1][j], roads[i+1][j+1]。

【代码实现】

class Solution:
    def minimumTotal(self, triangle):
        """
        :type triangle: List[List[int]]
        :rtype: int
        """
        roads = [[triangle[i][j] for j in range(0, i+1)] for i in range(0, len(triangle))]
        # down-top approach
        for i in range(len(roads)-2, -1, -1):
            for j in range(0, i+1):
                roads[i][j] += min(roads[i+1][j], roads[i+1][j+1])

        return roads[0][0]

'''
sol = Solution()
tri = [[2], [3,4], [6,5,1], [4,1,8,1]]
print(sol.minimumTotal(tri))
'''