Number Spiral Diagonals

// https://projecteuler.net/problem=28

// 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?
//
// Answer: 669171001

// Authored by: Tim Varley 💘
// Assisted-by: Grok Code Fast via Crush 💘 <crush@charm.land>

#include <iostream>

long long spiral_diagonal_sum(int size) {
    if (size == 1) return 1;
    long long sum = 1;  // center
    for (int n = 3; n <= size; n += 2) {
        // corners: n², n²-n+1, n²-2n+2, n²-3n+3
        long long corner1 = (long long)n * n;
        long long corner2 = corner1 - (n - 1);
        long long corner3 = corner2 - (n - 1);
        long long corner4 = corner3 - (n - 1);
        sum += corner1 + corner2 + corner3 + corner4;
    }
    return sum;
}

#if ! defined UNITTEST_MODE
int main(int argc, char const *argv[]) {
    std::cout << spiral_diagonal_sum(1001) << std::endl;
}
#endif // UNITTEST_MODE

package org.tvarley.euler.solutions;

import org.tvarley.euler.Solution;

public class Solution028 implements Solution {
  public String solve() {
    long sum = 1;
    long num = 1;

    for (int step = 2; step <= 1001; step += 2) {
      for (int corner = 0; corner < 4; corner++) {
        num += step;
        sum += num;
      }
    }

    return Long.toString(sum);
  }
}

module.exports = {
  answer: () => {
    let sum = 1;
    let num = 1;

    for (let step = 2; step <= 1001; step += 2) {
      for (let corner = 0; corner < 4; corner++) {
        num += step;
        sum += num;
      }
    }

    return sum;
  }
};

def solve():
    """
    Number spiral diagonals
    Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral
    is formed. 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?
    https://projecteuler.net/problem=28
    """
    total = 1
    n = 1
    for step in range(2, 1002, 2):
        for _ in range(4):
            n += step
            total += n
    return total

def euler028_solution
  sum = 1
  (1..500).each do |k|
    side = 2 * k + 1
    corner = side * side
    sum += corner + (corner - 2 * k) + (corner - 4 * k) + (corner - 6 * k)
  end
  sum
end

puts euler028_solution if __FILE__ == $PROGRAM_NAME

package main

import "fmt"

func main() {
    sum := 1
    for n := 3; n <= 1001; n += 2 {
        corner := n * n
        sum += corner + (corner - (n - 1)) + (corner - 2*(n-1)) + (corner - 3*(n-1))
    }
    fmt.Println(sum)
}

// https://projecteuler.net/problem=28
//
// Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5
// spiral is formed as follows:
//
// 43 44 45 46 47 48 49
// 42 21 22 23 24 25 26
// 41 20  7  8  9 10 27
// 40 19  6  1  2 11 28
// 39 18  5  4  3 12 29
// 38 17 16 15 14 13 30
// 37 36 35 34 33 32 31
//
// 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?
//
// Answer: 669171001

pub fn spiral_diagonals(size: u64) -> u64 {
    let mut sum = 1u64;
    let mut n = 1u64;
    let mut step = 2u64;
    while step < size {
        for _ in 0..4 {
            n += step;
            sum += n;
        }
        step += 2;
    }
    sum
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn euler_028() {
        assert_eq!(spiral_diagonals(5), 101);
        assert_eq!(spiral_diagonals(1001), 669_171_001);
    }
}