120. Triangle

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.

Solutions:

class Solution {  

public:  

        int minimumTotal(vector<vector<int> > &triangle) {  

        int  tri_size=(int)triangle.size();  

        if(tri_size==0)  

            return 0;  

        vector<int> sum_vec(triangle[tri_size-1]);  

        for(int i=tri_size-2;i>=0;i--){  

            for(int j=0;j<i+1;j++){  

                if(sum_vec[j]<sum_vec[j+1])  

                    sum_vec[j]+=triangle[i][j];  

                else  

                    sum_vec[j]=triangle[i][j]+sum_vec[j+1];  

            }  

        }  

        return sum_vec[0];  

    }  

};