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[p10] still nothing…

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master
Jacopo De Simoi 3 months ago
parent 47e567b8f8
commit 60d24f2986
1 changed files with 256 additions and 44 deletions
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@ -4,7 +4,7 @@ This problem is pretty hard. I have not yet completely understood the
linear algebra behind it.
#+begin_src emacs-lisp :results none
(with-temp-buffer
(insert-file-contents "input-test")
(insert-file-contents "input")
(advent/replace-multiple-regex-buffer
'(("," . " ")
("^" . "(")
@ -80,7 +80,7 @@ There is a little complication, since the matrices involved are
degenerate and we have constraints;
#+begin_src emacs-lisp :results none
(setq machines (--map (-rotate 1 (cdr it)) data) machines)
(setq machines (--map (-rotate 1 (cdr it)) data))
#+end_src
These are some auxiliary functions to create and deal with matrices
@ -134,44 +134,258 @@ These are some auxiliary functions to create and deal with matrices
(let* ((pivot-coeff (nth pivot-index original-row)))
(when (< pivot-coeff 0)
(setq rMt (--map (flip-index base-index it) rMt)))
(assert (= 1 (abs pivot-coeff)))
(if (not (= 1 (abs pivot-coeff))) (setq pivot-coeff (* 1.0 pivot-coeff)))
(let* ((lambdas (append (-repeat (1+ base-index) 0)
(-drop (1+ base-index) (nth it rMt))))
(lambdas-corrected (--map (/ it (abs pivot-coeff)) lambdas)))
(setq rMt (--map (subtract-composite lambdas-corrected base-index it) rMt)
base-index (1+ base-index)))))))
(apply '-zip-lists rMt)))
#+end_src
#+RESULTS:
: row-reduce
#+begin_src emacs-lisp :results none
(defun fix-machine (machine)
(let ((machine-1 (let ((permutation (-grade-up '> (car machine))))
(cons (-sort '> (car machine)) (--map (--map (nth it permutation) it) (cdr machine))))))
(cons (car machine-1)
(--sort (< (-max it) (-max other))
(--sort (> (length it) (length other)) (cdr machine-1))))))
(setq machines (-map #'fix-machine machines))
#+end_src
#+RESULTS:
| 10 | 1 | 1 | 1 | 0 |
| -1 | 0 | 1 | 0 | -1 |
| 5 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 |
arst
| (29 26 26 12 9 26 26) | (0 1 3 5) | (1 2 4 5 6) | (0 1 2 5 6) | (0 2 3 4 6) | (0 3 4 6) | | | | | | | | |
| (31 51 38 61 77 74 49 72) | (1 3 4) | (0 1 2 3 4 5) | (1 3 4 5 6) | (3 4 6) | (0 4 5 7) | (2 3 4 7) | (1 5 7) | (2 6 7) | (0 5 7) | (5 6 7) | | | |
| (59 21 65 80 39 32 29 43) | (1 2 3) | (0 2 4 5 6) | (0 3 6) | (2 5 6) | (0 2 3 4 5 7) | (0 1 3 5 7) | (0 2 3 4 7) | (1 3 5 7) | | | | | |
| (45 34 45 25 51 61 41) | (0 1 2 3 4) | (1 4) | (0 2 3 5) | (0 1 2 4 5 6) | (0 2 3 5 6) | (4 5 6) | | | | | | | |
| (84 50 59 44 21 77 61 83) | (0 1 3 4 5 6) | (0 3 4 5 6) | (0 1 3 5 6) | (0 1 2 4 6 7) | (0 1 5 6 7) | (0 2 4 5 7) | (0 2 3 5 7) | (0 1 2 6 7) | (2 6 7) | (5 7) | | | |
| (35 18 29 30 49 28 30 35 48) | (1 2 3 4 6 7) | (0 1 2 4 5 7) | (0 2 7) | (0 3 4 5 6 7 8) | (0 1 3 4 6 8) | (0 2 3 4 6 8) | (2 4 5 7 8) | | | | | | |
| (45 8 50 30 16 45) | (1 2) | (0 2 3) | (0 2 3 4 5) | (1 2 4 5) | (0 5) | (2 5) | (5) | | | | | | |
| (26 33 44 35 25 48 30 33 11 45) | (2 5) | (1 3 6) | (1 7) | (2 3 4 6 7 8) | (0 1 2 4 5 6 7 9) | (2 3 4 5 8 9) | (1 3 5 7 9) | (0 5 9) | (3 9) | | | | |
