Word puzzle - DFS with generator

puzzle.py

#!/usr/local/bin/python3
N = 4

DICTIONARY = set([
    'A',
    'AB',
    'ABC',
    'ABCDEDCB',
    'ABCDEFAFEDCDEDCB'
])


def dfs(N, i, j, board, path=[], visited=None, results=None):
    if visited is None:
        visited = {}
    if results is None:
        results = set()
    if not visited.get((i, j)):
        visited[i, j] = True
        path.append(board[i, j])
        word = ''.join(path)
        if (word in DICTIONARY) and (word not in results):
            results.add(word)
            yield word
        for di, dj in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
            if (0 <= i + di < N) and (0 <= j + dj < N):
                yield from dfs(N, i + di, j + dj, board, path, visited, results)

        path.pop()
        visited[(i, j)] = False


def gen_board(N):
    from itertools import product
    board = {}
    for i, j in product(range(N), range(N)):
        board[i, j] = 'ABCDEF'[(i + j) % 6]
    return board


board = gen_board(N)
for i in range(N):
    for j in range(N):
        print(board[i, j], end=' ')
    print()

results = dfs(N, 0, 0, board)
for word in results:
    print(word)