Add arrays/sudoku_solver.py (#10623)

* Create Sudoku_Solver

Each of the digits 1-9 must occur exactly once in each row.
Each of the digits 1-9 must occur exactly once in each column.
Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.
The '.' character indicates empty cells.

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* Rename Sudoku_Solver to sudoku_solver.py

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* Update sudoku_solver.py

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

Diff for: data_structures/arrays/sudoku_solver.py

@@ -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)