| (49 37 54 32 31 23) | (0 1 2) | (0 1 2 3) | (2 3 4) | (0 2 3 4 5) | (0 1 3 4 5) | (0 2 4 5) | (0 1 5) | (4 5) | | | | | |
| (46 18 33 22) | (0) | (0 1) | (0 1 2) | (0 2 3) | (2 3) | | | | | | | | |
| (23 50 24 46 47 43) | (0 1) | (0 2 3) | (0 1 3 4) | (1 3 4) | (2 3 4) | (0 1 2 3 5) | (1 4 5) | (5) | | | | | |
| (22 15 45 45 48 49) | (0) | (2 4) | (0 2 3 4 5) | (1 3 4 5) | (0 1 2 5) | (0 2 3 5) | (2 3 4 5) | (1 2 5) | | | | | |
| (42 51 56 67 54 34 32 69 49) | (0 3 4 5 6 7) | (1 3 4 7) | (2 6 7) | (5 7) | (0 1 2 3 4 5 8) | (0 1 2 3 5 6 8) | (1 3 4 7 8) | (0 2 3 7 8) | (1 2 4 8) | | | | |
| (74 36 61 78 36 34 19 46 17 29) | (2 3) | (1 3 4) | (0 1 2 3 4 5 6 7) | (0 2 3 7) | (0 1 2 3 4 6 7 8) | (0 1 3 4 5 7 8) | (1 3 4 5 7 8) | (0 2 3 5 8 9) | (2 3 9) | (0 9) | | | |
| (30 19 38 38 32) | (0 2 3) | (2 3) | (0 2 3 4) | (1 4) | | | | | | | | | |
| (42 58 43 59 47 32 29 70 66 53) | (0 3 4 7) | (4 7) | (1 6 7 8) | (0 8) | (1 8) | (0 1 2 3 6 7 8 9) | (1 2 3 4 5 7 8 9) | (0 3 4 5 7 8 9) | (0 1 2 3 4 6 9) | (1 2 5 6 7 9) | | | |
| (9 194 203 18 194) | (0 2 3) | (1 2 3 4) | (1 2 4) | | | | | | | | | | |
| (1 16 1 16) | (0 2) | (1 3) | | | | | | | | | | | |
| (19 23 23 62 25 60 23) | (0) | (2) | (3 4) | (0 1 3 4 5) | (3 5) | (1 2 3 4 5 6) | (0 3 4 5 6) | (2 3 5 6) | (1 2 5 6) | | | | |
| (38 71 40 20 34 45 46 22 57) | (4) | (0 1 2 6 7) | (0 1 2 4 5 6 8) | (1 2 3 5 6 7 8) | (0 1 4 5 6 8) | (1 2 3 8) | (1 5 8) | | | | | | |
| (21 34 25 11 38) | (1) | (2) | (0 2 3) | (1 2 3) | (0 1 4) | (1 4) | (4) | | | | | | |
| (18 24 25 33 23 31) | (0 1 3) | (1 3) | (0 4) | (0 2 3 4 5) | (1 3 4 5) | (1 5) | (2 5) | | | | | | |
| (210 12 211 19 219) | (0) | (1 2) | (0 2 3 4) | (1 3 4) | (0 2 4) | (2 4) | | | | | | | |
| (44 25 62 37 54 51 26 74 57) | (0 2 5) | (0 3 4 5 6 7) | (0 3 7) | (1 2 4 5 6 7 8) | (0 2 3 4 5 7 8) | (0 1 4 5 6 8) | (1 3 5 6 7 8) | (2 4 7 8) | | | | | |
| (66 66 214 278 231 77 256 48 78 46) | (2 3 4 6) | (0 1 3 5 6 7) | (0 2 7) | (1 3 4 5 7 8) | (0 2 3 4 6 8) | (0 1 3 4 8) | (3 6 8) | (0 8) | (0 2 3 5 6 8 9) | (0 3 5 6 7 8 9) | (1 3 4 5 6 9) | (1 2 5 9) | (3 6 9) |
| (19 13 16 50 42) | (1 2 3) | (0 3) | (2 3 4) | (3 4) | (1 4) | | | | | | | | |
| (71 22 39 41 31 39 55) | (0 2) | (0 1 2 3 4) | (2 4) | (0 1 2 3 4 5) | (0 3 4 5 6) | (0 1 2 3 6) | (0 3 5 6) | (0 4 5 6) | | | | | |
| (147 46 37 53 31 26 46 109 31) | (1 2 3 5 6) | (0 3 6) | (0 7) | (0 1 2 3 4 6 8) | (0 1 3 4 5 6 8) | (0 1 2 3 4 5 8) | (1 4 8) | | | | | | |
| (11 11 10 6) | (0 2) | (1 2) | (0 1 3) | | | | | | | | | | |
| (49 39 214 216 34 83 235 89 223 64) | (2 3 5 6 7) | (3 5 7 8) | (2 3 6 8) | (0 2 3 4 5 6 7 8 9) | (1 2 3 5 6 7 8 9) | (0 1 2 4 5 6 7 9) | (0 1 5 6 7 8 9) | (6 7 9) | | | | | |
| (45 28 7 23 28 27 13 14 21) | (0 1 3 4 5) | (0 5 6) | (2 6) | (0 1 6 7) | (0 1 2 3 6 7 8) | (0 4 5 7 8) | (0 8) | (4 8) | | | | | |
| (54 28 43 21 41 57 26) | (0 2) | (0 1 3 5) | (1 2 4 5) | (0 3 5) | (2 5) | (0 2 4 5 6) | (0 1 4 6) | | | | | | |
| (38 18 3 17 18) | (0 2) | (0 3) | (0 1 4) | (1 2 4) | | | | | | | | | |
| (163 183 34 36) | (0 1) | (1 2 3) | (0 1 3) | (1 3) | (2 3) | | | | | | | | |
