
AutoToS prompt:

The task is a 5x5 mini crosswords. A state is a 2D array representing the current puzzle state, where the initial grid is all "None". Note that some of the possible answers are not exactly 5 character long. Given an input of possible answers to horizontal clues and vertical clues, how is the successor state function defined? Please first think step by step. Then provide the successor state function in Python code. 

The possible clues for each row and each column are given separately. Here is an example of possible horizontal and vertical clues:

horizontal_answers = [
        ["tasks", "goals", "plans", "agend", "chores", "works", "deeds", "items", "lists", "brief"],
        ["motor", "power", "drive", "diesel", "steam", "pumps", "crank", "gears", "turbn", "motor"],
        ["grand", "artsy", "showy", "ornate", "fancy", "vain", "proud", "vogue", "swank", "luxus"], 
        ["venue", "salle", "forum", "atria", "lobby", "parls", "court", "malls", "mall", "lobby"], 
        ["jeer", "scoff", "sleer", "deris", "sneer", "scorn", "derid", "gibes", "gibed", "flout"] 
]
vertical_answers = [
        ["amass", "stack", "hoard", "pile", "store", "heaps", "massy", "gathe", "lumps", "mound"],
        ["nilga", "goral", "eland", "lepus", "gazal", "kudu", "oryx", "gnu", "imps", "carb"],
        ["scheme", "design", "ettle", "nettle", "sting", "wiles", "plans", "ideas", "plots", "cocks"], 
        ["spout", "nosle", "snout", "mouth", "nostr", "ports", "inlet", "vents", "outlt", "beaks"], 
        ["drier", "arid", "sere", "parch", "dryer", "wring", "drear", "sear", "pall", "lack"]
]

where horizontal_answers is a list where element i is a list of possible answers to clue in row i, and vertical_answers is a list where element i is a list of possible answers to clue in column i.

Model response:
Successor State Function for 5x5 Mini Crosswords
```Python
def successor_state(state, horizontal_answers, vertical_answers):
    """
    Generates all possible successor states for the given 5x5 mini crossword state.

    Args:
    state (list of lists): 2D array representing the current puzzle state.
    horizontal_answers (list of lists): Possible answers to horizontal clues.
    vertical_answers (list of lists): Possible answers to vertical clues.

    Yields:
    list of lists: A possible successor state.
    """
    def is_valid(state, row, col, answer, direction):
        # Check if the answer can be placed at the given position
        if direction == 'h':
            if col + len(answer) > 5:
                return False
            for i, char in enumerate(answer):
                if state[row][col + i] is not None and state[row][col + i] != char:
                    return False
        else:
            if row + len(answer) > 5:
                return False
            for i, char in enumerate(answer):
                if state[row + i][col] is not None and state[row + i][col] != char:
                    return False
        return True

    def place_answer(state, row, col, answer, direction):
        # Place the answer at the given position
        new_state = [row[:] for row in state]
        if direction == 'h':
            for i, char in enumerate(answer):
                new_state[row][col + i] = char
        else:
            for i, char in enumerate(answer):
                new_state[row + i][col] = char
        return new_state

    # Generate all possible successor states
    for row in range(5):
        for col in range(5):
            if state[row][col] is None:
                # Try to place horizontal answers
                for answer in horizontal_answers[row]:
                    if is_valid(state, row, col, answer, 'h'):
                        yield place_answer(state, row, col, answer, 'h')
                # Try to place vertical answers
                for answer in vertical_answers[col]:
                    if is_valid(state, row, col, answer, 'v'):
                        yield place_answer(state, row, col, answer, 'v')
```
This function generates all possible successor states by trying to place each possible answer at each empty position in the grid. It checks if the answer can be placed at the given position without conflicting with existing letters, and if so, yields the resulting state. The is_valid function checks if an answer can be placed at a given position, and the place_answer function creates a new state with the answer placed at the given position.
Generated by Meta Llama 3.1-405B

AutoToS prompt:

Please provide a goal test function in Python ensuring that all cells are not None, all words horizontally are matching at least one of the horizontal answers, and all words vertically match at least one of the vertical answers. The function should receive a state, horizontal_answers, and vertical_answers as before and return True for a goal state and False otherwise.

Model response:
Goal Test Function for 5x5 Mini Crosswords
```Python
def is_goal_state(state, horizontal_answers, vertical_answers):
    """
    Checks if the given state is a goal state.

    Args:
    state (list of lists): 2D array representing the current puzzle state.
    horizontal_answers (list of lists): Possible answers to horizontal clues.
    vertical_answers (list of lists): Possible answers to vertical clues.

    Returns:
    bool: True if the state is a goal state, False otherwise.
    """
    def is_valid_word(word, answers):
        # Check if the word matches at least one of the answers
        return any(len(word) == len(answer) and all(a == b for a, b in zip(word, answer)) for answer in answers)

    # Check if all cells are not None
    if any(cell is None for row in state for cell in row):
        return False

    # Check horizontal words
    for row in range(5):
        word = ''.join(state[row])
        if not is_valid_word(word, horizontal_answers[row]):
            return False

    # Check vertical words
    for col in range(5):
        word = ''.join(state[row][col] for row in range(5))
        if not is_valid_word(word, vertical_answers[col]):
            return False

    return True
```
This function first checks if all cells in the state are not None. Then, it checks each horizontal word and each vertical word to ensure that they match at least one of the corresponding answers. If all checks pass, it returns True, indicating that the state is a goal state. Otherwise, it returns False. The is_valid_word function checks if a word matches at least one of the answers by comparing the word with each answer.
Generated by Meta Llama 3.1-405B

System message:
Goal Soundness Test Passed
Soundness test

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Evaluating the final outcome
Success: 20, failure: 0, total expansions 4514757, total generated 16830232
