feat: add sol1 to project euler 096

project_euler/problem_096/sol1.py

@@ -0,0 +1,209 @@
+"""
+Project Euler Problem 96: https://projecteuler.net/problem=96
+
+Problem Statement:
+Su Doku (Japanese meaning number place) is the name given to a popular puzzle
+concept. Its origin is unclear, but credit must be attributed to Leonhard
+Euler who invented a similar, and much more difficult, puzzle idea called
+Latin Squares. The objective of Su Doku puzzles, however, is to replace
+the blanks (or zeros) in a 9 by 9 grid in such that each row, column, and
+3 by 3 box contains each of the digits 1 to 9. Below is an example of a
+typical starting puzzle grid and its solution grid.
+
+003020600
+900305001
+001806400
+008102900
+700000008
+006708200
+002609500
+800203009
+005010300
+
+483921657
+967345821
+251876493
+548132976
+729564138
+136798245
+372689514
+814253769
+695417382
+
+A well constructed Su Doku puzzle has a unique solution and can be
+solved by logic, although it may be necessary to employ "guess and test"
+methods in order to eliminate options (there is much contested opinion over this).
+The complexity of the search determines the difficulty of the puzzle; the
+example above is considered easy because it can be solved by straight
+forward direct deduction.
+
+The 6K text file, sudoku.txt (right click and 'Save Link/Target As...'),
+contains fifty different Su Doku puzzles ranging in difficulty, but all
+with unique solutions (the first puzzle in the file is the example above).
+
+By solving all fifty puzzles find the sum of the 3-digit numbers found in
+the top left corner of each solution grid; for example, 483 is the 3-digit
+number found in the top left corner of the solution grid above.
+
+Solution:
+We keep a track of the digits that are already present in each row,
+column and box, and use that to check which digits can be used to fill an unfilled
+cell. This process is then repeated recursively until the puzzle is solved, after
+which the 3 digit numbers formed by the top left corner of each puzzle are added.
+
+References:
+https://en.wikipedia.org/wiki/Sudoku
+https://en.wikipedia.org/wiki/Backtracking
+"""
+
+import os
+
+
+def solve(
+    unfilled: list[tuple[int, int]],
+    row: list[int],
+    col: list[int],
+    box: list[int],
+    board: list[list[str]],
+    i: int,
+    n: int,
+) -> bool:
+    """
+    Recursive backtracking function to solve the sudoku
+
+    >>> solve(
+    ... [(0, 0)],
+    ... [0b111110111, 0b111111111, 0b111111111, 0b111111111,
+    ... 0b111111111, 0b111111111, 0b111111111, 0b111111111, 0b111111111],
+    ... [0b111110111, 0b111111111, 0b111111111, 0b111111111,
+    ... 0b111111111, 0b111111111, 0b111111111, 0b111111111, 0b111111111],
+    ... [0b111110111, 0b111111111, 0b111111111, 0b111111111,
+    ... 0b111111111, 0b111111111, 0b111111111, 0b111111111, 0b111111111],
+    ... [["0","8","3","9","2","1","6","5","7"],
+    ... ["9","6","7","3","4","5","8","2","1"],
+    ... ["2","5","1","8","7","6","4","9","3"],
+    ... ["5","4","8","1","3","2","9","7","6"],
+    ... ["7","2","9","5","6","4","1","3","8"],
+    ... ["1","3","6","7","9","8","2","4","5"],
+    ... ["3","7","2","6","8","9","5","1","4"],
+    ... ["8","1","4","2","5","3","7","6","9"],
+    ... ["6","9","5","4","1","7","3","8","2"]],
+    ... 0,
+    ... 1)
+    True
+    """
+    if i == n:
+        return True
+
+    # Get the row and column numbers for the current unfilled cell
+    r, c = unfilled[i]
+
+    for val in range(9):
+        # Check if value (val+1) can be placed at position (r, c)
+        if (
+            ((row[r] & (1 << val)) == 0)
+            and ((col[c] & (1 << val)) == 0)
+            and ((box[r // 3 * 3 + c // 3] & (1 << val)) == 0)
+        ):
+            # Place the value
+            row[r] ^= 1 << val
+            col[c] ^= 1 << val
+            box[r // 3 * 3 + c // 3] ^= 1 << val
+            board[r][c] = str(val + 1)
+
+            # Recursively solve
+            if solve(unfilled, row, col, box, board, i + 1, n):
+                return True
+
+            # Backtrack
+            row[r] ^= 1 << val
+            col[c] ^= 1 << val
+            box[r // 3 * 3 + c // 3] ^= 1 << val
+            board[r][c] = "0"
+
+    return False
+
+
+def solve_sudoku(board: list[list[str]]) -> int:
+    """
+    Solve a single sudoku puzzle and return the first 3 digits
+
+    >>> solve_sudoku(
+    ... [["0","0","3","0","2","0","6","0","0"],
+    ... ["9","0","0","3","0","5","0","0","1"],
+    ... ["0","0","1","8","0","6","4","0","0"],
+    ... ["0","0","8","1","0","2","9","0","0"],
+    ... ["7","0","0","0","0","0","0","0","8"],
+    ... ["0","0","6","7","0","8","2","0","0"],
+    ... ["0","0","2","6","0","9","5","0","0"],
+    ... ["8","0","0","2","0","3","0","0","9"],
+    ... ["0","0","5","0","1","0","3","0","0"]])
+    483
+    """
+    unfilled = []
+    row = [0] * 9
+    col = [0] * 9
+    box = [0] * 9
+
+    # Initialize the state and find unfilled positions
+    for i in range(0, 9, 3):
+        for j in range(0, 9, 3):
+            for ii in range(3):
+                for jj in range(3):
+                    r = i + ii
+                    c = j + jj
+                    if board[r][c] == "0":
+                        unfilled.append((r, c))
+                    else:
+                        val = int(board[r][c]) - 1
+                        row[r] |= 1 << val
+                        col[c] |= 1 << val
+                        box[i + j // 3] |= 1 << val
+
+    # Solve the puzzle
+    solve(unfilled, row, col, box, board, 0, len(unfilled))
+
+    # Return the first 3 digits as a number
+    return int(board[0][0]) * 100 + int(board[0][1]) * 10 + int(board[0][2])
+
+
+def solution() -> int:
+    """
+    Finds the sum of the 3 digit numbers formed by the 3 digits in the
+    top left corner of the solved sudoku puzzles as described by the problem statement.
+
+    >>> solution()
+    24702
+    """
+    try:
+        script_dir = os.path.dirname(os.path.realpath(__file__))
+        sudoku = os.path.join(script_dir, "sudoku.txt")
+        with open(sudoku) as file:
+            lines = file.readlines()
+
+    except FileNotFoundError:
+        print("Error: Could not find sudoku.txt file")
+        return 0
+
+    res = 0
+    count = 0
+    board = []
+
+    for line in lines:
+        line = line.strip()
+        if line.startswith("G"):
+            continue
+
+        board.append(list(line))
+        count = (count + 1) % 9
+
+        if count == 0:
+            solution = solve_sudoku(board)
+            res += solution
+            board = []
+
+    return res
+
+
+if __name__ == "__main__":
+    print(f"{solution()=}")