part2 day21

1 files changed, 69 insertions, 0 deletions

diff --git a/AoC2023/day21/solver.lisp b/AoC2023/day21/solver.lisp
index 05c4c74..a120be0 100644
--- a/AoC2023/day21/solver.lisp
+++ b/AoC2023/day21/solver.lisp
@@ -50,3 +50,72 @@
 (test solutions
   (is (= 16 (solver1 (uiop:read-file-lines "eg-in") 6)))
   (is (= 3574 (solver1 (uiop:read-file-lines "input") 64))))
+
+(defun solver2 (lines step-count)
+  (let* ((field (make-array (list (length lines) (length (car lines)))
+                            :initial-contents lines))
+         pending
+         (end-positions (make-hash-table :test #'equal))
+         (visited (make-hash-table :test #'equal))
+         (start (find-start field)))
+    (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.
+            when (evenp steps-left)
+              do (setf (gethash (list row col) end-positions) 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))
+                             (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))))
+    (hash-table-count end-positions)))
+
+(solver2 (uiop:read-file-lines "eg-in") 6)
+(solver2 (uiop:read-file-lines "eg-in") 10)
+(solver2 (uiop:read-file-lines "eg-in") 50)
+(solver2 (uiop:read-file-lines "eg-in") 100)
+;; (time (solver2 (uiop:read-file-lines "eg-in") 500))
+
+(defun solve-part2 ()
+  (let ((x 202300))
+    (multiple-value-bind (a b c)
+        (solve-quadratic 3719 33190 91987)
+      (+ (* a x x) (* b x) c))))
+
+(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))
+
+(test sols
+  (loop for steps in (list 65 (+ 65 131) (+ 65 (* 131 2)))
+        for result in '(3719 33190 91987)
+        do (is (= result (solver2 (uiop:read-file-lines "input") steps))))
+  (is (= 600090522932119 (solve-part2))))