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/**
* Problem 28 - Number spiral diagonals
*
* @see {@link 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 07 08 09 10
* 19 06 01 02 11
* 18 05 04 03 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?
*
* @author ddaniel27
*/
function problem28(dim) {
if (dim % 2 === 0) {
throw new Error('Dimension must be odd')
}
if (dim < 1) {
throw new Error('Dimension must be positive')
}
let result = 1
for (let i = 3; i <= dim; i += 2) {
/**
* Adding more dimensions to the matrix, we will find at the top-right corner the follow sequence:
* 01, 09, 25, 49, 81, 121, 169, ...
* So this can be expressed as:
* i^2, where i is all odd numbers
*
* Also, we can know which numbers are in each corner dimension
* Just develop the sequence counter clockwise from top-right corner like this:
* First corner: i^2
* Second corner: i^2 - (i - 1) | The "i - 1" is the distance between corners in each dimension
* Third corner: i^2 - 2 * (i - 1)
* Fourth corner: i^2 - 3 * (i - 1)
*
* Doing the sum of each corner and simplifying, we found that the result for each dimension is:
* sumDim = 4 * i^2 + 6 * (1 - i)
*
* In this case I skip the 1x1 dim matrix because is trivial, that's why I start in a 3x3 matrix
*/
result += 4 * i * i + 6 * (1 - i) // Calculate sum of each dimension corner
}
return result
}
export { problem28 }