src/number-spiral.lisp @ 5f1511ebec96
Add scratch.lisp to .hgignore.
author |
Steve Losh <steve@stevelosh.com> |
date |
Tue, 05 Dec 2017 21:00:36 -0500 |
parents |
11607ca439c4 |
children |
(none) |
(in-package :advent.spiral)
(defun layer-side-length (layer)
"Return the length of one side of `layer`."
(1+ (* 2 layer)))
(defun layer-size (layer)
"Return the total size of a number spiral with a final layer of `layer`."
(square (layer-side-length layer)))
(defun layer-for-number (number)
"Return the index of the layer containing `number`."
(ceiling (/ (1- (sqrt number)) 2)))
(defun layer-start (layer)
"Return the smallest number in `layer`."
(if (zerop layer)
1
(1+ (layer-size (1- layer)))))
(defun layer-leg-length (layer)
"Return the length of one \"leg\" of `layer`."
(1- (layer-side-length layer)))
(defun leg (layer number)
"Return the leg index and offset of `number` in `layer`."
(if (= 1 number)
(values 0 0)
(let ((idx (- number (layer-start layer)))
(legsize (layer-leg-length layer)))
(values (floor idx legsize)
(1+ (mod idx legsize))))))
(defun corner-coordinates (layer leg)
"Return the coordinates of the corner starting `leg` in `layer`.
Leg | Corner
0 | Bottom Right
1 | Top Right
2 | Top Left
3 | Bottom Left
"
;; 2 1
;;
;; 3 0
(ccase leg
(0 (complex layer (- layer)))
(1 (complex layer layer))
(2 (complex (- layer) layer))
(3 (complex (- layer) (- layer)))))
(defun leg-direction (leg)
"Return the direction vector for the given `leg`.
"
;; <--
;; 11110
;; | 2 0 ^
;; | 2 0 |
;; v 2 0 |
;; 23333
;; -->
(ccase leg
(0 (complex 0 1))
(1 (complex -1 0))
(2 (complex 0 -1))
(3 (complex 1 0))))
(defun number-coordinates (number)
(nest
;; Find the layer the number falls in.
(let ((layer (layer-for-number number))))
;; Find which leg of that layer it's in, and how far along the leg it is.
(multiple-value-bind (leg offset) (leg layer number))
;; Find the coordinates of the leg's corner, and its direction vector.
(let ((corner (corner-coordinates layer leg))
(direction (leg-direction leg))))
;; Start at the corner and add the offset in the leg's direction to find the
;; number's coordinates.
(+ corner (* direction offset))))