| (57 40 57 53 234 58 29 49 76 44) | (0 1 2) | (4) | (3 5) | (0 5 6) | (0 1 2 4 5 7 8) | (1 2 3 5 6 8) | (2 3 4 7 8) | (3 4 6 8) | (0 3 4 5 7 8 9) | (0 6 8 9) | (5 7 8 9) | (9) | |
| (38 25 29 19 26 40 9 31) | (0) | (2 3 5) | (3 4 5) | (0 1 2 3 4 6) | (0 5 6) | (1 6) | (0 1 2 4 5 7) | (2 4 6 7) | (3 5 7) | | | | |
| (9 1 27 8 1) | (2) | (0 2 3) | (0 1 4) | | | | | | | | | | |
| (48 17 224 48 26 16) | (0 1 2) | (2) | (0 3) | (3) | (0 1 2 4) | (0 2 3 4) | (0 2 3 4 5) | (1 3 5) | | | | | |
| (214 20 197 17) | (0 1 2) | (0 2) | (0 1 3) | | | | | | | | | | |
| (25 50 13 26 27) | (1 2) | (1 3) | (0 1 3 4) | (1 2 4) | (0 1 4) | | | | | | | | |
| (32 37 40 36 26 33 39 33 23) | (2 5) | (0 1 2 3 4 6 7) | (0 1 2 3 5 6 7) | (3 5 7) | (1 3 4 6 7 8) | (0 4 5 6 7 8) | (0 3 5 6 8) | (1 8) | | | | | |
| (21 23 1 24 8 28 35) | (3) | (0 1 2 3 4 5) | (1 4 5) | (0 3 5 6) | (1 6) | | | | | | | | |
| (92 58 43 92 54 73 46) | (0 1 2) | (0 1 2 3 4) | (0 1 3 4 5) | (0 2 3 5) | (0 3 5) | (2 3 4 5 6) | (1 3 4 5 6) | (0 3 4 6) | (0 3 5 6) | | | | |
| (27 14 36 69 36 40) | (0 1 3) | (2 3 4) | (4) | (0 2 3 5) | (1 3 5) | (3 5) | | | | | | | |
| (19 15 69 27) | (1 2) | (0 2) | (2) | (0 2 3) | (2 3) | | | | | | | | |
| (57 154 139 128 143 13) | (0 1 2) | (1 3) | (0 1 2 3 4) | (1 2 3 4) | (0 4) | (0 3 4 5) | (1 5) | | | | | | |
| (58 47 61 54 71 45 39 45) | (3 4) | (1 4 5) | (4 5) | (0 1 2 3 6) | (4 6) | (1 2 4 5 6 7) | (0 1 5 6 7) | (0 2 4 5 7) | (0 1 2 3 7) | | | | |
| (87 24 5 78 65 95 69 62 69 62) | (0 3) | (5 6) | (6) | (3 4 5 7) | (3 4 7) | (1 3 4 5 8) | (0 8) | (5 8) | (0 3 5 6 7 9) | (0 4 6 7 8 9) | (1 5 6 7 9) | (2 3 4 5 9) | (0 5 9) |
| (19 45 13 142 172 161 156) | (1 2 4) | (1 4 5) | (0 3 4 5 6) | (0 2 3 5 6) | (3 4 5 6) | (1 6) | | | | | | | |
| (9 4 17 133) | (1 2) | (0 2) | (2 3) | (3) | | | | | | | | | |
| (15 7 27 12 25 25) | (0 2 3) | (1 2 3) | (2 3 4 5) | (0 2 4 5) | (1 3 4 5) | (2 4 5) | | | | | | | |
| (39 45 71 73 97 91 65 68 71) | (0 4) | (3 5 6) | (1 2 3 4 5 6 7) | (7) | (0 1 2 3 4 5 6 8) | (2 3 4 5 6 7 8) | (0 1 2 4 5 8) | (0 1 2 3 4 8) | (0 2 4 7 8) | (4 5 7 8) | (8) | | |
| (6 35 41 16 13 35) | (1 2 4) | (0 2 3 5) | (1 2 4 5) | (1 2 3 5) | (1 2 5) | | | | | | | | |
| (50 59 51 46 50 33 28 49 71 68) | (6 7) | (0 2 3 4 5 6 8) | (1 4 8) | (0 2 3 4 5 7 8 9) | (1 2 4 6 7 8 9) | (1 3 4 5 6 7 9) | (0 1 2 5 8 9) | (0 1 3 7 8 9) | (2 3 4 5 9) | (0 1 2 8 9) | (7 9) | | |
| (46 19 31 32 25 32) | (0) | (1 3) | (0 1 2 3 4) | (1 2 3 4) | (3 4) | (3 4 5) | (0 2 5) | | | | | | |
| (12 24 7 17 36) | (1 3 4) | (2 3 4) | (1 2 4) | (0 4) | | | | | | | | | |
| (17 12 35 29 23 29) | (0 2 4) | (0 2 3 4 5) | (2 3 4 5) | (1 2 3 5) | | | | | | | | | |
| (42 210 196 207 47 232 92 48 233 227) | (4 6) | (0 6) | (0 1 2 4 5 6 8) | (0 3 4 5 6 8) | (1 3 6 7 8) | (0 1 2 4 5 6 8 9) | (0 2 4 5 7 8 9) | (1 2 3 5 8 9) | (1 3 5 7 8 9) | (1 3 5 6 9) | (2 5 6 8 9) | | |
| (177 139 153 37 38 62 49 56) | (0 1 2) | (1 2 3 4 5) | (1 2 3 4 5 6) | (0 1 2 4 5 6) | (0 2 5 6) | (2 4 6) | (0 1 2 3 4 5 7) | (0 3 6 7) | (0 5 7) | (7) | | | |
| (189 197 199 38 46 190 25) | (2) | (0 2 3 4) | (1 3 4) | (0 1 2 3 4 5) | (0 1 2 5) | (2 5) | (0 1 4 6) | (0 3 4 6) | (3 5 6) | | | | |
| (71 55 64 38 41 63 44) | (2) | (1 3 4) | (0 1 3 4 5) | (0 1 2 5) | (0 5) | (0 1 2 4 5 6) | (0 1 2 4 6) | (0 3 4 6) | (2 3 6) | | | | |
