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;;; 5x5.el --- simple little puzzle game -*- lexical-binding: t -*-
;; Copyright (C) 1999-2024 Free Software Foundation, Inc.
;; Author: Dave Pearson <davep@davep.org>
;; Created: 1998-10-03
;; Keywords: games puzzles
;; This file is part of GNU Emacs.
;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
;;; Commentary:
;; The aim of 5x5 is to fill in all the squares. If you need any more of an
;; explanation you probably shouldn't play the game.
;;; TODO:
;; o The code for updating the grid needs to be re-done. At the moment it
;; simply re-draws the grid every time a move is made.
;;
;; o Look into improving the display with color. gamegrid.el looks
;; interesting, perhaps that is the way to go?
;;; Thanks:
;; Ralf Fassel <ralf@akutech.de> for his help and introduction to writing an
;; emacs mode.
;;
;; Pascal Q. Porcupine <joshagam@cs.nmsu.edu> for inspiring the animated
;; cracker.
;;
;; Vincent Belaïche <vincentb1@users.sourceforge.net> & Jay P. Belanger
;; <jay.p.belanger@gmail.com> for the math solver.
;;; Code:
(eval-when-compile (require 'cl-lib))
;; Customize options.
(defgroup 5x5 nil
"5x5 - Silly little puzzle game."
:group 'games
:prefix "5x5-")
(defcustom 5x5-grid-size 5
"Size of the playing area."
:type 'integer)
(defcustom 5x5-x-scale 4
"X scaling factor for drawing the grid."
:type 'integer)
(defcustom 5x5-y-scale 3
"Y scaling factor for drawing the grid."
:type 'integer)
(defcustom 5x5-animate-delay .01
"Delay in seconds when animating a solution crack."
:type 'number)
(defcustom 5x5-hassle-me t
"Should 5x5 ask you when you want to do a destructive operation?"
:type 'boolean)
(defcustom 5x5-mode-hook nil
"Hook run on starting 5x5."
:type 'hook)
;; Non-customize variables.
(defvar-local 5x5-grid nil
"5x5 grid contents.")
(defvar-local 5x5-x-pos 2
"X position of cursor.")
(defvar-local 5x5-y-pos 2
"Y position of cursor.")
(defvar-local 5x5-moves 0
"Moves made.")
(defvar-local 5x5-cracking nil
"Are we in cracking mode?")
(defvar 5x5-buffer-name "*5x5*"
"Name of the 5x5 play buffer.")
(defvar-keymap 5x5-mode-map
:doc "Local keymap for the 5x5 game."
:suppress 'nodigits
"?" #'describe-mode
"RET" #'5x5-flip-current
"SPC" #'5x5-flip-current
"<up>" #'5x5-up
"<down>" #'5x5-down
"<left>" #'5x5-left
"<tab>" #'5x5-right
"<right>" #'5x5-right
"C-a" #'5x5-bol
"C-e" #'5x5-eol
"C-p" #'5x5-up
"C-n" #'5x5-down
"C-b" #'5x5-left
"C-f" #'5x5-right
"<home>" #'5x5-bol
"<end>" #'5x5-eol
"<prior>" #'5x5-first
"<next>" #'5x5-last
"r" #'5x5-randomize
"C-c C-r" #'5x5-crack-randomly
"C-c C-c" #'5x5-crack-mutating-current
"C-c C-b" #'5x5-crack-mutating-best
"C-c C-x" #'5x5-crack-xor-mutate
"n" #'5x5-new-game
"s" #'5x5-solve-suggest
"<" #'5x5-solve-rotate-left
">" #'5x5-solve-rotate-right
"q" #'5x5-quit-game)
(defvar-local 5x5-solver-output nil
"List that is the output of an arithmetic solver.
This list L is such that
L = (M S_1 S_2 ... S_N)
M is the move count when the solve output was stored.
S_1 ... S_N are all the solutions ordered from least to greatest
number of strokes. S_1 is the solution to be displayed.
Each solution S_1, ..., S_N is a list (STROKE-COUNT GRID) where
STROKE-COUNT is the number of strokes to achieve the solution and
GRID is the grid of positions to click.")
;; Menu definition.
