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.

Solution:
Brute-force: use an array list to record all paths' sum, and update it level by level. 

//  bottom-up!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

public class Solution {
    public int minimumTotal(ArrayList> triangle) {
        int n = triangle.size();
        int[] total = new int[n];
        
        // assign last row elements to total
        for(int i = 0; i < n; i++)
            total[i] = triangle.get(n-1).get(i);
            
        // bottom-up left-right
        for(int i = n-2; i >= 0; i--){
            for(int j = 0; j <= i; j++){
                total[j] = triangle.get(i).get(j) + Math.min(total[j], total[j+1]);
            }
        }
        
        return total[0];
    }
}