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).

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.

Analyse: DP. From bottom to up, compute the shortest path from next level to this level‘s elements. 

 1 class Solution {
 2 public:
 3     int minimumTotal(vector<vector<int>>& triangle) {
 4         if(triangle.empty() || triangle[0].empty()) return 0;
 5         
 6         vector<int> dp = triangle.back();
 7         for(int i = triangle.size() - 2; i >= 0; i--) {
 8             for(int j = 0; j <= i; j++)
 9                 dp[j] = triangle[i][j] + min(dp[j], dp[j + 1]);
10         }
11         
12         return dp[0];
13     }
14 };

Triangle

原文：http://www.cnblogs.com/amazingzoe/p/5722971.html