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Improve crossword puzzle solver implementation (#14568)

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* Improve crossword puzzle solver implementation

The original `is_valid` returned `False` for any non-empty cell, which meant two words sharing a letter could never be placed together. Since crossword grids are built on exactly those intersections, this broke the core use case. Related to that, `remove_word` during backtracking blindly blanked every cell of the removed word, wiping out letters that belonged to already-placed crossing words. The fix snapshots the grid before placement and only clears cells that were empty beforehand. There was also a mutation bug: `words.remove(word)` does an O(n) scan and modifies state shared across the call stack, replaced here with a local slice per frame. On top of the fixes, the solver now tries the longest word first at each level, a standard "most-constrained variable" heuristic that cuts down backtracks significantly on larger inputs.

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* Refactor character check in crossword solver

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
This commit is contained in:
Ewan John Dennis
2026-09-17 16:31:42 +02:00
committed by GitHub
co-authored by pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Christian Clauss
parent 2a3a6974b7
commit 06b0756b38
1 changed files with 64 additions and 73 deletions
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backtracking/crossword_puzzle_solver.py
+64 -73
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@@ -6,29 +6,28 @@ def is_valid(
) -> bool:
"""
Check if a word can be placed at the given position.
A cell is valid if it is empty or already contains the correct letter
(enabling crossing/intersection between words).
>>> puzzle = [
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', '']
... ]
>>> puzzle = [['', '', '', ''], ['', '', '', ''],
... ['', '', '', ''], ['', '', '', '']]
>>> is_valid(puzzle, 'word', 0, 0, True)
True
>>> puzzle = [
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', '']
... ]
>>> is_valid(puzzle, 'word', 0, 0, False)
True
>>> puzzle2 = [['w', '', ''], ['o', '', ''], ['r', '', ''], ['d', '', '']]
>>> is_valid(puzzle2, 'word', 0, 0, True)
True
>>> is_valid(puzzle2, 'cat', 0, 0, True)
False
"""
for i in range(len(word)):
if vertical:
if row + i >= len(puzzle) or puzzle[row + i][col] != "":
return False
elif col + i >= len(puzzle[0]) or puzzle[row][col + i] != "":
rows, cols = len(puzzle), len(puzzle[0])
for i, ch in enumerate(word):
r, c = (row + i, col) if vertical else (row, col + i)
if r >= rows or c >= cols:
return False
cell = puzzle[r][c]
if cell not in ("", ch):
return False
return True
@@ -37,95 +36,87 @@ def place_word(
puzzle: list[list[str]], word: str, row: int, col: int, vertical: bool
) -> None:
"""
Place a word at the given position.
Place a word at the given position in the puzzle.
>>> puzzle = [
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', '']
... ]
>>> puzzle = [['', '', '', ''], ['', '', '', ''],
... ['', '', '', ''], ['', '', '', '']]
>>> place_word(puzzle, 'word', 0, 0, True)
>>> puzzle
[['w', '', '', ''], ['o', '', '', ''], ['r', '', '', ''], ['d', '', '', '']]
"""
for i, char in enumerate(word):
for i, ch in enumerate(word):
if vertical:
puzzle[row + i][col] = char
puzzle[row + i][col] = ch
else:
puzzle[row][col + i] = char
puzzle[row][col + i] = ch
def remove_word(
puzzle: list[list[str]], word: str, row: int, col: int, vertical: bool
puzzle: list[list[str]],
word: str,
row: int,
col: int,
vertical: bool,
snapshot: list[list[str]],
) -> None:
"""
Remove a word from the given position.
Remove a word from the puzzle, restoring only cells that were empty
before placement. Cells shared with crossing words are preserved.
>>> puzzle = [
... ['w', '', '', ''],
... ['o', '', '', ''],
... ['r', '', '', ''],
... ['d', '', '', '']
... ]
>>> remove_word(puzzle, 'word', 0, 0, True)
>>> puzzle = [['w', 'o', 'r', 'd'], ['', '', '', ''],
... ['', '', '', ''], ['', '', '', '']]
>>> snap = [['', 'o', 'r', 'd'], ['', '', '', ''],
... ['', '', '', ''], ['', '', '', '']]
>>> remove_word(puzzle, 'word', 0, 0, False, snap)
>>> puzzle
[['', '', '', ''], ['', '', '', ''], ['', '', '', ''], ['', '', '', '']]
[['', 'o', 'r', 'd'], ['', '', '', ''], ['', '', '', ''], ['', '', '', '']]
"""
for i in range(len(word)):
if vertical:
puzzle[row + i][col] = ""
else:
puzzle[row][col + i] = ""
r, c = (row + i, col) if vertical else (row, col + i)
if snapshot[r][c] == "":
puzzle[r][c] = ""
def solve_crossword(puzzle: list[list[str]], words: list[str]) -> bool:
"""
Solve the crossword puzzle using backtracking.
Words are tried longest-first to prune the search space early.
Intersections between words (shared letters) are supported.
>>> puzzle = [
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', '']
... ]
>>> words = ['word', 'four', 'more', 'last']
>>> solve_crossword(puzzle, words)
>>> puzzle = [['', '', '', ''], ['', '', '', ''],
... ['', '', '', ''], ['', '', '', '']]
>>> solve_crossword(puzzle, ['word', 'four', 'more', 'last'])
True
>>> puzzle = [
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', ''],
... ['', '', '', '']
... ]
>>> words = ['word', 'four', 'more', 'paragraphs']
>>> solve_crossword(puzzle, words)
>>> puzzle2 = [['', '', '', ''], ['', '', '', ''],
... ['', '', '', ''], ['', '', '', '']]
>>> solve_crossword(puzzle2, ['word', 'four', 'more', 'paragraphs'])
False
"""
if not words:
return True
remaining = sorted(words, key=len, reverse=True)
word, rest = remaining[0], remaining[1:]
for row in range(len(puzzle)):
for col in range(len(puzzle[0])):
if puzzle[row][col] == "":
for word in words:
for vertical in [True, False]:
if is_valid(puzzle, word, row, col, vertical):
place_word(puzzle, word, row, col, vertical)
words.remove(word)
if solve_crossword(puzzle, words):
return True
words.append(word)
remove_word(puzzle, word, row, col, vertical)
return False
return True
for vertical in (True, False):
if is_valid(puzzle, word, row, col, vertical):
snapshot = [r[:] for r in puzzle]
place_word(puzzle, word, row, col, vertical)
if solve_crossword(puzzle, rest):
return True
remove_word(puzzle, word, row, col, vertical, snapshot)
return False
if __name__ == "__main__":
PUZZLE = [[""] * 3 for _ in range(3)]
WORDS = ["cat", "dog", "car"]
if solve_crossword(PUZZLE, WORDS):
print("Solution found:")
for row in PUZZLE:
print(" ".join(row))
print(" ".join(cell or "." for cell in row))
else:
print("No solution found:")
print("No solution found.")