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Determine chain of words using complete set of input
Status: Accepted
'''
from sys import setrecursionlimit
from string import ascii_lowercase
setrecursionlimit(2048)
CATENYMS, MATRIX = None, None
LEN_WORDS = 0
###############################################################################
def start_end(in_degrees, out_degrees):
"""Determine the start and end nodes of a euler walk"""
valid = True
start, end = None, None
for letter in ascii_lowercase:
if in_degrees[letter] - out_degrees[letter] == 1:
valid &= (end is None)
end = letter
elif out_degrees[letter] - in_degrees[letter] == 1:
valid &= (start is None)
start = letter
elif out_degrees[letter] != in_degrees[letter]:
valid = False
if valid:
if start:
return start, end
for letter in ascii_lowercase:
if in_degrees[letter]:
return letter, letter
return None, None
###############################################################################
def dfs(location):
"""Determine longest possible path searching in lexicographic order"""
global LEN_WORDS, MATRIX, CATENYMS
if len(CATENYMS) == LEN_WORDS:
return True
for word in sorted(set(MATRIX[location])):
MATRIX[location].remove(word)
CATENYMS.append(word)
if dfs(word[-1]):
return True
CATENYMS.pop()
MATRIX[location].append(word)
return False
###############################################################################
def euler_walk(words):
"""Return lexicographically least traversal of all words"""
global LEN_WORDS, MATRIX, CATENYMS
CATENYMS = []
MATRIX, in_degree, out_degree = {}, {}, {}
for first_letter in ascii_lowercase:
out_degree[first_letter] = 0
in_degree[first_letter] = 0
MATRIX[first_letter] = []
for word in words:
in_degree[word[-1]] += 1
out_degree[word[0]] += 1
MATRIX[word[0]].append(word)
start, end = start_end(in_degree, out_degree)
if start and end:
LEN_WORDS = len(words)
if not dfs(start):
CATENYMS = []
###############################################################################
def main():
"""Read input and print output for euler walk with words as edges"""
global CATENYMS
for _ in range(int(input().strip())):
words = []
for _ in range(int(input().strip())):
words.append(input().strip())
euler_walk(words)
if CATENYMS:
print('.'.join(CATENYMS))
else:
print('***')
###############################################################################
if __name__ == '__main__':
main()
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