def eulerian_path(G: DirectedGraph) -> list:
"""
Find eulerian path in the given graph
Args:
graph to find eulerian path in
Return:
path if found or None if not found
"""
cycle = eulerian_cycle(G)
if cycle is not None:
return cycle
in_edges = [0] * G.V()
out_edges = [0] * G.V()
for u in range(G.V()):
for v, c in G.adj(u):
in_edges[v] += c
out_edges[u] += c
# start vertex
s = -1
cnt = 0
for v in range(G.V()):
if (in_edges[v] + out_edges[v]) % 2 == 1:
cnt += 1
if cnt > 2:
return None
if s == -1 or out_edges[s] % 2 == 0:
s = v
if s == -1:
return None
G = deepcopy(G)
E = G.E()
tour = []
cur = s
while True:
try:
tour.append(cur)
(v, c) = G.adj(cur).__next__()
G.remove_edge(DirectedEdge(cur, v))
cur = v
except StopIteration:
break
def selfloop(u: int):
nonlocal G
path = []
cur = u
while cur != u or not path:
path.append(cur)
(v, c) = G.adj(cur).__next__()
G.remove_edge(DirectedEdge(cur, v))
cur = v
path.append(u)
return path
index = 0
while index < len(tour):
try:
G.adj(tour[index]).__next__()
tour = tour[:index] + selfloop(tour[index]) + tour[index + 1:]
except StopIteration:
index += 1
return tour if len(tour) == E + 1 else None
#!/usr/bin/env python3
from common import IO
from graph.directed import Graph, GraphMatrix
from graph import algorithm
io = IO()
G = Graph.fromfile(io.filein)
G_matrix = GraphMatrix.from_graph(G)
# Eulerian cycle, part 1
io.section('Eulerian cycle')
eulerian_cycle = algorithm.eulerian_cycle(G_matrix)
if eulerian_cycle is not None:
io.print('Eulerian cycle found: ')
io.print_path(eulerian_cycle)
else:
io.print('Eulerian cycle not found!')
# Eulerian path, part 2
io.section('Eulerian path')
eulerian_path = algorithm.eulerian_path(G_matrix)
if eulerian_path is not None:
io.print('Eulerian path found: ')
io.print_path(eulerian_path)
else:
io.print('Eulerian path not found!')
# Hamiltonian cycle, part 1
io.section('Hamiltonian cycle')