add generalized pivot optimizer

MiniZinc_scripts/parameterized_board_generator_pivot.mzn

@@ -0,0 +1,79 @@
+enum Letter = { A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z }; % english letters in alphabetical order
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%% Variables whose values need to be passed in %%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+int: n; % board size
+int: m; % number of words
+
+int: max_len; % length of the longest word being passed in
+
+array [1..m] of int: word_lens; % array giving the length of each word
+array [1..m] of int: pivot_inds; % array giving the 0-index the pivot-letter
+array [1..m,1..max_len] of Letter: words; % array whose rows are words, with excess length padded with other letters
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+array [1..n,1..n] of var Letter: board;
+
+array [1..m] of var 1..n: word_pos_y; % values constrained by board size
+array [1..m] of var 1..n: word_pos_x; % values constrained by board size
+array [1..m] of var -1..1: word_delta_y; % values constrained by {-1,0,1}
+array [1..m] of var -1..1: word_delta_x; % values constrained by {-1,0,1}
+
+
+constraint forall(i in 1..m)(word_delta_y[i] != 0 \/ word_delta_x[i] != 0); % at least one of dy,dx must be nonzero
+
+% Pivot helper functions
+function int: num_letters_lt_pivot_idx(int: i) = pivot_inds[i];
+function int: num_letters_gte_pivot_idx(int: i) = word_lens[i] - pivot_inds[i];
+
+% For each word, enforce that its last letter lies within the board.
+% Since its first letter also lies within the board, this implies that the entire word lies within the board, by convexity.
+constraint forall(i in 1..m)(
+  % End-of-word constraints
+  word_pos_y[i]+word_delta_y[i]*(num_letters_gte_pivot_idx(i)-1) >= 1
+  /\ word_pos_y[i]+word_delta_y[i]*(num_letters_gte_pivot_idx(i)-1) <= n
+  /\ word_pos_x[i]+word_delta_x[i]*(num_letters_gte_pivot_idx(i)-1) >= 1
+  /\ word_pos_x[i]+word_delta_x[i]*(num_letters_gte_pivot_idx(i)-1) <= n
+  % Start-of-word constraints
+  /\ word_pos_y[i]-word_delta_y[i]*num_letters_lt_pivot_idx(i) >= 1
+  /\ word_pos_y[i]-word_delta_y[i]*num_letters_lt_pivot_idx(i) <= n
+  /\ word_pos_x[i]-word_delta_x[i]*num_letters_lt_pivot_idx(i) >= 1
+  /\ word_pos_x[i]-word_delta_x[i]*num_letters_lt_pivot_idx(i) <= n
+);
+
+% Link the words to the board by linking letters to board positions.
+constraint forall(i in 1..m)(
+  forall(j in (-1*num_letters_lt_pivot_idx(i)+1)..num_letters_gte_pivot_idx(i))(
+    words[i,num_letters_lt_pivot_idx(i)+j] = board[word_pos_y[i] + word_delta_y[i]*(j-1), word_pos_x[i] + word_delta_x[i]*(j-1)]
+  )
+);
+
+% Search the variables in order of decreasing word length (words are passed in as shortest-to-longest).
+% For each word first search the positions in min-to-max order (intuition: start from the left/top of the board then work your way in).
+% Then search the orientations in horizontal-to-diagonalmax order (intuition: diagonal words interfere with more other words)
+
+annotation pos_var_strat;
+annotation pos_val_strat;
+
+% Define position searches and orientation searches separately, then interleave them in reverse order.
+solve :: seq_search([
+  if x = 1 then int_search([word_pos_y[i], word_pos_x[i]], pos_var_strat, pos_val_strat)
+  else int_search([word_delta_y[i], word_delta_x[i]], first_fail, indomain_median)
+  endif | i in reverse(1..m), x in 1..2])
+      satisfy;
+
+
+% Function which outputs, for a given board position, whether there is a word which overlaps that position
+function bool: square_is_covered(int: i, int: j) = 
+  exists(k in 1..m)(
+    exists(l in (-1*num_letters_lt_pivot_idx(k)+1)..num_letters_gte_pivot_idx(k))(
+      (i == fix(word_pos_y[k]) + fix(word_delta_y[k])*(l-1)) /\ (j == fix(word_pos_x[k]) + fix(word_delta_x[k])*(l-1))
+  )
+);
+
+output [ if square_is_covered(i,j) then format(fix(board[i,j])) else "_" endif ++
+if j == n then "\n" else " " endif | i,j in 1..n ] ++ ["\n"];

