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A-Puzzle-A-Day - Draw Symmetrical Solutions.py
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A-Puzzle-A-Day - Draw Symmetrical Solutions.py
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from collections import defaultdict
from itertools import combinations
from pyx import *
# PYX TEXT SETTINGS:
text.set(text.LatexEngine)
text.preamble(r"\renewcommand{\familydefault}{\sfdefault}")
### PROBLEM DATA ###############################################################
TEXT = {(0,6):"Jan",(1,6):"Feb",(2,6):"Mar",(3,6):"Apr",(4,6):"May",(5,6):"Jun",
(0,5):"Jul",(1,5):"Aug",(2,5):"Sep",(3,5):"Oct",(4,5):"Nov",(5,5):"Dec",
(0,4):"01",(1,4):"02",(2,4):"03",(3,4):"04",(4,4):"05",(5,4):"06",(6,4):"07",
(0,3):"08",(1,3):"09",(2,3):"10",(3,3):"11",(4,3):"12",(5,3):"13",(6,3):"14",
(0,2):"15",(1,2):"16",(2,2):"17",(3,2):"18",(4,2):"19",(5,2):"20",(6,2):"21",
(0,1):"22",(1,1):"23",(2,1):"24",(3,1):"25",(4,1):"26",(5,1):"27",(6,1):"28",
(0,0):"29",(1,0):"30",(2,0):"31"}
BLACK = color.rgbfromhexstring("#000000")
WHITE = color.rgbfromhexstring("#FFFFFF")
GREY = color.rgbfromhexstring("#AAAAAA")
LIGHT_GREY = color.rgbfromhexstring("#CCCCCC")
### AUXILIARY FUNCTIONS AND DATA STRUCTURES ####################################
def contour(pixels):
# Get all segments:
segments = []
for x,y in pixels:
if (x-1,y) not in pixels: segments.append(((x, y), (x, y+1)))
if (x+1,y) not in pixels: segments.append(((x+1, y), (x+1,y+1)))
if (x,y-1) not in pixels: segments.append(((x, y), (x+1,y )))
if (x,y+1) not in pixels: segments.append(((x, y+1), (x+1,y+1)))
# Remove redundant points:
points = set([s[0] for s in segments] + [s[1] for s in segments])
for p in points:
q,r = [_ for _ in points if (p,_) in segments or (_,p) in segments]
if p[0] == q[0] == r[0] or p[1] == q[1] == r[1]:
if (p,q) in segments: segments.remove((p,q))
if (q,p) in segments: segments.remove((q,p))
if (p,r) in segments: segments.remove((p,r))
if (r,p) in segments: segments.remove((r,p))
segments.append((q,r))
# Get polygon:
q = segments[0][0]
p, r = [_ for _ in points if (q,_) in segments or (_,q) in segments]
polygon = [p, q, r]
while polygon[-1] != polygon[0]:
q = polygon[-1]
p, r = [_ for _ in points if (q,_) in segments or (_,q) in segments]
if p == polygon[-2]: polygon.append(r)
else: polygon.append(p)
return polygon[1:]
def draw(name, pieces):
drawing = []
# STYLES:
BASE = [style.linecap.round, style.linejoin.round, style.linestyle.solid]
BASE += [style.linewidth.THick, BLACK]
BOARD = BASE + [style.linewidth.THIck, deco.filled([GREY])]
# BORDER:
drawing.append((path.path(path.moveto(-0.5, -0.5),
path.lineto(-0.5, 7.5),
path.lineto( 6.5, 7.5),
path.lineto( 6.5, 5.5),
path.lineto( 7.5, 5.5),
path.lineto( 7.5, -0.5),
path.closepath()), BOARD))
for (x,y) in TEXT:
drawing.append((path.path(path.moveto(x , y ),
path.lineto(x+1, y ),
path.lineto(x+1, y+1),
path.lineto(x, y+1),
path.closepath()),
BASE + [deco.filled([WHITE])]))
# PIECES:
for n,piece in enumerate(pieces[2:]):
