Problem 28(Number spiral diagonals)

Problem 28(Number spiral diagonals)

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

 

21	22	23	24	25
20	7	8	9	10
19	6	1	2	11
18	5	4	3	12
17	16	15	14	13

 

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

 

In Python:

import time

startTime = time.time()
sumDiagonals = 1
i = 1
numFirst = [4 * n ** 2 -2 * n + 1 for n in range(1, 501)]
for n in numFirst:
    subList = [n, n + 2 * i, n + 4 * i, n + 6 * i]
    sumDiagonals += sum(subList)
    i += 1
print(sumDiagonals)
print(time.time() - startTime, "seconds")

Run time: 0.0018131732940673828 seconds

 

In Java:

package project_euler21_30;

import java.util.ArrayList;

public class Euler28 {
	public static void main(String[] args) {
		long startTime = System.currentTimeMillis();
		int sumDiagonals = 1;
		int i = 1;
		ArrayList<Integer> numFirst = new ArrayList<Integer>();
		for (int n = 1; n < 501; n++) {
			numFirst.add(4 * (int)Math.pow(n, 2) - 2 * n + 1);
		}
		for (Integer n : numFirst) {
			sumDiagonals += 4 * n + 12 * i;
			i++;
		}
		System.out.println(sumDiagonals);
		long endTime = System.currentTimeMillis();
		System.out.println((double)(endTime - startTime)/(double)1000 + "seconds");
	}
}

Run time: 0.001seconds

 

Solution: 669171001