make_puzzle_v2.py

@@ -157,38 +157,48 @@ def get_most_common_letter_indexes(board_words):
     return most_common_letter_idx
 
 
-def get_spiral_indices(board_size):
+def get_jiggled_word_centers(board_words, max_jiggle=0.15):
     """
-    Adapted from https://stackoverflow.com/a/398302/2562771
-    Note: goes down-->right-->up-->left due to change in indexing
+    Get the randomly-perturbed center of each word. Ok to perturb up to 0.15 away from the geometric center.
+    For default max_jiggle=0.15, this translates to the following possibilities for centers for common word lengths:
+    4 : xOxx, xxOx
+    5 : xxOxx
+    6 : xxOxxx, xxxOxx
+    7 : xxOxxxx, xxxOxxx, xxxxOxx
+    8 : xxxOxxxx, xxxxOxxx
+    9 : xxxOxxxxx, xxxxOxxxx, xxxxxOxxx
+    10 : xxxOxxxxxx, xxxxOxxxxx, xxxxxOxxxx, xxxxxxOxxx
     """
-    y = x = 0
-    dy, dx = 0, -1
-    inds = []
-    for i in range(board_size**2):
-        if (-board_size/2 < y <= board_size/2) and (-board_size/2 < x <= board_size/2):
-            # Figure out how to simplify these expressions down
-            y_shift, x_shift = int(np.floor(y+(board_size-1)/2))+1, int(np.floor(x+(board_size-1)/2))+1
-            inds.append((y_shift, x_shift))
-        if y == x or (y < 0 and y == -x) or (y > 0 and y == 1-x):
-            dy, dx = -dx, dy
-        y, x = y+dy, x+dx
-    return inds
-
-
-def make_data_file(board_words, board_size, strategy, filepath="tmp/data.dzn"):
+    jiggled_centers = []
+    for word in board_words:
+        possible_centers = [idx for idx in range(len(word)) if abs((len(word)-1)/2 - idx)/len(word) <= max_jiggle]
+        jiggled_centers.append(random.sample(possible_centers, 1)[0])
+    return jiggled_centers
+
+
+def make_data_file(board_words, board_size, strategy, pivot, filepath="tmp/data.dzn"):
     """Generated a temporary data.dzn file to pass to the minizinc script."""
-    ys, xs = zip(*get_spiral_indices(board_size))
     with open(filepath, "w") as outfile:
         outfile.write(f"n = {board_size};\n")
         outfile.write(f"m = {len(board_words)};\n\n")
-        outfile.write(f"y_pos_map = [ {', '.join([str(y) for y in ys])} ];\n")
-        outfile.write(f"x_pos_map = [ {', '.join([str(x) for x in xs])} ];\n\n")
         outfile.write(f"max_len = {max([len(word) for word in board_words])};\n")
         outfile.write(f"word_lens = [ {', '.join([str(len(word)) for word in board_words])} ];\n")
-        outfile.write(f"max_freq_idx = [ {', '.join([str(idx) for idx in get_most_common_letter_indexes(board_words)])} ];\n")
+
+        if pivot == "start":
+            pivots = [0]*len(board_words)
+        elif pivot == "center":
+            pivots = [(len(word)-1) // 2 for word in board_words]
+        elif pivot == "max_freq":
+            pivots = get_most_common_letter_indexes(board_words)
+        elif pivot == "jiggle":
+            pivots = get_jiggled_word_centers(board_words)
+        else:
+            raise ValueError(f"Pivot type must be one of 'start', 'center', 'max_freq', 'jiggle'. Received value: 'f{pivot}'")
+        outfile.write(f"pivot_inds = [ {', '.join([str(idx) for idx in pivots])} ];\n")
+
         # ADDING THE BUFFER LIKE THIS IS HACKY, MAKE IT CLEANER
-        outfile.write(f"words = [| {' | '.join([', '.join(word + 'A'*(len(board_words[-1])-len(word))) for word in board_words])} |];\n\n")
+        outfile.write(f"words = [| {' | '.join([', '.join(word + 'Z'*(len(board_words[-1])-len(word))) for word in board_words])} |];\n\n")
+
         # Add the search strategy conditional on the input strategy
         if strategy == "min":
             pos_var_strat = "smallest"
@@ -305,7 +315,7 @@ def find_words_in_board(board, word_tuples):
     return covered_up_words, doubled_up_words, flattened_deltas
 
