120. Triangle

120. Triangle

0. 参考文献

序号	文献
1	Leetcode-120-Triangle
2	[eetCode 120 - Triangle]

1.题目

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.

2. 思路

本题求解的是给到的一组三角形矩阵中，从上到下的路径中和最小的是多少。这里我们反过来求解，自底向上，设dp[i]是从底部开始到顶部的第条路径的和。这里怎么理解呢？假如，三角形的底部有4个元素，那么从底部出发到达顶部的路径应该是有4条。因此dp[i]代表了第条路径的和。因为题目中的规则是在第i层的第j个数字，往下只能走i+1,j 或者i+1,j+1 2个数字。因此，dp[i] = 当前数字 + min(dp[i],dp[i+1])。到这里思路就很清晰了，我们来看下实现。

3. 实现

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