polygon = contour(piece)
if len(polygon) == 4:
drawing.append((path.path(path.moveto(*polygon[0]),
path.lineto(*polygon[1]),
path.lineto(*polygon[2]),
path.lineto(*polygon[3]),
path.closepath()),
BASE + [deco.filled([LIGHT_GREY])]))
elif len(polygon) == 6:
drawing.append((path.path(path.moveto(*polygon[0]),
path.lineto(*polygon[1]),
path.lineto(*polygon[2]),
path.lineto(*polygon[3]),
path.lineto(*polygon[4]),
path.lineto(*polygon[5]),
path.closepath()),
BASE + [deco.filled([LIGHT_GREY])]))
elif len(polygon) == 8:
drawing.append((path.path(path.moveto(*polygon[0]),
path.lineto(*polygon[1]),
path.lineto(*polygon[2]),
path.lineto(*polygon[3]),
path.lineto(*polygon[4]),
path.lineto(*polygon[5]),
path.lineto(*polygon[6]),
path.lineto(*polygon[7]),
path.closepath()),
BASE + [deco.filled([LIGHT_GREY])]))
else: print("WRONG POLYGON:", polygon)
# DRAW:
mycanvas = canvas.canvas()
for (p, s) in drawing: mycanvas.stroke(p, s)
# TEXT:
mycanvas.text(5.1, 0.3, r"\Large A-Puzzle-A-Day", [text.halign.center, text.vshift.mathaxis])
for piece in pieces[:2]:
x,y = piece[0][0],piece[0][1]
mycanvas.text(x+0.5, y+0.4, r"\Large "+TEXT[piece[0]], [text.halign.center, text.vshift.mathaxis])
mycanvas.writePDFfile("./symmetrical/"+name)
def dist(P, Q):
return sum(1 for (p,q) in zip(P,Q) if p!=q)
def symmetries(pieces):
pixels = [pixel for piece in pieces for pixel in piece]
x_min = min(x for x,y in pixels)
y_min = min(y for x,y in pixels)
P = tuple((x-x_min, y-y_min) for x,y in pixels)
X = max(x for x,y in P)
Y = max(y for x,y in P)
return (all((X-x, y) in P for x,y in P), # Horizontal symmetry
all(( x,Y-y) in P for x,y in P), # Vertical symmetry
all((X-x,Y-y) in P for x,y in P), # Central symmetry
all(( y, x) in P for x,y in P), # Diagonal symmetry
all((Y-y,X-x) in P for x,y in P)) # Diagonal symmetry
### MAIN FUNCTION ##############################################################
if __name__ == "__main__":
# Pre-computed for efficiency:
COMBINATIONS = ((5, 9), (7, 9), (2, 6), (3, 7), (4, 6), (6, 8), (3, 9),
(4, 8), (2, 7), (6, 7), (5, 8), (6, 9), (7, 8), (2, 3),
(5, 6, 8), (3, 5, 9), (4, 6, 7), (2, 4, 5), (6, 7, 8),
(3, 7, 8), (2, 6, 7), (4, 6, 9), (2, 4, 7), (4, 8, 9),
(2, 6, 9), (2, 7, 8), (2, 4, 9), (2, 8, 9), (3, 5, 6),
(4, 5, 6), (3, 4, 7), (5, 7, 9), (2, 3, 6), (5, 6, 7),
(3, 5, 8), (2, 5, 6), (3, 4, 9), (2, 3, 8), (4, 5, 8),
(3, 8, 9), (2, 5, 8), (4, 6, 8), (6, 7, 9), (4, 7, 9),
(3, 6, 7), (7, 8, 9), (2, 7, 9), (3, 4, 6), (5, 7, 8),
(3, 6, 9), (5, 6, 9), (3, 4, 8), (2, 3, 7), (2, 4, 6),
(2, 5, 7), (3, 7, 9), (4, 5, 9), (2, 6, 8), (2, 3, 9),
(2, 4, 8), (6, 8, 9), (2, 5, 9), (3, 5, 7), (2, 3, 4),
(3, 6, 8), (2, 5, 6, 8), (3, 5, 7, 9), (3, 4, 5, 6),
(4, 5, 6, 9), (4, 5, 7, 8), (2, 4, 6, 8), (2, 4, 5, 9),
(3, 4, 6, 7), (2, 3, 7, 9), (5, 6, 7, 9), (2, 6, 7, 8),
(2, 4, 7, 9), (2, 6, 8, 9), (3, 4, 6, 9), (2, 7, 8, 9),
(4, 6, 7, 9), (2, 3, 4, 6), (3, 5, 6, 7), (3, 6, 8, 9),
(2, 3, 6, 8), (3, 5, 7, 8), (2, 3, 4, 8), (4, 7, 8, 9),
(2, 4, 5, 6), (4, 6, 8, 9), (3, 5, 6, 9), (2, 3, 5, 9),
