LeetCode -- Triangle 路径求最小和（ 动态规划问题）

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.

这个问题分为两种情况，一种不可以修改原数组元素，另一种可以修改数组元素

1、可以修改数组元素

 class Solution {
 public:
     int minimumTotal(vector<vector<int>>& triangle) {
         for(int i = triangle.size()-; i >= ; --i)
         {
             for(int j = ; j < i+;++j)
             {
                 if(triangle[i+][j]<triangle[i+][j+])
                     triangle[i][j] += triangle[i+][j];
                 else
                     triangle[i][j] += triangle[i+][j+];
             }

         }
         return triangle[][];
     }
 };

2、不能修改数组元素