| (220 33 198 38 18 55 42) | (0 2) | (1 3 5) | (3 5) | (0 2 3 4 5 6) | (0 1 3 5 6) | (1 2 4 6) | (0 1 5 6) | (3 6) | | | | | |
| (71 27 201 51 60 53 41 39 56) | (2) | (3 4) | (0 1 3 4 5 6 7) | (0 1 3 5 6 7) | (0 2 3 4 7 8) | (0 4 5 6 8) | (1 4 6 8) | (0 2 5 8) | | | | | |
| (33 37 33 38 40 33 51 38 33) | (1 3) | (4) | (0 1 2 3 4 6) | (3 6) | (6 7) | (0 2 4 5 6 7 8) | (1 2 4 5 6 7 8) | (0 1 2 3 5 7 8) | (5 6 7 8) | | | | |
| (19 0 5 15 16 11) | (0 1 3) | (0 3 4) | (1 2 4) | (3 4) | (0 2 3 5) | (0 4 5) | | | | | | | |
| (35 0 13 59 30) | (2) | (0 3) | (3) | (0 3 4) | (2 3 4) | (1 2 4) | (4) | | | | | | |
| (20 15 5 20) | (0 1 3) | (0 2 3) | | | | | | | | | | | |
| (22 11 11 31) | (0 1 2) | (0 1 3) | (0 3) | (2 3) | | | | | | | | | |
| (11 1 11 1) | (0 2) | (1 3) | | | | | | | | | | | |
| (45 45 32 29 45 43 28 49 38 32) | (5 6) | (0 3 4 5 7) | (0 1 2 4 5 6 7 8) | (0 1 4 5 6 7 8) | (1 2 5 7 8) | (0 3 4 6 9) | (1 2 8 9) | (1 7 9) | | | | | |
| (8 9 6 23) | (2 3) | (1 3) | (0 3) | | | | | | | | | | |
| (242 110 78 295 305 83 116 282 116 76) | (0 3 4 7) | (1 4 6 7) | (0 6 7) | (1 2 3 4 5 6 7 8) | (0 1 2 3 5 6 7 8) | (1 2 3 4 5 6 8) | (0 1 3 4 6 7 8 9) | (0 2 3 4 6 7 8 9) | (1 3 4 5 6 7 8 9) | (0 1 2 3 4 5 7 9) | (1 2 3 4 6 8 9) | (1 4 5 7 8 9) | (0 4 5 8 9) |
| (5 5 0 23 23 5) | (0 2 4) | (3 4) | (0 1 3 4 5) | (1 2 5) | | | | | | | | | |
| (9 13 22 13) | (0 2) | (1 2 3) | | | | | | | | | | | |
| (51 29 19 41 52 29 38 34) | (0 2 3 4) | (4 5) | (1 3 4 5 6) | (3 6) | (0 1 2 5 6 7) | (0 1 5 6 7) | (0 4 7) | | | | | | |
| (181 23 187 183) | (1) | (0 1 2) | (1 2) | (0 2 3) | (1 3) | (0 3) | | | | | | | |
| (16 16 22 16 33) | (0 2 3) | (0 1 3) | (1 2 3) | (0 3) | (0 3 4) | (1 2 4) | (4) | | | | | | |
| (41 32 18 32 27 24 21) | (1 2 3) | (0 4) | (0 1 3 5) | (1 2 3 6) | (0 4 6) | (5 6) | | | | | | | |
| (42 195 42 45 188 221) | (0 1 2 3 5) | (0 2 3 4 5) | (2 3 4 5) | (0 1 5) | (1 4 5) | (0 3 5) | | | | | | | |
| (28 187 185 45 187 30 171 35) | (1) | (0 1 2) | (2 4) | (2 3 5) | (1 2 4 6) | (0 1 2 4 5 6 7) | (1 2 3 4 5 6 7) | (0 1 3 4 6 7) | (4 5 7) | | | | |
| (51 64 57 59 81 67 39 70 53 50) | (1 4) | (0 5 6 7) | (1 2 3 4 5 6 7 8) | (1 2 3 5 6 7 8) | (0 4 5 6 7 8) | (0 1 3 4 5 6 7 8 9) | (0 2 3 4 5 7 8 9) | (0 1 2 3 4 7 9) | (0 2 3 5 9) | (2 4 5 9) | (1 5 9) | | |
| (151 20 21 130 150) | (0 2) | (0 1 2 4) | (0 3 4) | | | | | | | | | | |
| (69 66 62 54 68 71 37 25 38) | (0 1 2 3) | (1 4) | (4) | (0 1 2 3 4 5) | (0 3 4 5) | (4 6) | (0 1 2 3 5 6 7 8) | (0 2 5 6 7 8) | (1 5 6 7 8) | (1 2 5 8) | | | |
| (36 33 40 13 50 20) | (0 3) | (0 1 2 4) | (2 4) | (1 4 5) | (0 2 5) | | | | | | | | |
| (18 210 210 14 10) | (1 2) | (0 1 2 3) | (1 2 3) | (0 4) | | | | | | | | | |
| (24 15 9 0) | (0 1) | (0 2) | (0 3) | | | | | | | | | | |
| (50 31 27 160 140 49 129 7 39 144) | (0 1 3 4 5 6) | (0 7) | (0 3 5 6 8) | (0 1 2 3 4 5 8 9) | (1 2 4 6 7 8 9) | (1 3 4 5 8 9) | (0 2 3 5 8 9) | (0 1 3 4 8 9) | (3 4 6 9) | | | | |
| (52 60 212 241 50 32 21 221 51 92) | (0 1 2 4 6 7) | (2 3 7) | (4 6 7 8) | (0 1 3 4 5 7 8 9) | (0 1 3 5 6 7 8 9) | (2 3 4 5 6 7 9) | (0 1 2 3 4 5 9) | (0 1 4 6 7 8 9) | (0 2 3 7 9) | (2 3 7 8 9) | (3 4 8 9) | (1 9) | |
