(ql:quickload '(fiveam))
(defpackage :day21
  (:use :cl :fiveam :alexandria))
(in-package :day21)
;;22:55
;;23:32

(defun find-start (field)
  (destructuring-bind (rows cols)
      (array-dimensions field)
    (loop for row below rows do
      (loop for col below cols do
        (when (eq (aref field row col) #\S)
          (return-from find-start (list row col)))))))

(defun read-field (filename)
  (let* ((lines (uiop:read-file-lines filename)))
    (make-array (list (length lines) (length (car lines)))
                :initial-contents lines)))

(defun solver (field boundedp &rest step-counts)
  (let* (pending
         (visited (make-hash-table :test #'equal))
         (start (find-start field))
         (step-count (car (last step-counts)))
         (end-positions (mapcar (lambda (s)
                                  (cons (- step-count s)
                                        (make-hash-table :test #'equal)))
                                step-counts)))
    (destructuring-bind (rows cols)
        (array-dimensions field)

      (push (cons step-count start) pending)
      (setf (gethash start visited) step-count)

      (loop while pending
            for (steps-left row col) = (pop pending)
            ;; an even number of steps left means it is possible
            ;; to go and return to the place in the steps available
            ;; Thus count to the solution.
            do
               (dolist (ep end-positions)
                 (destructuring-bind (check-point . tracker) ep
                   (let ((mark-left (- steps-left check-point)))
                     (when (and (not (minusp mark-left))
                                (evenp mark-left))
                       (setf (gethash (list row col) tracker) t)))))
            unless (zerop steps-left)
              do (loop
                   for (dr dc) in '((-1 0) (0 -1) (1 0) (0 1))
                   for nr = (+ row dr)
                   for nc = (+ col dc)
                   for new-pos = (list nr nc)
                   when (and (< (gethash new-pos visited -1) (1- steps-left))
                             (if boundedp
                                 (and
                                  (< -1 nr rows)
                                  (< -1 nc cols))
                                 t)
                             (not (eq #\# (aref field (mod nr rows) (mod nc cols)))))
                     do (setf (gethash new-pos visited) (1- steps-left))
                        (push (cons (1- steps-left) new-pos) pending))))
    (mapcar (compose #'hash-table-count #'cdr) end-positions)))


(defun solve-quadratic (r-one r-two r-three)
  ;; The covered area grows proportional to the square of steps taken.
  ;; The requested numbers of steps (= 26501365 (+ (* 202300 131) 65))
  ;; The function that takes to the the edge of the field g(x) = 65 + x * 131
  ;; The standard quadratic function q(x) = a*x^2 + b*x + c
  ;; r₁ = q o g (0) = c
  ;; r₂ = q o g (1) = a  +  b + c
  ;; r₃ = q o g (2) = 4a + 2b + c
  ;;
  ;; solving is simple
  ;; a = (r₃  - 2r₂ + r₁) / 2
  ;; b = (4r₂ - 3r₁ - r₃) / 2
  ;; c = r₁
  (values (/ (+ (- r-three (* 2 r-two))
                r-one)
             2)
          (/ (- (* 4 r-two) (* 3 r-one) r-three) 2)
          r-one))

(defun solve-part2 (places)
  (let ((x 202300))
    (multiple-value-bind (a b c)
        (apply #'solve-quadratic places)
      (+ (* a x x) (* b x) c))))

(test solutions
  (is (= 16 (car (solver (read-field "eg-in") t 6))))
  (is (= 3574 (car (solver (read-field "input") t 64))))
  (mapc (lambda (solution calculated)
          (is (= solution calculated)))
        '(16 50 1594 6536 26538 59895)
        (solver (read-field "eg-in") nil 6 10 50 100 200 300))

  (let ((results '(3719 33190 91987))
        (places (solver (read-field "input") nil 65 (+ 65 131) (+ 65 (* 131 2)))))
    (mapc (lambda (solution calculated)
            (is (= solution calculated)))
          results
          places)
    (is (= 600090522932119 (solve-part2 results)))))