alexgolec

def count_sequences(start_position, num_hops):
    cache = {}

    def helper(position, num_hops):
        if (position, num_hops) in cache:
            return cache[ (position, num_hops) ]

        if num_hops == 0:
            return 1

alexgolec

from neighbors import neighbors                                 
                                                                
def count_sequences(start_position, num_hops):                  
    if num_hops == 0:                                           
        return 1                                                
                                                                
    num_sequences = 0                                           
    for position in neighbors(start_position):                  
        num_sequences += count_sequences(position, num_hops - 1)
    return num_sequences                                        

alexgolec

def yield_sequences(starting_position, num_hops, sequence=None):
    if sequence is None:
        sequence = [starting_position]
    
    if num_hops == 0:
        yield sequence
        return

    for neighbor in neighbors(starting_position):
        yield from yield_sequences(

alexgolec

NEIGHBORS_MAP = {
    1: (6, 8),
    2: (7, 9),
    3: (4, 8),
    4: (3, 9, 0),
    5: tuple(),  # 5 has no neighbors
    6: (1, 7, 0),
    7: (2, 6),
    8: (1, 3),
    9: (2, 4),