(easy-menu-define 5x5-mode-menu 5x5-mode-map "5x5 menu."
'("5x5"
["New game" 5x5-new-game t]
["Random game" 5x5-randomize t]
["Quit game" 5x5-quit-game t]
"---"
["Use Calc solver" 5x5-solve-suggest t]
["Rotate left list of Calc solutions" 5x5-solve-rotate-left t]
["Rotate right list of Calc solutions" 5x5-solve-rotate-right t]
"---"
["Crack randomly" 5x5-crack-randomly t]
["Crack mutating current" 5x5-crack-mutating-current t]
["Crack mutating best" 5x5-crack-mutating-best t]
["Crack with xor mutate" 5x5-crack-xor-mutate t]))
;; Gameplay functions.
(define-derived-mode 5x5-mode special-mode "5x5"
"A mode for playing `5x5'."
:interactive nil
(setq buffer-read-only t
truncate-lines t)
(buffer-disable-undo))
;;;###autoload
(defun 5x5 (&optional size)
"Play 5x5.
The object of 5x5 is very simple, by moving around the grid and flipping
squares you must fill the grid.
5x5 keyboard bindings are:
\\<5x5-mode-map>
Flip \\[5x5-flip-current]
Move up \\[5x5-up]
Move down \\[5x5-down]
Move left \\[5x5-left]
Move right \\[5x5-right]
Start new game \\[5x5-new-game]
New game with random grid \\[5x5-randomize]
Random cracker \\[5x5-crack-randomly]
Mutate current cracker \\[5x5-crack-mutating-current]
Mutate best cracker \\[5x5-crack-mutating-best]
Mutate xor cracker \\[5x5-crack-xor-mutate]
Solve with Calc \\[5x5-solve-suggest]
Rotate left Calc Solutions \\[5x5-solve-rotate-left]
Rotate right Calc Solutions \\[5x5-solve-rotate-right]
Quit current game \\[5x5-quit-game]"
(interactive "P")
(setq 5x5-cracking nil)
(switch-to-buffer 5x5-buffer-name)
(5x5-mode)
(when (natnump size)
(setq 5x5-grid-size size))
(if (or (not 5x5-grid) (not (= 5x5-grid-size (length (aref 5x5-grid 0)))))
(5x5-new-game))
(5x5-draw-grid (list 5x5-grid))
(5x5-position-cursor))
(defun 5x5-new-game ()
"Start a new game of `5x5'."
(interactive nil 5x5-mode)
(when (if (called-interactively-p 'interactive)
(5x5-y-or-n-p "Start a new game? ") t)
(setq 5x5-x-pos (/ 5x5-grid-size 2)
5x5-y-pos (/ 5x5-grid-size 2)
5x5-moves 0
5x5-grid (5x5-make-move (5x5-make-new-grid) 5x5-y-pos 5x5-x-pos)
5x5-solver-output nil)
(5x5-draw-grid (list 5x5-grid))
(5x5-position-cursor)))
(defun 5x5-quit-game ()
"Quit the current game of `5x5'."
(interactive nil 5x5-mode)
(kill-buffer 5x5-buffer-name))
(defun 5x5-make-new-grid ()
"Create and return a new `5x5' grid structure."
(let ((grid (make-vector 5x5-grid-size nil)))
(dotimes (y 5x5-grid-size)
(aset grid y (make-vector 5x5-grid-size nil)))
grid))
(defun 5x5-cell (grid y x)
"Return the value of the cell in GRID at location X,Y."
(aref (aref grid y) x))
(defun 5x5-set-cell (grid y x value)
"Set the value of cell X,Y in GRID to VALUE."
(aset (aref grid y) x value))
(defun 5x5-flip-cell (grid y x)
"Flip the value of cell X,Y in GRID."
(5x5-set-cell grid y x (not (5x5-cell grid y x))))
(defun 5x5-copy-grid (grid)
"Make a new copy of GRID."
(let ((copy (5x5-make-new-grid)))
(dotimes (y 5x5-grid-size)
(dotimes (x 5x5-grid-size)
(5x5-set-cell copy y x (5x5-cell grid y x))))
copy))
(defun 5x5-make-move (grid row col)
"Make a move on GRID at row ROW and column COL."