| (2 26 26 17 19 24) | (1 3) | (0 1 2 4) | (1 2 3 4 5) | (1 2 5) | | | | | | | | | |
| (53 34 19 122 32 140 151 51 44) | (3 5 6) | (0 1 2 3 5 7) | (0 6 7) | (0 1 3 5 6 7 8) | (0 1 2 4 6 7 8) | (0 1 4 5 7 8) | (1 2 4 7 8) | (0 1 7 8) | (2 3 5 8) | (4 5 6 8) | (0 2 3 8) | | |
| (24 36 8 16 20) | (0 2) | (0 1 3) | (1 3) | (0 1 4) | (1 4) | | | | | | | | |
| (27 40 47 51 31 38) | (1 2 3) | (3 4) | (0 2 3 4 5) | (0 1 2 5) | (1 5) | | | | | | | | |
| (64 57 76 53 61 66 28 43 34 43) | (0 1 2 4 5 7) | (2 6 7) | (0 7) | (0 1 3 4 5 8) | (0 1 2 3 4 6 7 9) | (0 1 2 3 4 5 8 9) | (0 1 2 3 4 7 8 9) | (1 2 3 5 6 8 9) | (0 2 3 4 5 9) | | | | |
| (39 57 68 14 50 54 35 70) | (1 2 5) | (2 4 6) | (0 1 2 4 5 6 7) | (0 1 2 5 6 7) | (0 1 4 5 6 7) | (0 1 3 4 7) | (2 4 7) | (5 7) | | | | | |
| (19 21 20 27 32) | (0 1 3) | (1 2 3 4) | (2 3 4) | (0 4) | | | | | | | | | |
| (32 10 12 12 40 32 50 12) | (0 1 2 4 5) | (4 5 6) | (0 6) | (4 6) | (0 1 3 4 5 6 7) | (0 2 3 4 5 6 7) | | | | | | | |
| (225 75 226 54 241 203 20 182 39 208) | (0 1 4) | (1 2 3 4 5) | (0 1 3 8) | (0 1 2 4 6 7 8 9) | (2 3 4 5 6 8 9) | (1 2 3 4 6 8 9) | (0 2 4 5 7 9) | (0 1 2 4 9) | | | | | |
| (37 32 46 56 23 40 37 56) | (1 5) | (0 1 4 6) | (1 2 3 4 5 7) | (0 2 3 5 6 7) | (0 1 2 4 5 7) | (0 2 3 6 7) | (1 3 4 7) | | | | | | |
| (131 150 133 9 151) | (1 2 3) | (0 1 2 4) | (0 3 4) | (1 4) | (3 4) | | | | | | | | |
| (79 59 72 88 29 73 77 23 38) | (0 1 3 4) | (2 5) | (0 1 2 4 5 6) | (0 1 2 3 6) | (0 3 5 6) | (5 6) | (1 2 3 4 5 6 8) | (0 2 3 6 7 8) | (1 2 3 4 5 8) | (1 3 4 7 8) | (1 3 5 8) | | |
| (63 43 43 55 65 19 58 55) | (0 1 2 3 4) | (0 2 3 4 5 6) | (0 1 3 4 6) | (0 2 3 4 6 7) | (0 1 2 3 6 7) | (0 1 2 4 6 7) | (0 2 6 7) | (3 4 5 7) | | | | | |
| (195 190 16 21 13 7 201) | (1 2) | (0 3 5) | (0 3 6) | (0 1 6) | (4 6) | | | | | | | | |
| (30 11 29 17) | (0) | (0 2) | (1 2) | (3) | | | | | | | | | |
| (70 36 63 23 42 69 62 71 89) | (0 1 4) | (1 2 6 7) | (0 2 4 5 6 7 8) | (0 3 5 6 7 8) | (0 1 4 5 7 8) | (2 3 5 7 8) | (4 5 6 8) | (0 2 5 8) | (0 2 6 8) | (3 8) | (0 8) | | |
| (53 57 81 50 47 94 41 81) | (0 1 2 5) | (0 1 5) | (2 5) | (0 6) | (0 1 2 3 6 7) | (0 3 4 5 6 7) | (4 5 6 7) | (1 2 4 7) | (2 3 5 7) | (1 3 7) | | | |
| (33 35 28 31 54 29 7) | (0 2 4) | (0 1 4) | (3 4) | (1 2 3 4 5) | (0 2 3 4 5) | (0 1 2 4 5) | (0 3 4 5 6) | | | | | | |
| (72 32 62 50 29 71 30 45 60 75) | (0 2 3) | (0 1 2 5 7 8) | (0 1 3 7 8) | (6 8) | (0 1 2 3 4 5 7 9) | (0 1 3 4 6 7 8 9) | (0 1 2 3 5 7 9) | (2 4 5 6 8 9) | (1 2 3 5 8 9) | (2 4 6 8 9) | (0 3 5 8 9) | (0 5 7 9) | (2 8 9) |
| (256 29 36 227 204 38 231) | (0 1 2) | (0 2) | (0 1 3 4 5) | (0 1 3 5 6) | (0 3 4 6) | (0 3 5 6) | (0 5 6) | (2 6) | | | | | |
| (9 14 20 13) | (1) | (2) | (0 2 3) | (1 2 3) | (0 3) | (3) | | | | | | | |
| (38 64 31 27 44 41 68) | (1 4) | (0 1 2 4 5 6) | (0 1 2 3 6) | (0 4 5 6) | (1 4 5 6) | (1 3 6) | | | | | | | |
| (24 18 18 6) | (0) | (0 1 2) | (1 3) | (3) | | | | | | | | | |
| (52 36 15 52 56) | (0 1 2) | (0 2 3) | (0 1 3 4) | (0 3 4) | (1 3 4) | (0 4) | | | | | | | |
| (76 49 67 39 55 23 72 56 52) | (0) | (0 4) | (0 5) | (0 1 3 4 6 7) | (1 2 7) | (0 1 7) | (0 2 3 4 6 8) | (0 2 5 6 7 8) | (1 2 4 6 7 8) | (1 2 6 8) | | | |
