Function fabricator
Create Python functions based on detailed specifications.
Here's a Python function that implements a backtracking algorithm to solve a Sudoku puzzle:
pythondef solve_sudoku(grid): """ Solves a Sudoku puzzle using backtracking algorithm. Args: grid (list): A 9x9 list representing the Sudoku grid. Empty cells are represented by 0. Returns: list or None: The solved Sudoku grid if the puzzle is solvable, None otherwise. Raises: ValueError: If the input grid is not a valid Sudoku puzzle. """ # Validate the input grid if not is_valid_grid(grid): raise ValueError("Invalid Sudoku grid") # Helper function to find the next empty cell def find_empty(grid): for i in range(9): for j in range(9): if grid[i][j] == 0: return i, j return None, None # Helper function to check if a value is valid in a given position def valid(grid, num, pos): # Check row if num in grid[pos[0]]: return False # Check column if num in [grid[i][pos[1]] for i in range(9)]: return False # Check box box_x = pos[1] // 3 box_y = pos[0] // 3 if num in [grid[box_y*3 + i][box_x*3 + j] for i in range(3) for j in range(3)]: return False return True # Recursive backtracking function def backtrack(): row, col = find_empty(grid) # If no empty cells, the puzzle is solved if row is None and col is None: return True # Try all possible values for num in range(1, 10): if valid(grid, num, (row, col)): grid[row][col] = num if backtrack(): return True # If the current value doesn't lead to a solution, reset the cell grid[row][col] = 0 return False # Call the backtracking function if backtrack(): return grid else: return None def is_valid_grid(grid): """ Checks if the input grid is a valid Sudoku puzzle. Args: grid (list): A 9x9 list representing the Sudoku grid. Returns: bool: True if the grid is valid, False otherwise. """ # Check if the grid has the correct dimensions if len(grid) != 9 or any(len(row) != 9 for row in grid): return False # Check if all values are in the range [0, 9] if any(val > 9 or val < 0 for row in grid for val in row): return False # Check rows, columns, and boxes for duplicates for i in range(9): row = [val for val in grid[i] if val != 0] if len(row) != len(set(row)): return False col = [grid[j][i] for j in range(9) if grid[j][i] != 0] if len(col) != len(set(col)): return False box = [grid[j//3*3 + i//3][j%3*3 + i%3] for j in range(9) for i in range(9) if grid[j//3*3 + i//3][j%3*3 + i%3] != 0] if len(box) != len(set(box)): return False return True
This function solve_sudoku
takes a 9x9 Sudoku grid as input, represented as a list of lists. Empty cells are represented by the value 0. It first validates the input grid using the is_valid_grid
function to ensure it is a valid Sudoku puzzle.
The solve_sudoku
function then implements a backtracking algorithm to solve the puzzle. It uses two helper functions: find_empty
to find the next empty cell, and valid
to check if a value is valid in a given position.
The backtracking function backtrack
recursively tries all possible values (1 to 9) for each empty cell. If a value is valid, it assigns that value to the cell and recursively calls itself. If a solution is found, it returns True
. Otherwise, it resets the cell to 0 and tries the next value.
If the backtrack
function completes without finding a solution, it means the puzzle is unsolvable, and solve_sudoku
returns None
. If a solution is found, it returns the solved Sudoku grid.
The is_valid_grid
function checks if the input grid is a valid Sudoku puzzle by performing the following checks:
- Ensuring the grid has the correct dimensions (9x9).
- Checking if all values are in the range [0, 9].
- Verifying that there are no duplicates in each row, column, and 3x3 box.
If any of these checks fail, the function returns False
, indicating an invalid Sudoku grid.
Here's an example usage:
python# Valid and solvable Sudoku grid grid = [ [5, 3, 0, 0, 7, 0, 0, 0, 0], [6, 0, 0, 1, 9, 5, 0, 0, 0], [0, 9, 8, 0, 0, 0, 0, 6, 0], [8, 0, 0, 0, 6, 0, 0, 0, 3], [4, 0, 0, 8, 0, 3, 0, 0, 1], [7, 0, 0, 0, 2, 0, 0, 0, 6], [0, 6, 0, 0, 0, 0, 2, 8, 0], [0, 0, 0, 4, 1, 9, 0, 0, 5], [0, 0, 0, 0, 8, 0, 0, 7, 9] ] solved_grid = solve_sudoku(grid) if solved_grid: for row in solved_grid: print(row) else: print("The puzzle is unsolvable.")
This example will print the solved Sudoku grid:
[5, 3, 4, 6, 7, 8, 9, 1, 2] [6, 7, 2, 1, 9, 5, 3, 4, 8] [1, 9, 8, 3, 4, 2, 5, 6, 7] [8, 5, 9, 7, 6, 1, 4, 2, 3] [4, 2, 6, 8, 5, 3, 7, 9, 1] [7, 1, 3, 9, 2, 4, 8, 5, 6] [9, 6, 1, 5, 3, 7, 2, 8, 4] [2, 8, 7, 4, 1, 9, 6, 3, 5] [3, 4, 5, 2, 8, 6, 1, 7, 9]
Note that the solve_sudoku
function assumes that the input grid is a valid Sudoku puzzle. If the input grid is invalid (e.g., contains duplicates or has incorrect dimensions), the function will raise a ValueError
exception. You can catch this exception and handle it appropriately in your code.
API request
pythonimport anthropic client = anthropic.Anthropic( # defaults to os.environ.get("ANTHROPIC_API_KEY") api_key="my_api_key", ) message = client.messages.create( model="claude-3-opus-20240229", max_tokens=2000, temperature=0, system="Your task is to create Python functions based on the provided natural language requests. Each request will describe the desired functionality of the function, including the input parameters and expected return value. Implement the functions according to the given specifications, ensuring that they handle edge cases, perform necessary validations, and follow best practices for Python programming. Please include appropriate comments in the code to explain the logic and assist other developers in understanding the implementation.", messages=[{"role":"user","content":"I want a function that can solve a Sudoku puzzle. The function should take a 9x9 Sudoku grid as input, where empty cells are represented by the value 0. The function should solve the puzzle using a backtracking algorithm and return the solved grid. If the puzzle is unsolvable, it should return None. The function should also validate the input grid to ensure it is a valid Sudoku puzzle."}] ) print(message.content)