Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

minimumTotal.java

/*
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.
*/
public class Solution {
    public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {
        // Start typing your Java solution below
        // DO NOT write main() function
        if (triangle.size() == 0) return 0;
        int size = triangle.size();
        int min = Integer.MAX_VALUE;
        
        int[] sum = new int[size];;
        sum[0] = triangle.get(0).get(0);
        for(int cur = 1; cur <= size - 1; cur++){
            int next_size = triangle.get(cur).size();
            // it has to start with the end of the array
            // because the further one need the clean sum 
            // value than the newer one.
            for(int next = next_size - 1; next >= 0; next--) {
                if (next == 0) {
                    sum[0] = sum[0] + triangle.get(cur).get(next);
                } else if (next == (next_size - 1)) {
                    sum[next] = sum[next-1] + triangle.get(cur).get(next);
                } else {
                    sum[next] = Math.min(sum[next-1], sum[next]) + triangle.get(cur).get(next);
                }
            }
        }
        
        for(int i = 0; i < size; i++){
            if(sum[i] < min){
               min = sum[i];
            }
        }
        return min;
    }
}

public static int minimumTotal(List<List> triangle) {

    Integer tot = 0;
    for (int i = 0; i < triangle.size(); i++) {
        List<Integer> row = triangle.get(i);
        Integer minimum = row.stream().sorted().findFirst().get();
        tot += minimum;
    }
    return tot;
}