| (58 35 48 49 51 71 49 49) | (0 1 3 4) | (0 1 2 3 5 6) | (0 4 5 6) | (2 3 6) | (1 2 3 4 7) | (0 2 3 5 7) | (0 4 5 7) | (5 7) | | | | | |
| (18 9 24 27 23 7) | (1 3) | (0 2 3 4) | (1 2 3 4 5) | (0 2 3 5) | | | | | | | | | |
| (21 55 74 70 51 64 49 26 53) | (0 2 3 5) | (0 1 3 6) | (2 4 6) | (1 2 3 4 5 6 7) | (0 1 3 5 6 7 8) | (1 2 3 4 5 6 8) | (1 3 4 5 7 8) | (0 2 3 5 7 8) | (1 2 3 5 8) | (0 3 5 8) | | | |
| (12 15 27 23 32 28) | (0 3) | (1 2 4) | (1 2 3 4 5) | (0 3 4 5) | (2 4 5) | | | | | | | | |
| (49 66 35 36 41 85 24 59 66 58) | (2) | (2 3 5) | (5 7) | (3 7 8) | (6 7 8) | (1 5 8) | (0 1 2 3 4 6 7 8 9) | (0 1 2 4 5 7 8 9) | (1 2 3 4 5 6 8 9) | (1 3 5 6 7 8 9) | (0 3 5 6 7 8 9) | (0 1 4 5 9) | |
| (32 36 28 28 46 32 41 45 30) | (4) | (1 4 5) | (2 3 4 6) | (0 2 3 6 7) | (0 1 2 3 6 7 8) | (1 5 7 8) | (0 6 7 8) | | | | | | |
| (143 136 128 21 145 109 42) | (1 2) | (0 1 2 4 5) | (2 4 5) | (0 1 3 4 6) | (0 3 4 6) | (0 4 6) | (0 6) | | | | | | |
| (30 29 30 165 131 61 11 13 24 71) | (3 4) | (3 4 5) | (0 2 3 5 6 8 9) | (0 2 4 5 7 8 9) | (0 2 3 4 5 9) | (3 5 7 8 9) | (1 3 9) | (1 5 9) | | | | | |
| (43 18 34 48 32 32 23) | (0 2 3 4 5) | (0 3 4 5) | (2 3 4 5 6) | (0 1 2 3 6) | (1 2 6) | | | | | | | | |
| (73 41 80 52 67 18 49 75 23 77) | (0 2 3 4 6 7) | (6 7) | (0 1 3 4 5 7 8) | (1 2 3 4 5 6 8 9) | (0 1 2 3 7 9) | (0 2 4 6 7 9) | (0 2 3 5 9) | (0 1 4 9) | (2 3 7 9) | (2 6 8 9) | (2 4 9) | | |
| (145 13 158 145 13) | (0 2) | (0 2 3) | (1 2 4) | | | | | | | | | | |
| (223 26 57 51 57 17 93 199 63 45) | (0 6) | (1 6) | (0 2 3 4 5 6 7) | (6 7) | (0 7) | (0 2 4 6 8) | (0 2 3 4 6 7 8 9) | (1 2 3 4 6 8 9) | (0 1 3 7 8 9) | (3 5 8 9) | | | |
| (41 41 43 68 46 46 61 65 69 29) | (1 6) | (0 1 7) | (3 4 7) | (2 3 4 5 6 7 8) | (0 2 3 6 7 8) | (2 3 4 5 8) | (3 5 8) | (0 1 2 3 4 7 8 9) | (1 2 3 4 7 8 9) | (0 3 5 6 8 9) | (0 3 4 6 8 9) | (1 2 4 6 8 9) | (5 6 8 9) |
| (48 83 75 50 66 48 89 93) | (0 2 5) | (3 4 5) | (2 3 6) | (4 6) | (1 2 4 5 6 7) | (0 1 2 3 6 7) | (1 3 4 6 7) | (2 4 5 6 7) | (0 1 6 7) | (1 4 7) | | | |
| (60 34 40 115 126 23 109) | (0) | (1 3) | (0 2 4) | (0 1 2 5) | (2 5) | (0 1 2 4 5 6) | (3 4 6) | | | | | | |
| (224 208 62 40 233 203 226 219) | (0 1 2 3 4) | (0 5) | (0 1 2 5 6) | (2 3 4 6) | (6) | (0 1 4 5 6 7) | (0 2 3 6 7) | (2 4 7) | (7) | | | | |
| (44 67 46 53 27 70 71 65 45 44) | (1 3 6) | (0 5 6) | (0 1 2 3 4 5 6 7) | (0 1 2 4 5 6 7) | (5 7) | (1 3 4 6 7 8) | (1 2 3 5 6 7 8 9) | (0 1 2 5 8 9) | (0 1 2 5 9) | (0 3 6 9) | | | |
| (157 16 30 30 64 29 43 43 47 49) | (0) | (4 6) | (1 2 3 4 7) | (0 1 2 3 4 6 7 8) | (0 2 3 5 8) | (0 2 4 7 8) | (1 3 4 5 6 7 9) | (4 5 6 7 8 9) | (2 3 4 6 8 9) | (3 4 5 6 8 9) | (0 2 4 6 9) | (0 9) | |
| (8 20 37 4) | (1) | (0 1 2) | (1 2) | (2) | (2 3) | (1 3) | | | | | | | |
| (60 71 64 56 11 87 91 44) | (0 2 4 5) | (0 1 2 3 5 6) | (1 2 3 5 6) | (0 1 2 6) | (1 2 3 5 6 7) | (1 3 5 6 7) | (0 5 6 7) | | | | | | |
| (27 82 67 61 47 74 82 63 69 56) | (1) | (5) | (0 4 5 7) | (1 5 6 7) | (1 2 3 4 5 6 7 8) | (0 1 2 4 6 7 8) | (1 2 3 6 8) | (1 2 5 6 7 8 9) | (2 3 4 6 7 9) | (1 2 3 4 7 9) | (1 4 5 6 8 9) | (0 3 9) | |
| (27 28 51 54 42 15 38 29 39 42) | (1 3 4 7) | (0 1 2 3 5 6 7 8) | (0 2 6 8) | (1 5 7 8) | (0 2 3 4 6 7 8 9) | (1 2 3 4 5 6 8 9) | (1 2 5 6 9) | (2 3 9) | (0 4 9) | | | | |
