LeetCode120. 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).

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找到一条路线，和最小。这道题从下往上找会比较容易，也就是所谓的bottom-up

代码比较简单容易看懂。注意的是从倒数第二行遍历到第一行要用 range（l-2, -1, -1)

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

或者只用O(n)空间，每次结果都存在同一个list中

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