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.

Analysis: DP. triangle[i][j] = min(triangle[i-1][j-1], triangle[i-1][j]) + triangle[i][j]. 

public class Solution {
    public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {
        int n = triangle.size();
        if(n==0) return 0;
        
        for(int i=1; i<n; i++) {
            for(int j=0; j<i+1; j++) {
                if(j==0) {
                    triangle.get(i).set(j, triangle.get(i-1).get(j)+triangle.get(i).get(j));
                }
                else if(j>0 && j<i) {
                    triangle.get(i).set(j, Math.min(triangle.get(i-1).get(j-1), triangle.get(i-1).get(j))+triangle.get(i).get(j));
                }
                else {
                    triangle.get(i).set(j, triangle.get(i-1).get(j-1)+triangle.get(i).get(j));
                }
            }
        }
        Collections.sort(triangle.get(n-1));
        return triangle.get(n-1).get(0);
    }
}