| (53 23 71 30 38 44 28 45) | (2 3 4) | (2 5) | (0 1 4 5 6) | (2 5 6) | (0 2 3 4 5 6 7) | (0 1 2 7) | (0 7) | | | | | | |
| (37 13 26 11 31 17 32 22) | (0 4) | (1 5) | (0 2 3 4 5 6) | (0 1 5 6) | (0 1 4 7) | (2 6 7) | | | | | | | |
| (33 28 29 36 32) | (1 2) | (1 2 3) | (0 3) | (1 2 3 4) | (2 3 4) | (0 4) | | | | | | | |
| (39 26 16 31 45 16 50 49) | (1 2 3 5 6) | (0 1 3 4 6 7) | (2 3 4 5 6 7) | (2 3 5 6 7) | (0 1 4 7) | (0 4 6 7) | | | | | | | |
| (42 60 31 44 73 44 49) | (0 2) | (0 2 3) | (0 1 2 3 4) | (0 2 4 5) | (5) | (0 1 3 4 6) | (1 3 4 5 6) | (1 4 6) | | | | | |
| (28 15 66 59 19) | (2) | (1 2 3) | (2 3) | (0 3) | (0 2 3 4) | (4) | | | | | | | |
| (19 24 44 39 33 18 56 44 30) | (2 5) | (1 2 4 5 6) | (2 6) | (3 6 7) | (3 7) | (0 7) | (1 2 4 8) | (0 8) | (4 8) | | | | |
| (22 32 28 28 24 36 14 17) | (0 1 3 5) | (2 5) | (2 4 6) | (0 1 2 4 5 6 7) | (1 2 3 4 5 7) | (0 2 3 5 6 7) | | | | | | | |
| (55 23 31 58 49 66 80 65 72) | (0 3) | (0 1 4 6 7) | (0 5 7) | (2 3 4 5 6 7 8) | (1 2 3 4 5 6 8) | (0 4 5 6 7 8) | (1 2 3 6 7 8) | (3 6 7 8) | (5 6 8) | (0 3 8) | | | |
| (29 33 4 16) | (0 1) | (1) | (1 2) | (0 1 3) | (0 3) | | | | | | | | |
| (30 78 105 170 48) | (0 1 2) | (0 1 3) | (1 3) | (2 3) | (1 3 4) | (0 3 4) | (1 4) | | | | | | |
| (31 81 67 81 83 40 55 17 29 78) | (1 2 3 4 5) | (1 3 4 5 6) | (1 3 4 6) | (2 6) | (0 1 2 3 4 6 8) | (0 1 2 3 5 7 8 9) | (1 2 3 4 5 7 8 9) | (0 1 2 3 4 6 9) | (0 1 2 3 5 8 9) | (2 4 9) | (1 3 9) | (4 9) | |
| (166 154 173 176 17 183 166) | (2 3) | (2 4) | (5) | (0 2 3 4 5 6) | (0 1 3 4 5 6) | (0 1 2 3 5 6) | | | | | | | |
| (33 181 19 39) | (0 1) | (1) | (2) | (0 2 3) | (2 3) | (3) | | | | | | | |
| (148 7 155 155) | (0 2 3) | (1 2 3) | | | | | | | | | | | |
| (138 146 47 31 160 41 32 24 54) | (0 1 4) | (0 1 2 3 4 5) | (1 5 7) | (3 4 7) | (0 1 4 5 6 8) | (0 2 3 5 8) | (2 4 6 8) | (4 5 7 8) | (1 2 6 8) | | | | |
This is the tricky part; we want solve the row-reduced form, but we
need to be careful with our choices if we have more than one
possibility
#+begin_src emacs-lisp
(defun find-possible-indices (matrix i)
(let* ((row (nth i matrix))
(next-row (nth (1+ i) matrix))
(i )
(j (if next-row (--find-index (not (= 0 it)) (cdr next-row))
(1- length row))))
(-iota (- j i) i)))
(defun solve-row-reduced (matrix)
;; we start from the last row
(let* ((soln (list (-repeat (1- (length (car matrix))) 0)))
(last-used-button (length (car soln)))
(current-row (1- (length matrix))))
(while (<= 0 current-row)
(let* ((row (nth current-row matrix))
(a (car row))
(i (--find-index (not (= 0 it)) (cdr row))))
(if i
(let ((possible-indices (--filter (not (= 0 (nth it (cdr row))))
(-iota (- last-used-button i) i))))
(if (= 1 (length possible-indices)) ;no choices here, easy
(setq soln (-non-nil (--map (let* ((correction (advent/dot it (-replace-at i 0 (cdr row))))
(corrected-a (- a correction))
(pushes (/ corrected-a (nth i (cdr row)))))
(unless (< pushes 0) (-replace-at i pushes it)))
soln))
last-used-button i
current-row (1- current-row))
;;otherwise, we create a number of solutions
(let* ((button (-last-item possible-indices)))
