#+title: Solution to p10

#+begin_src emacs-lisp :results none
  (with-temp-buffer
    (insert-file-contents "input-test")
    (advent/replace-multiple-regex-buffer
     '(("," . " ")
       ("^" . "(")
       ("$" . ")")
       ("\\[" . "\"")
       ("\\]" . "\"")
       ("{" . "(")
       ("}" . ")")
       ))
    (goto-char (point-min))
    (insert "(setq data '(")
    (goto-char (point-max))
    (insert "))")
    (eval-buffer))
#+end_src
#+begin_src emacs-lisp :results none
  (defun zero-one (n)
    (if (eq n ?#) 1 0))

  (setq cleanedup-data (--map (cons (-map #'zero-one (advent/split-string-into-char-list (car it))) (cdr it)) data))
  #+end_src

for part 1 we do not need the last item
#+begin_src emacs-lisp
  (setq machines (--map (-drop-last 1 it) cleanedup-data))

  (defun to-bin (l)
    (-sum  (--map-indexed (* it (expt 2 it-index)) l)))

  (defun to-mask (l)
    (-sum (--map (expt 2 it) l)))

  (setq mask-machines (--map (cons (to-bin (car it)) (-map #'to-mask (cdr it))) machines))

  (-sum
   (-map (lambda (machine)
  	 (-min (-map 'length  (--filter (= (car machine) (apply 'logxor it))
  					(-powerset (cdr machine))))))
         mask-machines))
#+end_src

#+RESULTS:
: 7

This approach blows the stack even for the test input
#+begin_src emacs-lisp
  (setq machines (--map (-rotate 1 (cdr it)) data))

  (defun apply-button (joltage button)
    (--map-indexed (if (-contains-p button it-index) (- it 1) it) joltage))

  (defun good-buttons (machine)
    (-filter (lambda (button) (--every (< 0 (nth it (car machine))) button)) (cdr machine)))

  (defun solve-machines (machines)
    (-mapcat (lambda (machine)
  	     (if (= 0 (-sum (car machine))) (list machine)
  	       (--map (cons it (cdr machine)) (--map (apply-button (car machine) it) (good-buttons machine)))))
  	    machines ))

  (-iterate 'solve-machines (list (car machines)) 19)

#+end_src

Instead, go depth first and memoize for the win… except that
it does not work for the true input
#+begin_src emacs-lisp
  (setq machines (--map (-rotate 1 (cdr it)) data)
        machines (--map (cons (car it) (--sort (> (length it) (length other)) (cdr it))) machines))

  (defun apply-button (joltage button)
    (--map-indexed (if (-contains-p button it-index) (- it 1) it) joltage))

  (defun good-buttons (machine)
    (-filter (lambda (button) (--every (< 0 (nth it (car machine))) button)) (cdr machine)))

  (defun or-min (l)
    (when l (-min l)))

  (defun nil-1+ (l)
    (when l (1+ l)))

  (defun solve-machine (machine)
    (when machine
      (if (= 0 (-sum (car machine))) 0
        (nil-1+ (solve-machine (-first 'solve-machine (--map (cons it (cdr machine)) (--map (apply-button (car machine) it) (good-buttons machine)))))))))

  (memoize 'solve-machine)
  (-sum (-map 'solve-machine machines))
#+end_src

#+RESULTS:
: 33

So we need to stop being a brute and realize that this
is a linear algebra problem.  Gauss elimination to the rescue
#+begin_src emacs-lisp :results none
  (setq machines (--map (-rotate 1 (cdr it)) data)
        machines (--map (cons (car it) (--sort (> (length it) (length other)) (cdr it))) machines))
#+end_src

#+begin_src emacs-lisp
   ;; Now take a machine, create an "augmented" matrix to be reduced
   ;; Notice that the "augmentation" is the first column for
   ;;  reasons of making things more idiomatic

   (defun matrix-buttons (machine)
     (--map-indexed (cons it (--map (if (-contains-p it it-index) 1 0) (cdr machine))) (car machine)))

