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();
        vector<int> dp(n, 0);
        vector<int> tmp(n, 0);
        dp[0] = triangle[0][0];
        for(int i=1;i<n;i++){
            for(int j=0;j<=i;j++){
                if( j>=1 && j <= i-1){
                    tmp[j] = min(dp[j-1], dp[j]) + triangle[i][j];
                }
                else if(j==0){
                    tmp[j] = triangle[i][j] + dp[j];
                }
                else if(j == i){
                    tmp[j] = triangle[i][j] + dp[j-1];
                }
            }
                            dp.swap(tmp);

        }
        int ans = dp[0];
        for(int i=0;i<n;i++){
            if(ans>dp[i])
                ans = dp[i];
        }
        return ans;
    }
};