(setq soln (--mapcat (let* ((correction (advent/dot it (-replace-at i 0 (cdr row))))
(corrected-a (- a correction))
(max-soln (/ corrected-a (nth button (cdr row)))))
(if (< max-soln 0) (list it)
(-map (lambda (candidate) (-replace-at button candidate it)) (-iota (1+ (round max-soln))))))
soln)
last-used-button button))))
(setq current-row (1- current-row)))))
soln))
(defun minimal-pushes (machine)
(-min (-map #'-sum (solve-row-reduced (row-reduce (matrix-buttons machine))))))
(setq problematic (--first (not (solve-row-reduced (row-reduce (matrix-buttons it)))) machines))
(row-reduce (matrix-buttons problematic))
#+end_src
#+RESULTS:
| 7 | 1 | 1 | 0 | 1 | 0 | 0 |
| 5 | 0 | 1 | 0 | 0 | 0 | 1 |
| 4 | 0 | 0 | 1 | 1 | 1 | 0 |
| 3 | 0 | 0 | 0 | 0 | 1 | 1 |
| 51.0 | 1.0 | 1.0 | 1.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 |
| 31.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 |
| 43.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 |
| 10.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | -1.0 | 0.0 | 0.0 | 0.0 |
| 16.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 23.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 1.0 | -1.0 | 0.0 |
| 33.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 2.0 | 1.0 |
| 19.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 2.0 | -1.0 | 0.0 |
#+begin_src emacs-lisp
(defun solve-row-reduced (matrix)
;; we start from the last row
(let ((soln (-repeat (length (cdar matrix)) 0)))
(--each (-iota (length matrix) (- (length matrix) 1) -1)
(let* ((row (nth it matrix))
(a (car row))
(i (--find-index (not (= 0 it)) (cdr row))))
(when i
(setq correction (advent/dot soln (append (-repeat (1+ i) 0) (drop (1+ i) (cdr row))))
soln (-replace-at i (/ (- a correction) (nth i (cdr row))) soln)))))
soln))
(solve-row-reduced (row-reduce (matrix-buttons (caddr machines))))
;; now, this is correct, but we need a positive solution that has
;; fewest button presses possible.
@ -182,30 +396,28 @@ arst
(--map (advent/dot it vector) matrix))
(defun solution-p (machine candidate)
(--every (= 0 it) (matrix-appl (matrix-buttons machine) (cons -1 candidate)))
)
(setq current-machine nil)
(--every (= 0 it) (matrix-appl (matrix-buttons machine) (cons -1 candidate))))
(defun solve--machine (machine)
(setq current-machine machine)
(let ((candidate (solve-row-reduced (row-reduce (matrix-buttons machine)))))
(setq canca candidate)
(and (--every (>= it 0) candidate) (solution-p machine candidate) candidate)))
(and (--every (= (round it) it) candidate)
(--every (>= it 0) candidate)
(solution-p machine candidate) candidate)))
(defun solve-machine (machine)
(let* ((reduced-mat (row-reduce (matrix-buttons machine)))
(rank (rank reduced-mat))
(bunch (--map (cons (car machine) it)
(--filter 'identity
;(<= rank (length it))
(-powerset (cdr machine))))))
(-min (-map '-sum (-non-nil (-map 'solve--machine bunch))))
))
(-sum (-map 'solve-machine machines))
current-machine
(solve--machine machine)
canca
(--filter (= rank (length it))
(-powerset (cdr machine))))))
(-min (-map '-sum (-non-nil (-map 'solve--machine bunch))))))
(-sum (-map 'solve-machine machines))
#+end_src
#+RESULTS:
: 33
*
*

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