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Add arrays/sudoku_solver.py #10623

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220 changes: 220 additions & 0 deletions data_structures/arrays/sudoku_solver.py
Original file line number Diff line number Diff line change
@@ -0,0 +1,220 @@
"""
Please do not modify this file! It is published at https://norvig.com/sudoku.html with
only minimal changes to work with modern versions of Python. If you have improvements,
please make them in a separate file.
"""
import random
import time


def cross(items_a, items_b):
"Cross product of elements in A and elements in B."
return [a + b for a in items_a for b in items_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 = {s: [u for u in unitlist if s in u] for s in squares}
peers = {s: set(sum(units[s], [])) - {s} for s in squares}


def test():
"A set of unit tests."
assert len(squares) == 81
assert len(unitlist) == 27
assert all(len(units[s]) == 3 for s in squares)
assert all(len(peers[s]) == 20 for s in squares)
assert units["C2"] == [
["A2", "B2", "C2", "D2", "E2", "F2", "G2", "H2", "I2"],
["C1", "C2", "C3", "C4", "C5", "C6", "C7", "C8", "C9"],
["A1", "A2", "A3", "B1", "B2", "B3", "C1", "C2", "C3"],
]
# fmt: off
assert peers["C2"] == {
"A2", "B2", "D2", "E2", "F2", "G2", "H2", "I2", "C1", "C3",
"C4", "C5", "C6", "C7", "C8", "C9", "A1", "A3", "B1", "B3"
}
# fmt: on
print("All tests pass.")


def parse_grid(grid):
"""Convert grid to a dict of possible values, {square: digits}, or
return False if a contradiction is detected."""
## To start, every square can be any digit; then assign values from the grid.
values = {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 ## Already eliminated
values[s] = values[s].replace(d, "")
## (1) If a square s is reduced to one value d2, then eliminate d2 from the peers.
if len(values[s]) == 0:
return False ## Contradiction: removed last value
elif len(values[s]) == 1:
d2 = values[s]
if not all(eliminate(values, s2, d2) for s2 in peers[s]):
return False
## (2) If a unit u is reduced to only one place for a value d, then put it there.
for u in units[s]:
dplaces = [s for s in u if d in values[s]]
if len(dplaces) == 0:
return False ## Contradiction: no place for this value
elif len(dplaces) == 1:
# d can only be in one place in unit; assign it there
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(
values[r + c].center(width) + ("|" if c in "36" else "") for c in cols
)
)
if r in "CF":
print(line)
print()


def solve(grid):
return search(parse_grid(grid))


def some(seq):
"Return some element of seq that is true."
for e in seq:
if e:
return e
return False


def search(values):
"Using depth-first search and propagation, try all possible values."
if values is False:
return False ## Failed earlier
if all(len(values[s]) == 1 for s in squares):
return values ## Solved!
## Chose the unfilled square s with the fewest possibilities
n, s = min((len(values[s]), s) for s in squares if len(values[s]) > 1)
return some(search(assign(values.copy(), s, d)) for d in values[s])


def solve_all(grids, name="", showif=0.0):
"""Attempt to solve a sequence of grids. Report results.
When showif is a number of seconds, display puzzles that take longer.
When showif is None, don't display any puzzles."""

def time_solve(grid):
start = time.monotonic()
values = solve(grid)
t = time.monotonic() - start
## Display puzzles that take long enough
if showif is not None and t > showif:
display(grid_values(grid))
if values:
display(values)
print("(%.5f seconds)\n" % t)
return (t, solved(values))

times, results = zip(*[time_solve(grid) for grid in grids])
if (n := len(grids)) > 1:
print(
"Solved %d of %d %s puzzles (avg %.2f secs (%d Hz), max %.2f secs)."
% (sum(results), n, name, sum(times) / n, n / sum(times), max(times))
)


def solved(values):
"A puzzle is solved if each unit is a permutation of the digits 1 to 9."

def unitsolved(unit):
return {values[s] for s in unit} == set(digits)

return values is not False and all(unitsolved(unit) for unit in unitlist)


def from_file(filename, sep="\n"):
"Parse a file into a list of strings, separated by sep."
return open(filename).read().strip().split(sep) # noqa: SIM115


def random_puzzle(assignments=17):
"""Make a random puzzle with N or more assignments. Restart on contradictions.
Note the resulting puzzle is not guaranteed to be solvable, but empirically
about 99.8% of them are solvable. Some have multiple solutions."""
values = {s: digits for s in squares}
for s in shuffled(squares):
if not assign(values, s, random.choice(values[s])):
break
ds = [values[s] for s in squares if len(values[s]) == 1]
if len(ds) >= assignments and len(set(ds)) >= 8:
return "".join(values[s] if len(values[s]) == 1 else "." for s in squares)
return random_puzzle(assignments) ## Give up and make a new puzzle


def shuffled(seq):
"Return a randomly shuffled copy of the input sequence."
seq = list(seq)
random.shuffle(seq)
return seq


grid1 = (
"003020600900305001001806400008102900700000008006708200002609500800203009005010300"
)
grid2 = (
"4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......"
)
hard1 = (
".....6....59.....82....8....45........3........6..3.54...325..6.................."
)

if __name__ == "__main__":
test()
# solve_all(from_file("easy50.txt", '========'), "easy", None)
# solve_all(from_file("top95.txt"), "hard", None)
# solve_all(from_file("hardest.txt"), "hardest", None)
solve_all([random_puzzle() for _ in range(99)], "random", 100.0)
for puzzle in (grid1, grid2): # , hard1): # Takes 22 sec to solve on my M1 Mac.
display(parse_grid(puzzle))
start = time.monotonic()
solve(puzzle)
t = time.monotonic() - start
print("Solved: %.5f sec" % t)