Euler Project – Problem 18 Solution

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

Solution:

import java.util.ArrayList;

public class Problem18 {

    public static void main(String[] args) {

        int max_sum = 0;
        String path = "";

        String numbers_string = "75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23";
        String[] numbers_array = numbers_string.split(" ");
        ArrayList<int[]> lines = new ArrayList<int[]>();

        // get lines count
        int num = 0;
        int sum = 0;
        while (sum < numbers_array.length) {
            num++;
            sum += num;
        }
        int lines_count = num;
        System.out.println(lines_count);

        //create all lines
        int numbers_count = 0;
        for (int i = 1; i <= lines_count; i++) {
            int[] line = new int[i];
            for (int j = numbers_count, k = 0; j < numbers_count + i; j++, k++) {
                line[k] = Integer.parseInt(numbers_array[j]);
            }
            lines.add(line);
            numbers_count += i;
        }

        //get maximum total
        for (int i = 0; i < Math.pow(2, lines_count - 1); i++) {
            int temp_sum = 0;
            String binary = Integer.toBinaryString(i);
            while (binary.length() < lines_count) {
                binary = "0" + binary;
            }
            char[] direction = binary.toCharArray();
            int index = 0;
            for (int j = 0; j < direction.length; j++) {
                if (direction[j] == '1') {
                    index++;
                }
                temp_sum += lines.get(j)[index];
            }
            if (temp_sum > max_sum) {
                max_sum = temp_sum;
                path = binary;
            }
            System.out.println(i + "th path=" + binary + ":" + temp_sum);
        }

        System.out.println(max_sum);
        System.out.println(path);

    }
}