[Leetcode] Triangle

Problem

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.

Algorithm

Let dp[i][j] be the minimal path sum to element j in level i. 

dp[i][j] = min(dp[i-1][j],dp[i-1][j+1]) + A[i][j].

Since computing each level only needs the result of previous level, we can reduce the  space to O(n).

Code