(5x5-flip-cell grid row col)
(if (> row 0)
(5x5-flip-cell grid (1- row) col))
(if (< row (- 5x5-grid-size 1))
(5x5-flip-cell grid (1+ row) col))
(if (> col 0)
(5x5-flip-cell grid row (1- col)))
(if (< col (- 5x5-grid-size 1))
(5x5-flip-cell grid row (1+ col)))
grid)
(defun 5x5-row-value (row)
"Get the \"on-value\" for grid row ROW."
(cl-loop for y from 0 to (1- 5x5-grid-size) sum (if (aref row y) 1 0)))
(defun 5x5-grid-value (grid)
"Get the \"on-value\" for grid GRID."
(cl-loop for y from 0 to (1- 5x5-grid-size)
sum (5x5-row-value (aref grid y))))
(defun 5x5-draw-grid-end ()
"Draw the top/bottom of the grid."
(insert "+")
(dotimes (_ 5x5-grid-size)
(insert "-" (make-string 5x5-x-scale ?-)))
(insert "-+ "))
(defun 5x5-draw-grid (grids)
"Draw the grids GRIDS into the current buffer."
(let ((inhibit-read-only t) grid-org)
(erase-buffer)
(dolist (_ grids) (5x5-draw-grid-end))
(insert "\n")
(setq grid-org (point))
(dotimes (y 5x5-grid-size)
(dotimes (_lines 5x5-y-scale)
(dolist (grid grids)
(dotimes (x 5x5-grid-size)
(insert (if (zerop x) "| " " ")
(make-string 5x5-x-scale
(if (5x5-cell grid y x) ?# ?.))))
(insert " | "))
(insert "\n")))
(when 5x5-solver-output
(if (= (car 5x5-solver-output) 5x5-moves)
(save-excursion
(goto-char grid-org)
(beginning-of-line (+ 1 (/ 5x5-y-scale 2)))
(let ((solution-grid (cdadr 5x5-solver-output)))
(dotimes (y 5x5-grid-size)
(save-excursion
(forward-char (+ 1 (/ (1+ 5x5-x-scale) 2)))
(dotimes (x 5x5-grid-size)
(when (5x5-cell solution-grid y x)
(if (= 0 (mod 5x5-x-scale 2))
(progn
(insert "()")
(delete-region (point) (+ (point) 2))
(backward-char 2))
(insert-char ?O 1)
(delete-char 1)
(backward-char)))
(forward-char (1+ 5x5-x-scale))))
(forward-line 5x5-y-scale))))
(setq 5x5-solver-output nil)))
(dolist (_grid grids) (5x5-draw-grid-end))
(insert "\n")
(insert (format "On: %d Moves: %d" (5x5-grid-value (car grids)) 5x5-moves))))
(defun 5x5-position-cursor ()
"Position the cursor on the grid."
(goto-char (point-min))
(forward-line (1+ (* 5x5-y-pos 5x5-y-scale)))
(goto-char (+ (point) (* 5x5-x-pos 5x5-x-scale) (+ 5x5-x-pos 1) 1)))
(defun 5x5-made-move ()
"Keep track of how many moves have been made."
(cl-incf 5x5-moves))
(defun 5x5-make-random-grid (&optional move)
"Make a random grid."
(setq move (or move (symbol-function '5x5-flip-cell)))
(let ((grid (5x5-make-new-grid)))
(dotimes (y 5x5-grid-size)
(dotimes (x 5x5-grid-size)
(if (zerop (random 2))
(funcall move grid y x))))
grid))
;; Cracker functions.
;;;###autoload
(defun 5x5-crack-randomly ()
"Attempt to crack 5x5 using random solutions."
(interactive)
(5x5-crack #'5x5-make-random-solution))
;;;###autoload
(defun 5x5-crack-mutating-current ()
"Attempt to crack 5x5 by mutating the current solution."
(interactive)
(5x5-crack #'5x5-make-mutate-current))
;;;###autoload
(defun 5x5-crack-mutating-best ()
"Attempt to crack 5x5 by mutating the best solution."
(interactive)
(5x5-crack #'5x5-make-mutate-best))
;;;###autoload
(defun 5x5-crack-xor-mutate ()
"Attempt to crack 5x5 by xoring the current and best solution.
