Triangle

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:

From bottom to top

1.keep an array to store the result.

2.First Round: res[0] = 4, res[1] = 1, res[2] = 8, res[3] = 3 

3.Second Round: res[0] = min(res[0], res[1]) + currentValue. Repeat until reach the top level of the triangle.

4. res[0] is the result.

public class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if (triangle ==null || triangle.size() == 0)
            return Integer.MIN_VALUE;
        
        int[] res = new int[triangle.size()];
        
        //initialize
        for (int i = 0; i < triangle.size(); i++) {
            res[i] = triangle.get(triangle.size() - 1).get(i);
        }
        
        //iteration
        for (int i = triangle.size() - 2; i >= 0; i--) {
            for (int j = 0; j <= i; j++) {
                res[j] = Math.min(res[j], res[j + 1]) + triangle.get(i).get(j);
            }
        }
        
        return res[0];
    }
}