Triangle

Problem

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

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.

Code - Java

public class Solution {
    /**
     * @param triangle: a list of lists of integers.
     * @return: An integer, minimum path sum.
     */
    public int minimumTotal(int[][] triangle) {
        int lenX = triangle.length;

        int[][] sum = new int[lenX][lenX];
        sum[0][0] = triangle[0][0];
        for (int i = 1; i < lenX; i++) {
            for (int j = 0; j < (i + 1); j++) {
                if (j == 0) {
                    sum[i][j] = triangle[i][j] + sum[i - 1][j];
                } else if (j == i) {
                    sum[i][j] = triangle[i][j] + sum[i - 1][j - 1];
                } else {
                    sum[i][j] = triangle[i][j] + Math.min(sum[i - 1][j], sum[i - 1][j - 1]);
                }
            }
        }
        int min = Integer.MAX_VALUE;
        for (int j = 0; j < lenX; j++) {
            min = Math.min(min, sum[lenX - 1][j]);
        }
        return min;
    }
}