Mutate the result."
(interactive)
(5x5-crack #'5x5-make-xor-with-mutation))
;;;###autoload
(defun 5x5-crack (breeder)
"Attempt to find a solution for 5x5.
`5x5-crack' takes the argument BREEDER which should be a function that takes
two parameters, the first will be a grid vector array that is the current
solution and the second will be the best solution so far. The function
should return a grid vector array that is the new solution."
(interactive "aBreeder function: ")
(5x5)
(setq 5x5-cracking t)
(let* ((best-solution (5x5-make-random-grid))
(current-solution best-solution)
(best-result (5x5-make-new-grid))
(current-result (5x5-make-new-grid))
(target (* 5x5-grid-size 5x5-grid-size)))
(while (and (< (5x5-grid-value best-result) target)
(not (input-pending-p)))
(setq current-result (5x5-play-solution current-solution best-solution))
(if (> (5x5-grid-value current-result) (5x5-grid-value best-result))
(setq best-solution current-solution
best-result current-result))
(setq current-solution (funcall breeder
(5x5-copy-grid current-solution)
(5x5-copy-grid best-solution)))))
(setq 5x5-cracking nil))
(defun 5x5-make-random-solution (&rest _ignore)
"Make a random solution."
(5x5-make-random-grid))
(defun 5x5-make-mutate-current (current _best)
"Mutate the current solution."
(5x5-mutate-solution current))
(defun 5x5-make-mutate-best (_current best)
"Mutate the best solution."
(5x5-mutate-solution best))
(defun 5x5-make-xor-with-mutation (current best)
"Xor current and best solution then mutate the result."
(let ((xored (5x5-make-new-grid)))
(dotimes (y 5x5-grid-size)
(dotimes (x 5x5-grid-size)
(5x5-set-cell xored y x
(xor (5x5-cell current y x)
(5x5-cell best y x)))))
(5x5-mutate-solution xored)))
(defun 5x5-mutate-solution (solution)
"Randomly flip bits in the solution."
(dotimes (y 5x5-grid-size)
(dotimes (x 5x5-grid-size)
(if (= (random (/ (* 5x5-grid-size 5x5-grid-size) 2))
(/ (/ (* 5x5-grid-size 5x5-grid-size) 2) 2))
(5x5-flip-cell solution y x))))
solution)
(defun 5x5-play-solution (solution best)
"Play a solution on an empty grid.
This destroys the current game in progress because it is an
animated attempt."
(5x5-new-game)
(let ((inhibit-quit t))
(dotimes (y 5x5-grid-size)
(dotimes (x 5x5-grid-size)
(setq 5x5-y-pos y
5x5-x-pos x)
(if (5x5-cell solution y x)
(5x5-flip-current))
(5x5-draw-grid (list 5x5-grid solution best))
(5x5-position-cursor)
(sit-for 5x5-animate-delay))))
5x5-grid)
;; Arithmetic solver
;;===========================================================================
(defun 5x5-grid-to-vec (grid)
"Convert GRID to an equivalent Calc matrix of (mod X 2) forms
where X is 1 for setting a position, and 0 for unsetting a
position."
(cons 'vec
(mapcar (lambda (y)
(cons 'vec
(mapcar (lambda (x)
(if x '(mod 1 2) '(mod 0 2)))
y)))
grid)))
(defun 5x5-vec-to-grid (grid-matrix)
"Convert a grid matrix GRID-MATRIX in Calc format to a grid in 5x5 format.
See function `5x5-grid-to-vec'."
(apply
#'vector
(mapcar
(lambda (x)
(apply
#'vector
(mapcar
(lambda (y) (/= (cadr y) 0))
(cdr x))))
(cdr grid-matrix))))
(eval-and-compile
(if nil; set to t to enable solver logging
;; Note these logging facilities were not cleaned out as the arithmetic
;; solver is not yet complete --- it works only for grid size = 5.
;; So they may be useful again to design a more generic solution.
(progn
(defvar 5x5-log-buffer nil)
(defun 5x5-log-init ()
(if (buffer-live-p 5x5-log-buffer)
(with-current-buffer 5x5-log-buffer (erase-buffer))
(setq 5x5-log-buffer (get-buffer-create "*5x5 LOG*"))))
(defun 5x5-log (name value)
"Debug purposes only.