 
-def make_puzzle(topic, board_size, packing_constant, strategy, optimize_words, relatedness_cutoff, n_proc=4):
+def make_puzzle(topic, board_size, packing_constant, strategy, pivot, optimize_words, relatedness_cutoff, n_proc=4):
     word_tuples, hidden_word_tuple_dict = get_related_words(topic, relatedness_cutoff)
     word_tuples = [wt for wt in word_tuples if len(wt.board) <= board_size]
 
@@ -325,7 +335,7 @@ def make_puzzle(topic, board_size, packing_constant, strategy, optimize_words, r
     # Answer: write a separate file for each to avoid needed to juggle read/write times
 
     board_found = False
-    max_retries = 15
+    max_retries = 10
     retries = 0
     timeout = 5
     while retries < max_retries and not board_found:
@@ -334,13 +344,10 @@ def make_puzzle(topic, board_size, packing_constant, strategy, optimize_words, r
             # Shuffle words separately for each run.
             word_tuples_to_fit = reshuffle_words_to_fit(word_tuples_to_fit)
             # Generate Minizinc data file to feed into the parameterizd script.
-            make_data_file([wt.board for wt in word_tuples_to_fit], board_size, strategy, f"tmp/data{i+1}.dzn")
+            make_data_file([wt.board for wt in word_tuples_to_fit], board_size, strategy, pivot, f"tmp/data{i+1}.dzn")
 
         # Run the script
-        # cmd = ["/Applications/MiniZincIDE.app/Contents/Resources/minizinc", "--solver", "Chuffed", "MiniZinc_scripts/parameterized_board_generator.mzn"]
-        # cmd = ["/Applications/MiniZincIDE.app/Contents/Resources/minizinc", "--solver", "Chuffed", "MiniZinc_scripts/parameterized_board_generator_centered.mzn"]
-        # cmd = ["/Applications/MiniZincIDE.app/Contents/Resources/minizinc", "--solver", "Chuffed", "MiniZinc_scripts/parameterized_board_generator_centered_max_freq.mzn"]
-        cmd = ["/Applications/MiniZincIDE.app/Contents/Resources/minizinc", "--solver", "Chuffed", "MiniZinc_scripts/parameterized_board_generator_centered_spiral.mzn"]
+        cmd = ["/Applications/MiniZincIDE.app/Contents/Resources/minizinc", "--solver", "Chuffed", "MiniZinc_scripts/parameterized_board_generator_pivot.mzn"]
         ps = [subprocess.Popen(cmd + [f"tmp/data{i+1}.dzn"], stdout=subprocess.PIPE) for i in range(n_proc)]
 
         time.sleep(timeout)
@@ -449,6 +456,8 @@ def make_puzzle(topic, board_size, packing_constant, strategy, optimize_words, r
                         help="Ratio of total letters to # board squares (default=1.10)")
     parser.add_argument("--strategy", type=str, default="median",
                         help="Search strategy to use, one of 'min', 'median', 'max' (default='median')")
+    parser.add_argument("--pivot", type=str, default="center",
+                        help="Letter to pivot the words on during optimization, one of 'start', 'center', 'jiggle', 'max_freq' (default='center')")
     parser.add_argument("--optimize-words", type=bool, default=False, action=argparse.BooleanOptionalAction,
                         help="Optimize the word distribution for letter-overlaps in advance (default=False)")
     parser.add_argument("--relatedness-cutoff", type=float, default=0.45,
@@ -457,5 +466,5 @@ def make_puzzle(topic, board_size, packing_constant, strategy, optimize_words, r
 
