LeetCode OJ - Triangle

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.

解题思路：

从底向上动规，可以减少从上向下动归后找最小值的过程。过程中可以直接修改triangle，而不需要重新开辟空间。

代码：

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        for (int i = triangle.size() - 2; i >= 0; i--) {
            for (int j = 0; j < triangle[i].size(); j++) {
                triangle[i][j] = min(triangle[i+1][j], triangle[i+1][j + 1]) + triangle[i][j];
            }
        }
        return triangle.empty() ? 0 : triangle[0][0];
    }
};