Log a matrix VALUE of (mod B 2) forms, only B is output and
Scilab matrix notation is used. VALUE is returned so that it is
easy to log a value with minimal rewrite of code."
(when (buffer-live-p 5x5-log-buffer)
(defvar calc-matrix-brackets)
(defvar calc-vector-commas)
(let* ((unpacked-value
(math-map-vec
(lambda (row) (math-map-vec 'cadr row))
value))
(calc-vector-commas "")
(calc-matrix-brackets '(C O))
(value-to-log (math-format-value unpacked-value)))
(with-current-buffer 5x5-log-buffer
(insert name ?= value-to-log ?\n))))
value))
(defsubst 5x5-log-init ())
(defsubst 5x5-log (_name value) value)))
(declare-function math-map-vec "calc-vec" (f a))
(declare-function math-sub "calc" (a b))
(declare-function math-mul "calc" (a b))
(declare-function math-make-intv "calc-forms" (mask lo hi))
(declare-function math-reduce-vec "calc-vec" (a b))
(declare-function math-format-number "calc" (a &optional prec))
(declare-function math-pow "calc-misc" (a b))
(declare-function calcFunc-arrange "calc-vec" (vec cols))
(declare-function calcFunc-cvec "calc-vec" (obj &rest dims))
(declare-function calcFunc-diag "calc-vec" (a &optional n))
(declare-function calcFunc-trn "calc-vec" (mat))
(declare-function calcFunc-inv "calc-misc" (m))
(declare-function calcFunc-mrow "calc-vec" (mat n))
(declare-function calcFunc-mcol "calc-vec" (mat n))
(declare-function calcFunc-vconcat "calc-vec" (a b))
(declare-function calcFunc-index "calc-vec" (n &optional start incr))
(defvar calc-word-size)
(defvar calc-leading-zeros)
(defvar calc-number-radix)
(defvar calc-command-flags)
(defun 5x5-solver (grid)
"Return a list of solutions for GRID.
Given some grid GRID, the returned a list of solution LIST is
sorted from least Hamming weight to greatest one.
LIST = (SOLUTION-1 ... SOLUTION-N)
Each solution SOLUTION-I is a cons cell (HW . G) where HW is the
Hamming weight of the solution --- ie the number of strokes to
achieve it --- and G is the grid of positions to click in order
to complete the 5x5.
Solutions are sorted from least to greatest Hamming weight."
(require 'calc-ext)
(cl-flet ((5x5-mat-mode-2
(a)
(math-map-vec
(lambda (y)
(math-map-vec
(lambda (x) `(mod ,x 2))
y))
a)))
(let* (calc-command-flags
(grid-size-squared (* 5x5-grid-size 5x5-grid-size))
;; targetv is the vector the origin of which is org="current
;; grid" and the end of which is dest="all ones".
(targetv
(5x5-log
"b"
(let (
;; org point is the current grid
(org (calcFunc-arrange (5x5-grid-to-vec grid)
1))
;; end point of game is the all ones matrix
(dest (calcFunc-cvec '(mod 1 2) grid-size-squared 1)))
(math-sub dest org))))
;; transferm is the transfer matrix, ie it is the 25x25
;; matrix applied every time a flip is carried out where a
;; flip is defined by a 25x1 Dirac vector --- ie all zeros
;; but 1 in the position that is flipped.
(transferm
(5x5-log
"a"
;; transfer-grid is not a play grid, but this is the
;; transfer matrix in the format of a vector of vectors, we
;; do it this way because random access in vectors is
;; faster. The motivation is just speed as we build it
;; element by element, but that could have been created
;; using only Calc primitives. Probably that would be a
;; better idea to use Calc with some vector manipulation
;; rather than going this way...
(5x5-grid-to-vec (let ((transfer-grid
(let ((5x5-grid-size grid-size-squared))
(5x5-make-new-grid))))
(dotimes (i 5x5-grid-size)
(dotimes (j 5x5-grid-size)
;; k0 = flattened flip position corresponding
;; to (i, j) on the grid.