(3, 4, 5, 8), (2, 4, 6, 7), (3, 4, 7, 8), (3, 6, 7, 8),
(2, 4, 7, 8), (6, 7, 8, 9), (4, 6, 7, 8), (2, 5, 6, 7),
(4, 5, 6, 8), (2, 3, 6, 7), (2, 5, 6, 9), (2, 5, 7, 8),
(2, 3, 4, 7), (3, 5, 6, 8), (3, 4, 5, 7), (4, 5, 7, 9),
(2, 3, 6, 9), (2, 3, 7, 8), (5, 6, 7, 8), (2, 4, 6, 9),
(2, 3, 8, 9), (5, 6, 8, 9), (3, 4, 5, 9), (2, 4, 8, 9),
(3, 4, 6, 8), (4, 5, 8, 9), (2, 6, 7, 9), (3, 4, 7, 9),
(2, 3, 5, 6), (3, 6, 7, 9), (5, 7, 8, 9), (3, 7, 8, 9),
(4, 5, 6, 7), (3, 4, 8, 9), (3, 5, 6, 8, 9),
(2, 3, 5, 7, 9), (5, 6, 7, 8, 9), (2, 5, 7, 8, 9),
(2, 5, 6, 8, 9), (2, 3, 4, 5, 6), (3, 6, 7, 8, 9),
(3, 4, 5, 6, 8), (2, 4, 5, 7, 8), (2, 3, 4, 5, 8),
(3, 5, 6, 7, 8), (2, 3, 6, 8, 9), (4, 5, 6, 7, 8),
(2, 3, 4, 8, 9), (2, 5, 6, 7, 8), (4, 5, 6, 8, 9),
(2, 3, 5, 6, 7), (2, 4, 6, 7, 8), (2, 4, 5, 6, 7),
(2, 4, 6, 8, 9), (2, 3, 5, 6, 9), (2, 3, 5, 7, 8),
(2, 3, 4, 6, 7), (2, 4, 7, 8, 9), (2, 4, 5, 6, 9),
(3, 4, 5, 7, 9), (3, 4, 5, 6, 7), (2, 4, 5, 8, 9),
(2, 3, 6, 7, 9), (3, 4, 6, 8, 9), (3, 5, 6, 7, 9),
(2, 3, 4, 7, 9), (4, 6, 7, 8, 9), (4, 5, 6, 7, 9),
(2, 6, 7, 8, 9), (2, 3, 7, 8, 9), (2, 5, 6, 7, 9),
(2, 4, 6, 7, 9), (3, 4, 7, 8, 9), (2, 4, 5, 6, 8),
(2, 3, 4, 5, 7), (3, 4, 5, 7, 8), (3, 4, 5, 8, 9),
(2, 4, 5, 7, 9), (2, 3, 6, 7, 8), (2, 3, 4, 7, 8),
(2, 3, 5, 6, 8), (3, 4, 5, 6, 8, 9), (2, 4, 6, 7, 8, 9),
(2, 3, 5, 6, 7, 8), (2, 4, 5, 6, 7, 8), (2, 3, 4, 5, 6, 7),
(2, 3, 4, 5, 7, 8), (2, 3, 4, 5, 6, 9), (2, 3, 4, 6, 7, 8),
(2, 3, 4, 6, 8, 9), (3, 4, 6, 7, 8, 9), (2, 3, 4, 5, 6, 8),
(3, 4, 5, 6, 7, 8), (2, 3, 4, 7, 8, 9),
(2, 3, 5, 6, 7, 8, 9), (2, 3, 4, 5, 7, 8, 9),
(2, 3, 4, 5, 6, 7, 8), (2, 4, 5, 6, 7, 8, 9))
############################################################################
day = defaultdict(list)
with open("solutions.txt", 'r') as solutions:
for solution in solutions:
pieces = eval(solution[12:])
day[solution[:5]].append(pieces)
for name in day:
best_score = tuple()
for P in day[name]:
score = []
for C in COMBINATIONS:
sym_C = symmetries([P[c] for c in C])
if any(sym_C):
valid = True
for n in range(1,len(C)):
for A in combinations(C,n):
B = tuple(c for c in C if c not in A)
sym_A = symmetries([P[a] for a in A])
sym_B = symmetries([P[b] for b in B])
V = tuple((a,b) for (a,b,c) in zip(sym_A, sym_B, sym_C) if c)
if V and all(a and b for a,b in V): valid = False
if valid: score.append(len(C))
if (len(score) > len(best_score) or
len(score) == len(best_score) and tuple(sorted(score)) < best_score):
best, best_score = P, tuple(sorted(score))
draw("{}".format(name), best)
i = 0
for C in COMBINATIONS:
sym_C = symmetries([best[c] for c in C])
if any(sym_C):
valid = True
for n in range(1,len(C)):
for A in combinations(C,n):
B = tuple(c for c in C if c not in A)
sym_A = symmetries([best[a] for a in A])
sym_B = symmetries([best[b] for b in B])
V = tuple((a,b) for (a,b,c) in zip(sym_A, sym_B, sym_C) if c)
if V and all(a and b for a,b in V): valid = False
if valid:
i += 1
draw("{}_{:02d}".format(name,i), best[:2]+[best[c] for c in C])
################################################################################