     # Can't find solutions for words: 'flamboyant', 'coffee', 'dishwasher'
 
-    random.seed(0)
-    make_puzzle(args.topic, args.board_size, args.packing_constant, args.strategy, args.optimize_words, args.relatedness_cutoff)
+    random.seed(1)
+    make_puzzle(args.topic, args.board_size, args.packing_constant, args.strategy, args.pivot, args.optimize_words, args.relatedness_cutoff)

other.rtf

@@ -5,24 +5,24 @@
 \margl1440\margr1440\vieww12820\viewh11940\viewkind0
 \pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\pardirnatural\qc\partightenfactor0
 
-\f0\fs32 \cf2 Topic:  blond / blue-eyed / baby\
+\f0\fs32 \cf2 Topic:  science / bedtime / stories\
 \
 \
-O A F H Y F L R I G S A M A M\
-P S A D E Y E T U C Y X E S R\
-B I D Y P P U P E H Y D D I K\
-R A G G A I I N U I T A E R T\
-D I B G Y D N A S L L A G E R\
-R H L E R Y D D S D I L D N H\
-O T A L E L N I I N O A E R T\
-B E T D P R O L L A P M V I R\
-A E R N A U L L A L S I O A I\
-L T O A I C B A N O G N L B B\
-R K M H D T H P K P N A M U H\
-I S U T E F A I Y T U O P X T\
-A A G O R P S L C S O U L O A\
-F T B A L D O L L K Y N G M R\
-G E N E W O M B A B Y D U M B\
+S W E N P E E L S B O O K E A\
+L A Y F F I J T W N T H W G M\
+E R S K I L L T R U O H A A R\
+V C A G C L F D O U I S T P W\
+E S E L A O H R T L T H R M I\
+L O O I L R L O E O E H O O T\
+Y A C H P E R C R S L G P M E\
+A T L A T I C E R A L P E E L\
+D I I W E A Y R T F R A R N O\
+D M M S A L B U P U L Y N T D\
+I I A E T Y B T Y O N O P N R\
+M S X T I U S A H T O I O E A\
+H T Y M T V D N F I X C M R M\
+N O V E L I O Y O L N I S O A\
+T A L E P I C M O G T G S Y Y\
 \
 \
-animal   asia   babe   baby   bairn   bald   \uc0\u739 beer\u739    birth   blond   brat   buxom   chick   child   curly   cute   daddy   diaper   doll   dumb   eyed   fair   fetus   gene   girl   hair   handle   human   india   inuit   issue   kiddy   labor   lager   lanky   latin   leggy   loved   mama   mortal   pallid   \u739 pallor\u739    poland   pouty   puppy   ragga   sandy   sexy   soul   spoil   sprog   task   teeth   treat   womb   young}
+always   annals   attic   bathos   book   cellar   climax   clock   drama   epic   fable   floor   garret   horary   hour   jiffy   legend   level   life   loft   math   midday   minute   moment   movie   myth   nature   news   novel   page   piece   plot   recital   record   report   saga   scoop   sixty   skill   sleep   storey   study   tale   thing   time   timist   truth   while   witelo   wrote   yore}

tmp/data1.dzn

@@ -1,13 +1,10 @@
 n = 15;
-m = 51;
-
-y_pos_map = [ 8, 9, 9, 8, 7, 7, 7, 8, 9, 10, 10, 10, 10, 9, 8, 7, 6, 6, 6, 6, 6, 7, 8, 9, 10, 11, 11, 11, 11, 11, 11, 10, 9, 8, 7, 6, 5, 5, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 11, 10, 9, 8, 7, 6, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ];
-x_pos_map = [ 8, 8, 9, 9, 9, 8, 7, 7, 7, 7, 8, 9, 10, 10, 10, 10, 10, 9, 8, 7, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10, 11, 11, 11, 11, 11, 11, 11, 10, 9, 8, 7, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 10, 9, 8, 7, 6, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ];
+m = 50;
 