   (defun find-pivot (row index)
     (let ((p (--find-index (not (= it 0)) (-drop index row))))
       (when p (+ p index))))

   (defun swap-indices (i j list)
     (if (= i j) list
       (let ((el-i (nth i list))
             (el-j (nth j list)))
         (-replace-at j el-i (-replace-at i el-j list)))))

   (defun subtract-indices (λ i j list)
     "Subtracts λ× element i from element j"
     (let ((el-i (nth i list))
           (el-j (nth j list)))
       (-replace-at j (- el-j (* λ el-i)) list)))

   (defun subtract-composite (lambdas i list)
     (--each (-iota (length lambdas))
       (setq list (subtract-indices (nth it lambdas) i it list)))
     list)

   ;; Here we row-reduce; this is non-unique
   (defun row-reduce (matrix)
     (let* ((v (-map #'car matrix)) ;; vector
            (rM (-map #'cdr matrix)) ;; reduced matrix
            (rMt (apply '-zip-lists rM)) ;transpose
            (base 0))
       (--each (-iota (length rMt))
         (let ((pivot (find-pivot (nth it rMt) base)))
           (when pivot
             (setq rMt (-map (lambda (row)
                               (swap-indices base pivot row))
                             rMt)
                   v (swap-indices base pivot v))
             ;; hopefully we never have to divide
             ;; now we have to clean the other bits
                                           ;          (fwq)
             ;; this is the pivot
             (let* ((pivot-coeff (nth base (nth it rMt)))
                    (lambdas (append (-repeat (1+ base) 0) (-drop (1+ base) (nth it rMt))))
                    (lambdas-corrected (--map (/ it (* 1 pivot-coeff)) lambdas)))
               (setq rMt (--map (subtract-composite lambdas-corrected base it) rMt)
                     v (subtract-composite lambdas-corrected base v)))
             (setq base (1+ base)))))
       (apply '-zip-lists (cons v rMt))))

   (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.

   (defun unshadowed-buttons (matrix)
     (let ((result))
       (--each (-iota (length matrix) (- (length matrix) 1) -1)
         (let* ((row (nth it matrix))
                (i (--find-index (not (= 0 it)) (cdr row))))
           (when i (push i result))))
       result))

   (defun shadowed-buttons (matrix)
     (-difference (-iota (length (cdar matrix))) (unshadowed-buttons matrix)))

   (defun shadowed-button-solution (i matrix)
     (solve-row-reduced (let ((transpose (apply '-zip-lists matrix)))
        (apply '-zip-lists (cons (nth (1+ i) transpose) (cdr transpose))))))

   (defun solve-machine (machine)
     (let* ((reduced-mat (row-reduce (matrix-buttons machine)))
            (candidate (solve-row-reduced reduced-mat)))
       (if (--every (<= 0 it) candidate) candidate
         (let ((shadowed (shadowed-buttons reduced-mat)))
           ;; try replacing the shadowed button with the previous one
           (solve-machine
            (swap-indices (car shadowed) (1+ (car shadowed))  machine))))))

  (defun vector- (v1 v2)
    (--map (- (car it) (cdr it)) (-zip-pair v1 v2)))

  (defun push-button (i machine-matrix)
    (let ((tr (apply '-zip-lists machine)))
      (apply '-zip-lists (cons (vector- (car tr) (nth (1+ i) tr)) (cdr tr)))))

  (defun machine-valid-p (machine)
    (arst)
    (--every (>= it 0) (-map #'car machine)))

   (defun solve-machine (machine)
     (let* ((reduced-mat (row-reduce (matrix-buttons machine)))
            (shadowed (shadowed-buttons reduced-mat))
            (max-iter (-max (car machine))))
       ;; we create a bunch of machines pushing the shadowed buttons a number of times.
       max-iter
       ))

  (push-button 0 (car machines))

  (car machines)
  (-map 'solve-machine machines)
#+end_src

#+RESULTS:
| 5 | 1 |  3 | 0 | 1 | 0 |
| 2 | 0 |  5 | 5 | 0 |   |
| 6 | 5 | -1 | 0 |   |   |