(let* ((k0 (+ (* 5 i) j)))
;; cross center
(5x5-set-cell transfer-grid k0 k0 t)
;; Cross top.
(and
(> i 0)
(5x5-set-cell transfer-grid
(- k0 5x5-grid-size) k0 t))
;; Cross bottom.
(and
(< (1+ i) 5x5-grid-size)
(5x5-set-cell transfer-grid
(+ k0 5x5-grid-size) k0 t))
;; Cross left.
(and
(> j 0)
(5x5-set-cell transfer-grid (1- k0) k0 t))
;; Cross right.
(and
(< (1+ j) 5x5-grid-size)
(5x5-set-cell transfer-grid
(1+ k0) k0 t)))))
transfer-grid))))
;; TODO: this is hard-coded for grid-size = 5, make it generic.
(transferm-kernel-size
(if (= 5x5-grid-size 5) 2
(error "Transfer matrix rank not known for grid-size != 5")))
;; TODO: this is hard-coded for grid-size = 5, make it generic.
;;
;; base-change is a 25x25 matrix, where topleft submatrix
;; 23x25 is a diagonal of 1, and the two last columns are a
;; base of kernel of transferm.
;;
;; base-change must be by construction invertible.
(base-change
(5x5-log
"p"
(let ((id (5x5-mat-mode-2 (calcFunc-diag 1 grid-size-squared))))
(setcdr (last id (1+ transferm-kernel-size))
(cdr (5x5-mat-mode-2
'(vec (vec 0 1 1 1 0 1 0 1 0 1 1 1 0 1
1 1 0 1 0 1 0 1 1 1 0)
(vec 1 1 0 1 1 0 0 0 0 0 1 1 0 1
1 0 0 0 0 0 1 1 0 1 1)))))
(calcFunc-trn id))))
(inv-base-change
(5x5-log "invp"
(calcFunc-inv base-change)))
;; B:= targetv
;; A:= transferm
;; P:= base-change
;; P^-1 := inv-base-change
;; X := solution
;; B = A * X
;; P^-1 * B = P^-1 * A * P * P^-1 * X
;; CX = P^-1 * X
;; CA = P^-1 * A * P
;; CB = P^-1 * B
;; CB = CA * CX
;; CX = CA^-1 * CB
;; X = P * CX
(ctransferm
(5x5-log
"ca"
(math-mul
inv-base-change
(math-mul transferm base-change)))); CA
(ctarget
(5x5-log
"cb"
(math-mul inv-base-change targetv))); CB
;; (row-1 (math-make-intv 3 1 transferm-kernel-size)) ; 1..2
(row-2 (math-make-intv 1 transferm-kernel-size
grid-size-squared)); 3..25
(col-1 (math-make-intv 3 1 (- grid-size-squared
transferm-kernel-size))); 1..23
;; (col-2 (math-make-intv 1 (- grid-size-squared
;; transferm-kernel-size)
;; grid-size-squared)) ; 24..25
;; (ctransferm-1-: (calcFunc-mrow ctransferm row-1))
;; (ctransferm-1-1 (calcFunc-mcol ctransferm-1-: col-1))
;; By construction ctransferm-:-2 = 0, so ctransferm-1-2 = 0
;; and ctransferm-2-2 = 0.
;;(ctransferm-1-2 (calcFunc-mcol ctransferm-1-: col-2))
(ctransferm-2-: (calcFunc-mrow ctransferm row-2))
(ctransferm-2-1
(5x5-log
"ca_2_1"
(calcFunc-mcol ctransferm-2-: col-1)))
;; By construction ctransferm-2-2 = 0.
;;
;;(ctransferm-2-2 (calcFunc-mcol ctransferm-2-: col-2))
;; (ctarget-1 (calcFunc-mrow ctarget row-1))
(ctarget-2 (calcFunc-mrow ctarget row-2))
;; ctarget-1(2x1) = ctransferm-1-1(2x23) *cx-1(23x1)
;; + ctransferm-1-2(2x2) *cx-2(2x1);
;; ctarget-2(23x1) = ctransferm-2-1(23x23)*cx-1(23x1)
;; + ctransferm-2-2(23x2)*cx-2(2x1);
;; By construction:
;;
;; ctransferm-1-2 == zeros(2,2) and ctransferm-2-2 == zeros(23,2)
;;
;; So:
;;
;; ctarget-2 = ctransferm-2-1*cx-1
;;
;; So:
;;
;; cx-1 = inv-ctransferm-2-1 * ctarget-2
(cx-1 (math-mul (calcFunc-inv ctransferm-2-1) ctarget-2))
;; Any cx-2 can do, so there are 2^{transferm-kernel-size} solutions.