 max_len = 6;
-word_lens = [ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 ];
-max_freq_idx = [ 1, 1, 2, 1, 0, 1, 2, 2, 3, 1, 1, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 3, 2, 4, 1, 4, 3, 1, 2, 3, 4, 2, 3, 2, 1, 1, 1, 4, 2, 1, 3, 1, 5, 0, 1, 3, 3, 3, 5, 0, 1 ];
-words = [| T, E, S, T, A, A | B, A, S, H, A, A | B, E, A, N, A, A | S, E, E, D, A, A | A, G, O, N, A, A | G, A, L, A, A, A | Q, U, A, L, A, A | K, H, A, T, A, A | C, O, L, A, A, A | M, I, L, K, A, A | M, I, L, L, A, A | B, E, E, R, A, A | C, O, R, N, A, A | C, A, K, E, A, A | S, O, D, A, A, A | F, E, T, E, A, A | C, H, A, I, A, A | T, R, E, E, A, A | B, R, E, W, A, A | J, A, V, A, A, A | W, I, N, E, A, A | C, O, K, E, A, A | P, L, A, N, T, A | C, O, C, O, A, A | R, E, V, E, L, A | F, E, R, I, A, A | U, M, B, E, R, A | P, A, R, T, Y, A | F, E, A, S, T, A | S, U, G, A, R, A | M, O, C, H, A, A | E, V, E, N, T, A | B, R, E, A, D, A | C, H, E, E, R, A | L, A, T, T, E, A | D, R, I, N, K, A | B, R, O, W, N, A | J, U, I, C, E, A | S, N, A, C, K, A | Y, E, M, E, N, A | D, E, C, A, F, A | E, A, S, T, E, R | F, I, E, S, T, A | A, C, I, D, I, C | V, E, N, I, C, E | P, A, R, A, D, E | B, A, N, A, N, A | A, F, F, A, I, R | P, E, R, S, I, A | A, F, R, I, C, A | C, A, N, C, E, R |];
+word_lens = [ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 ];
+pivot_inds = [ 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 3 ];
+words = [| S, A, G, A, Z, Z | T, I, M, E, Z, Z | P, A, G, E, Z, Z | L, O, F, T, Z, Z | Y, O, R, E, Z, Z | B, O, O, K, Z, Z | N, E, W, S, Z, Z | E, P, I, C, Z, Z | H, O, U, R, Z, Z | M, A, T, H, Z, Z | T, A, L, E, Z, Z | M, Y, T, H, Z, Z | P, L, O, T, Z, Z | L, I, F, E, Z, Z | C, L, O, C, K, Z | S, I, X, T, Y, Z | L, E, V, E, L, Z | S, T, U, D, Y, Z | P, I, E, C, E, Z | T, H, I, N, G, Z | D, R, A, M, A, Z | W, H, I, L, E, Z | F, L, O, O, R, Z | J, I, F, F, Y, Z | F, A, B, L, E, Z | N, O, V, E, L, Z | A, T, T, I, C, Z | W, R, O, T, E, Z | S, K, I, L, L, Z | S, C, O, O, P, Z | M, O, V, I, E, Z | T, R, U, T, H, Z | S, L, E, E, P, Z | B, A, T, H, O, S | N, A, T, U, R, E | H, O, R, A, R, Y | S, T, O, R, E, Y | M, I, D, D, A, Y | A, L, W, A, Y, S | M, O, M, E, N, T | R, E, P, O, R, T | C, L, I, M, A, X | A, N, N, A, L, S | W, I, T, E, L, O | L, E, G, E, N, D | C, E, L, L, A, R | R, E, C, O, R, D | T, I, M, I, S, T | G, A, R, R, E, T | M, I, N, U, T, E |];
 
 pos_var_strat = first_fail;
 pos_val_strat = indomain_median;