Triangle

空间复杂度为n

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).

题目不难，但是判断细节好复杂

sum[i][j]=min(sum[i-1][j-1],sum[i-1][j])+triangle[i][j]

class Solution(object):
    """
    :type triangle: List[List[int]]
    :rtype: int
    """
    def minimumTotal(self, triangle):
        F = []
        T = 0
        for L in triangle:
            for i in range(len(L)):
                if i == 0: #the begin
                    if len(F) == 0:
                        T = L[i]
                    else:
                        T = F[i] + L[i]
                elif i == len(L)-1: # the end\
                    S = T
                    T = F[i-1] + L[i]
                    F[i-1] = S
                else:
                    S = T
                    if F[i] < F[i-1]:
                        T = F[i]+L[i]
                    else:
                        T =F[i-1]+L[i]
                    F[i-1] = S
            F.append(T)
        #find the min
        Min = F[0]
        for temp in F:
            if temp < Min:
                Min = temp
        return Min

S = Solution()
print(S.minimumTotal([[-1],[2,3],[1,-1,-1]]))

改进，逆向思维

（1）在遍历每一行的时候可以从后往前，这样就省掉一个变量
（2）还可以从最底层向上变量，这样又简化了步骤