120. Triangle

problem description

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 thought

典型的动态规划问题，从底部出发向上遍历。每次选择两个子节点中最小的那一个，并且将它加到自己当前值上。重复操作，知道到根节点。

code

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]);   
            }
        }
        return triangle[0][0];
    }
};

algorithm analysis

复杂度时间和之前求三角形问题一样，都是O(n²)