(solution-list
;; Within solution-list each element is a cons cell:
;;
;; (HW . SOL)
;;
;; where HW is the Hamming weight of solution, and SOL is
;; the solution in the form of a grid.
(sort
(cdr
(math-map-vec
(lambda (cx-2)
;; Compute `solution' in the form of a 25x1 matrix of
;; (mod B 2) forms --- with B = 0 or 1 --- and
;; return (HW . SOL) where HW is the Hamming weight
;; of solution and SOL a grid.
(let ((solution (math-mul
base-change
(calcFunc-vconcat cx-1 cx-2)))); X = P * CX
(cons
;; The Hamming Weight is computed by matrix reduction
;; with an ad-hoc operator.
(math-reduce-vec
;; (cadadr '(vec (mod x 2))) => x
(lambda (r x) (+ (if (integerp r) r (cadadr r))
(cadadr x)))
solution); car
(5x5-vec-to-grid
(calcFunc-arrange solution 5x5-grid-size));cdr
)))
;; A (2^K) x K matrix, where K is the dimension of kernel
;; of transfer matrix --- i.e. K=2 in if the grid is 5x5
;; --- for I from 0 to K-1, each row rI correspond to the
;; binary representation of number I, that is to say row
;; rI is a 1xK vector:
;; [ n{I,0} n{I,1} ... n{I,K-1} ]
;; such that:
;; I = sum for J=0..K-1 of 2^(n{I,J})
(let ((calc-number-radix 2)
(calc-leading-zeros t)
(calc-word-size transferm-kernel-size))
(math-map-vec
(lambda (x)
(cons 'vec
(mapcar (lambda (x) `(vec (mod ,(logand x 1) 2)))
(substring (math-format-number x)
(- transferm-kernel-size)))))
(calcFunc-index (math-pow 2 transferm-kernel-size) 0))) ))
;; Sort solutions according to respective Hamming weight.
(lambda (x y) (< (car x) (car y)))
)))
(message "5x5 Solution computation done.")
solution-list)))
(defun 5x5-solve-suggest (&optional _n)
"Suggest to the user where to click.
Argument N is ignored."
;; For the time being n is ignored, the idea was to use some numeric
;; argument to show a limited amount of positions.
(interactive "P" 5x5-mode)
(5x5-log-init)
(let ((solutions (5x5-solver 5x5-grid)))
(setq 5x5-solver-output
(cons 5x5-moves solutions)))
(5x5-draw-grid (list 5x5-grid))
(5x5-position-cursor))
(defun 5x5-solve-rotate-left (&optional n)
"Rotate left by N the list of solutions in 5x5-solver-output.
If N is not supplied rotate by 1, that is to say put the last
element first in the list.
The 5x5 game has in general several solutions. For grid size=5,
there are 4 possible solutions. When function
`5x5-solve-suggest' (press `\\[5x5-solve-suggest]') is called the
solution that is presented is the one that needs least number of
strokes --- other solutions can be viewed by rotating through the
list. The list of solution is ordered by number of strokes, so
rotating left just after calling `5x5-solve-suggest' will show
the solution with second least number of strokes, while rotating
right will show the solution with greatest number of strokes."
