欧拉计划＃18：最大路径总和I

Question

So basically I interpreted this problem as follows:

   3
  7 4
 2 4 6
8 5 9 3

The two number below the starting should be compared and the larger should be picked as the new number. So in this case, it would be 3, then 7, then 4, then 9. Sum them up, get the answer of 23. I wrote a program to achieve this:

public class ProblemEighteen {

private static int pos = 1;

public static void main(String[] args) {
    try {
        Scanner in = new Scanner(new File("Problem18Text"));
        int sum = 0;
        while (in.hasNextLine()) {
            final String line = in.nextLine();
            int big = getBiggestNum(line);
            sum += big;
            System.out.println(big);
        }
        System.out.println(sum);
        in.close();
    } catch (Exception e) {
        e.printStackTrace();
    }
}

private static int getBiggestNum(String line) {
    final String[] numbers = line.split(" ");
    if (numbers.length == 1) {
        pos = 1;
        return Integer.parseInt(numbers[0]);
    } else {
        int i = 1;
        int numOne = -1;
        int numTwo = -1;
        for (final String num : numbers) {
            if (pos == i) {
                numOne = Integer.parseInt(num);
            } else if (pos + 1 == i) {
                numTwo = Integer.parseInt(num);
            }
            i++;
            if (numOne != -1 && numTwo != -1)
                break;
        }
        if (numOne > numTwo) {
            return numOne;
        } else {
            pos += 1;
            return numTwo;
        }
    }
}

It works fine for the example I gave above, but when I put in the actual problem to solve, it said I got it wrong (I got 1064). I added a print statement to see what numbers it was selecting and it got them all right (based on how I understood what I was trying to find) but I still got it wrong... Anyone know why?

Answer 1

It's been a while since I've solved this problem, but you'll find that it's best that you start at the bottom of the triangle and work your way up. Especially, when you get to problem 67.

If you read your data into an array as baum suggested, you'd have data that looks like this:

3  0  0  0
7  4  0  0
2  4  6  0
8  5  9  3

So start at the bottom taking two numbers at a time and comparing a sum to their adjacent number in the next above row.

8 + 2 = 10 or 5 + 2 = 7.  10 is greater so replace the 2 with the 10.  
5 + 4 = 9 or 9 + 4 = 13.  13 is greater so replace the 4 with the 13.
9 + 6 = 15 or 3 + 6 = 9.  15 is greater so replace the 6 with 15.

Now move up one row and perform the same checks until you get to the very top and the very top should contain the correct answer.