【leetcode】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.

 

class Solution{
public:
    int minimumTotal(vector<vector<int> > &triangle){
        int n=triangle.size();
        if(n==0) return 0;

        int *sum=new int[n+1];

        sum[0]=triangle[0][0];

        for(int i=1;i<n;i++)
        {
            sum[i]=sum[i-1]+triangle[i][i];
            for(int j=i-1;j>0;j--)
                sum[j]=min(sum[j],sum[j-1])+triangle[i][j];
            sum[0]=sum[0]+triangle[i][0];
        }

        int min=INT_MAX;
        for(int i=0;i<n;i++)
            if(sum[i]<min)
                min=sum[i];

        return min;
    }
};