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search_solver.py
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search_solver.py
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# Based on: http://norvig.com/sudoku.html
from tensorflow import keras
import numpy as np
import time
def cross(A, B):
"""Cross product of elements in A and elements in B."""
return [a + b for a in A for b in B]
digits = '123456789'
rows = 'ABCDEFGHI'
cols = digits
squares = cross(rows, cols)
unitlist = ([cross(rows, c) for c in cols] +
[cross(r, cols) for r in rows] +
[cross(rs, cs) for rs in ('ABC', 'DEF', 'GHI') for cs in ('123', '456', '789')])
units = dict((s, [u for u in unitlist if s in u])
for s in squares)
peers = dict((s, set(sum(units[s], [])) - set([s]))
for s in squares)
search_count = 0
def parse_grid(grid):
"""Convert grid to a dict of possible values, {square: digits}, or
return False if a contradiction is detected."""
values = dict((s, digits) for s in squares)
for s, d in grid_values(grid).items():
if d in digits and not assign(values, s, d):
return False ## (Fail if we can't assign d to square s.)
return values
def grid_values(grid):
"Convert grid into a dict of {square: char} with '0' or '.' for empties."
chars = [c for c in grid if c in digits or c in '0.']
assert len(chars) == 81
return dict(zip(squares, chars))
def assign(values, s, d):
"""Eliminate all the other values (except d) from values[s] and propagate.
Return values, except return False if a contradiction is detected."""
other_values = values[s].replace(d, '')
if all(eliminate(values, s, d2) for d2 in other_values):
return values
else:
return False
def eliminate(values, s, d):
"""Eliminate d from values[s]; propagate when values or places <= 2.
Return values, except return False if a contradiction is detected."""
if d not in values[s]:
return values
values[s] = values[s].replace(d, '')
if len(values[s]) == 0:
return False
elif len(values[s]) == 1:
d2 = values[s]
if not all(eliminate(values, s2, d2) for s2 in peers[s]):
return False
for u in units[s]:
dplaces = [s for s in u if d in values[s]]
if len(dplaces) == 0:
return False
elif len(dplaces) == 1:
if not assign(values, dplaces[0], d):
return False
return values
def display(values):
"""Display these values as a 2-D grid."""
width = 1 + max(len(values[s]) for s in squares)
line = '+'.join(['-' * (width * 3)] * 3)
for r in rows:
print(''.join([''.join(values[r + c].center(width) + ('|' if c in '36' else ''))
for c in cols]))
if r in 'CF':
print(line)
print()
def solve(grid, prediction=None):
prob = None
if prediction is not None:
prob = {}
for i, p in enumerate(squares):
prob[p] = prediction[i]
return search(parse_grid(grid), prob)
def search(values, prob=None):
"Using depth-first search and propagation, try all possible values."
global search_count
search_count += 1
if values is False:
return False
if all(len(values[s]) == 1 for s in squares):
return values
n, s = min((len(values[s]), s) for s in squares if len(values[s]) > 1)
if prob is not None:
search_order_dict = {}
for d in values[s]:
search_order_dict[d] = prob[s][int(d) - 1]
search_order = [k for k, v in sorted(search_order_dict.items(), key=lambda item: item[1], reverse=True)]
else:
search_order = values[s]
return some(search(assign(values.copy(), s, d), prob) for d in search_order)
def some(seq):
"""Return some element of seq that is true."""
for e in seq:
if e:
return e
return False
def predict(model, problems):
n = len(problems)
tensor = np.array([int(c) for c in ''.join(problems).replace('.', '0')]).reshape((n, 9, 9, 1))
prediction = model.predict(tensor)
return prediction
def solve_all(problems, model=None):
if model is not None:
prediction = predict(model, problems)
for i, problem in enumerate(problems):
solve(problem, prediction[i])
else:
for problem in problems:
solve(problem)
def solve_all_in_file(file_path, model=None):
with open(file_path, 'r') as f:
lines = f.readlines()
solve_all([line.strip() for line in lines], model)
if __name__ == '__main__':
model = keras.models.load_model('model')
grid1 = '003020600900305001001806400008102900700000008006708200002609500800203009005010300'
hardest = '.....6....59.....82....8....45........3........6..3.54...325..6..................'
predict(model, [grid1]) # warm up gpu and the framework
# solve the hardest problem
start = time.process_time()
search_count = 0
prediction = predict(model, [hardest])[0]
solution = solve(hardest, prediction)
print(f'Model On: Solved in: {time.process_time() - start} s')
print(f'Search Count: {search_count}')
display(solution)
start = time.process_time()
search_count = 0
solution = solve(hardest)
print(f'Model Off: Solved in: {time.process_time() - start} s')
print(f'Search Count: {search_count}')
display(solution)
# solve a list of hard problems
with open('data/hard95.txt', 'r') as f:
lines = f.readlines()
problems = [line.strip() for line in lines]
start = time.process_time()
search_count = 0
solve_all(problems, model)
print(f'Model On: Solved in: {time.process_time() - start} s')
print(f'Search Count: {search_count}')
start = time.process_time()
search_count = 0
solve_all(problems)
print(f'Model Off: Solved in: {time.process_time() - start} s')
print(f'Search Count: {search_count}')