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.

Have you met this question in a real interview?

Yes

Example

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 {

    /**

     * @param triangle: a list of lists of integers.

     * @return: An integer, minimum path sum.

     */

    public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {

        // write your code here

        if(triangle == null || triangle.size() == 0) return 0;

        int n = triangle.size();

        int[][] record = new int[n][n];

        for(int i = 0; i < n; i++){

            record[n-1][i] = triangle.get(n-1).get(i);

        }

        

        for(int i = n - 2; i>= 0; i--){

            ArrayList<Integer> tri = triangle.get(i);

            for(int j = 0; j < tri.size(); j++){

                record[i][j] = Math.min(tri.get(j) + record[i+1][j], tri.get(j) + record[i+1][j+1]);

            }

        }

        return record[0][0];

    }

}