very well done FEN BW MTM == 5 OK

import chess

def simplify_fen(fen):
    """Simplifies a FEN string to only include position, turn, castling availability, and en passant target."""
    return ' '.join(fen.split(' ')[:4])

def add_descendants_iteratively(game_tree, fen_to_node_id):
    """Expands the game tree by iteratively adding legal move descendants of each game state."""
    queue = [(1, 0)]
    while queue:
        node_id, _ = queue.pop(0)
        board = chess.Board(game_tree[node_id]['fen'] + " 0 1")
        for move in board.legal_moves:
            move = chess.Move(move.from_square, move.to_square, promotion=chess.QUEEN) if move.promotion else move
            board.push(move)
            simplified_fen = simplify_fen(board.fen())
            if simplified_fen not in fen_to_node_id:
                new_node_id = len(game_tree) + 1
                game_tree[new_node_id] = {
                    'fen': simplified_fen,
                    'moves_to_mate': None,
                    'parent': node_id,
                    'color': chess.WHITE if board.turn else chess.BLACK,
                    'result': None,
                    'processed': False,
                    'sequence': [],
                    'children': [],
                    'to_end': None,
                }
                fen_to_node_id[simplified_fen] = new_node_id
                game_tree[node_id]['children'].append(new_node_id)
                queue.append((new_node_id, 0))
            board.pop()

def initialize_game_tree(initial_fen):
    """Initializes the game tree with the root node based on the initial FEN."""
    simplified_fen = simplify_fen(initial_fen)
    game_tree = {1: {'fen': simplified_fen, 'moves_to_mate': None, 'parent': None,
                     'color': chess.WHITE if 'w' in initial_fen else chess.BLACK,
                     'result': None, 'processed': False, 'sequence': [], 'children': [], 'to_end': None}}
    fen_to_node_id = {simplified_fen: 1}
    return game_tree, fen_to_node_id

def update_game_outcomes(game_tree):
    """Updates game outcomes based on the current board state for each node."""
    for node in game_tree.values():
        board = chess.Board(node['fen'] + " 0 1")
        if board.is_game_over():
            outcome = board.outcome()
            node['processed'] = True
            node['result'] = 1 if outcome and outcome.winner == chess.WHITE else -1 if outcome and outcome.winner == chess.BLACK else 0
            node['moves_to_mate'] = 0 if node['result'] != 0 else None
            node['to_end'] = 0


def update_parent_preferences(node_id, game_tree, stronger):
    node = game_tree[node_id]
    if node['processed']:
        return node['to_end'], node['moves_to_mate'], node['result']

    is_maximizing = node['color'] == stronger
    desired_result = 1 if stronger == chess.WHITE else -1

    # Initialize best_path_length based on whether we are maximizing or minimizing
    best_path_length = None  # We start with None to be agnostic about the direction of comparison initially
    best_child_id = None
    best_result = None

    for child_id in node['children']:
        _, child_moves_to_mate, child_result = update_parent_preferences(child_id, game_tree, stronger)
        if child_moves_to_mate is None:
            continue

        # Decide when to update based on maximizing or minimizing player logic
        if is_maximizing:
            # For maximizing, we look for a smaller number than currently best (shortest path to checkmate)
            if best_path_length is None or (child_moves_to_mate < best_path_length):
                best_path_length, best_child_id, best_result = child_moves_to_mate, child_id, child_result
        else:
            # For minimizing, we look for a larger number than currently best (longest path to avoid checkmate)
            if best_path_length is None or (child_moves_to_mate > best_path_length):
                best_path_length, best_child_id, best_result = child_moves_to_mate, child_id, child_result

    if best_child_id is not None:
        node['sequence'] = [best_child_id]
        node['result'] = best_result
        node['to_end'] = best_path_length + 1 if best_path_length is not None else None
        node['moves_to_mate'] = best_path_length + 1 if best_result == desired_result else None
    else:
        node['to_end'], node['moves_to_mate'], node['sequence'] = None, None, []

    node['processed'] = True
    return node['to_end'], node['moves_to_mate'], node['result']


def print_sequence_from_root(A):
    current_node_id = 1
    A[1]['sequence'] = [29]
 #   A[1]['sequence'] = [13]

    while True:
        node = A[current_node_id]
        board = chess.Board(node['fen'] + " 0 1")
        print(f"Node ID: {current_node_id}, Moves to Mate: {node['moves_to_mate']}, Result: {node['result']}")
        print(board, "\n", node['fen'],"\n\n")

        if not node['sequence']:
            break
        current_node_id = node['sequence'][0]


def main():
    initial_fen = "7Q/8/8/6k1/2K5/8/8/8 w - - 0 1"
    initial_fen = "8/5k1Q/3K4/8/8/8/8/8 b - - 0 1"
    initial_fen = "8/2k5/8/5Q2/8/8/2K5/8 w - - 0 1"

    initial_fen = "2k5/8/5Q2/3K4/8/8/8/8 w - - 0 1"

    game_tree, fen_to_node_id = initialize_game_tree(initial_fen)
    add_descendants_iteratively(game_tree, fen_to_node_id)
    update_game_outcomes(game_tree)
    update_parent_preferences(1, game_tree, chess.WHITE)
    print("Final Output:")
    print(game_tree[1])
    print(game_tree[2])
    print(game_tree[3])
    print(game_tree[4])

    print_sequence_from_root(game_tree)

    for key in range(1,20000):
        if game_tree[key]['to_end'] != None: # and A[key]['to_end'] > 9:
            print(f"{key}:: {game_tree[key]['to_end']} {game_tree[key]}\n{chess.Board(game_tree[key]['fen'])}<\n")



if __name__ == "__main__":
    main()