(interactive "P" 5x5-mode)
(let ((len (length 5x5-solver-output)))
(when (>= len 3)
(setq n (if (integerp n) n 1)
n (mod n (1- len)))
(unless (eq n 0)
(setq n (- len n 1))
(let* ((p-tail (last 5x5-solver-output (1+ n)))
(tail (cdr p-tail))
(l-tail (last tail)))
;;
;; For n = 2:
;;
;; +--+--+ +--+--+ +--+--+ +--+--+ +--+--+
;; |M | ---->|S1| ---->|S2| ---->|S3| ---->|S4| ----> nil
;; +--+--+ +--+--+ +--+--+ +--+--+ +--+--+
;; ^ ^ ^ ^
;; | | | |
;; + 5x5-solver-output | | + l-tail
;; + p-tail |
;; + tail
;;
(setcdr l-tail (cdr 5x5-solver-output))
(setcdr 5x5-solver-output tail)
(unless (eq p-tail 5x5-solver-output)
(setcdr p-tail nil)))
(5x5-draw-grid (list 5x5-grid))
(5x5-position-cursor)))))
(defun 5x5-solve-rotate-right (&optional n)
"Rotate right by N the list of solutions in 5x5-solver-output.
If N is not supplied, rotate by 1. Similar to function
`5x5-solve-rotate-left' except that rotation is right instead of
lest."
(interactive "P" 5x5-mode)
(setq n
(if (integerp n) (- n)
-1))
(5x5-solve-rotate-left n))
;; Keyboard response functions.
(defun 5x5-flip-current ()
"Make a move on the current cursor location."
(interactive nil 5x5-mode)
(setq 5x5-grid (5x5-make-move 5x5-grid 5x5-y-pos 5x5-x-pos))
(5x5-made-move)
(unless 5x5-cracking
(5x5-draw-grid (list 5x5-grid)))
(5x5-position-cursor)
(when (= (5x5-grid-value 5x5-grid) (* 5x5-grid-size 5x5-grid-size))
(beep)
(message "You win!")))
(defun 5x5-up ()
"Move up."
(interactive nil 5x5-mode)
(unless (zerop 5x5-y-pos)
(cl-decf 5x5-y-pos)
(5x5-position-cursor)))
(defun 5x5-down ()
"Move down."
(interactive nil 5x5-mode)
(unless (= 5x5-y-pos (1- 5x5-grid-size))
(cl-incf 5x5-y-pos)
(5x5-position-cursor)))
(defun 5x5-left ()
"Move left."
(interactive nil 5x5-mode)
(unless (zerop 5x5-x-pos)
(cl-decf 5x5-x-pos)
(5x5-position-cursor)))
(defun 5x5-right ()
"Move right."
(interactive nil 5x5-mode)
(unless (= 5x5-x-pos (1- 5x5-grid-size))
(cl-incf 5x5-x-pos)
(5x5-position-cursor)))
(defun 5x5-bol ()
"Move to beginning of line."
(interactive nil 5x5-mode)
(setq 5x5-x-pos 0)
(5x5-position-cursor))
(defun 5x5-eol ()
"Move to end of line."
(interactive nil 5x5-mode)
(setq 5x5-x-pos (1- 5x5-grid-size))
(5x5-position-cursor))
(defun 5x5-first ()
"Move to the first cell."
(interactive nil 5x5-mode)
(setq 5x5-x-pos 0
5x5-y-pos 0)
(5x5-position-cursor))
(defun 5x5-last ()
"Move to the last cell."
(interactive nil 5x5-mode)
(setq 5x5-x-pos (1- 5x5-grid-size)
5x5-y-pos (1- 5x5-grid-size))
(5x5-position-cursor))
(defun 5x5-randomize ()
"Randomize the grid."
(interactive nil 5x5-mode)
(when (5x5-y-or-n-p "Start a new game with a random grid? ")
(setq 5x5-x-pos (/ 5x5-grid-size 2)
5x5-y-pos (/ 5x5-grid-size 2)
5x5-moves 0
5x5-grid (5x5-make-random-grid (symbol-function '5x5-make-move))
5x5-solver-output nil)
(unless 5x5-cracking
(5x5-draw-grid (list 5x5-grid)))
(5x5-position-cursor)))
;; Support functions
(defun 5x5-y-or-n-p (prompt)
"5x5 wrapper for `y-or-n-p' which respects the `5x5-hassle-me' setting."
(if 5x5-hassle-me
(y-or-n-p prompt)
t))
(define-obsolete-function-alias '5x5-xor #'xor "27.1")
(define-obsolete-function-alias '5x5-defvar-local #'defvar-local "28.1")
(provide '5x5)
;;; 5x5.el ends here
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