# Source code for tryalgo.eulerian_tour

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""\
Eulerian cycle
jill-jênn vie et christoph dürr - 2015-2020
"""

import random
from tryalgo.graph import write_graph

# snip{ eulerian_tour_undirected
[docs]def eulerian_tour_undirected(graph):
"""Eulerian tour on an undirected graph

:param graph: directed graph in listlist format, cannot be listdict
:assumes: graph is eulerian
:returns: eulerian cycle as a vertex list
:complexity: O(|V|+|E|)
"""
P = []                            # resulting tour
Q =                            # vertices to be explored, start at 0
R = []                            # path from start node
next_ =  * len(graph)          # initialize next_ to 0 for each node
seen = [set() for _ in graph]     # mark backward arcs
while Q:
start = Q.pop()               # explore a cycle from start node
node = start                            # current node on cycle
while next_[node] < len(graph[node]):   # visit all allowable arcs
neighbor = graph[node][next_[node]]  # traverse an arc
next_[node] += 1                     # mark arc traversed
if neighbor not in seen[node]:      # not yet traversed
R.append(neighbor)              # append to path from start
node = neighbor                 # move on
while R:
Q.append(R.pop())         # add to Q the discovered cycle R
P.append(start)               # resulting path P is extended
return P
# snip}

# snip{ eulerian_tour_directed
[docs]def eulerian_tour_directed(graph):
"""Eulerian tour on a directed graph

:param graph: directed graph in listlist format, cannot be listdict
:assumes: graph is eulerian
:returns: eulerian cycle as a vertex list
:complexity: O(|V|+|E|)
"""
P = []                            # resulting tour
Q =                            # vertices to be explored, start at 0
R = []                            # path from start node
next_ =  * len(graph)          # initialize next_ to 0 for each node
while Q:
start = Q.pop()               # explore a cycle from start node
node = start                            # current node on cycle
while next_[node] < len(graph[node]):   # visit all allowable arcs
neighbor = graph[node][next_[node]]  # traverse an arc
next_[node] += 1                     # mark arc traversed
R.append(neighbor)                  # append to path from start
node = neighbor                     # move on
while R:
Q.append(R.pop())         # add to Q the discovered cycle R
P.append(start)               # resulting path P is extended
return P
# snip}

[docs]def write_cycle(filename, graph, cycle, directed):
"""Write an eulerian tour in DOT format

:param filename: the file to be written in DOT format
:param graph: graph in listlist format, cannot be listdict
:param bool directed: describes the graph
:param cycle: tour as a vertex list
:returns: nothing
:complexity: O(|V|^2 + |E|)
"""
n = len(graph)
weight = [[float('inf')] * n for _ in range(n)]
for r in range(1, len(cycle)):
weight[cycle[r-1]][cycle[r]] = r
if not directed:
weight[cycle[r]][cycle[r-1]] = r
write_graph(filename, graph, arc_label=weight, directed=directed)

[docs]def random_eulerien_graph(n):
"""Generates some random eulerian graph

:param int n: number of vertices
:returns: undirected graph in listlist representation
:complexity: linear
"""
graphe = [[] for _ in range(n)]
for v in range(n - 1):
noeuds = random.sample(range(v + 1, n), random.choice(
range(0 if len(graphe[v]) % 2 == 0 else 1, (n - v), 2)))
graphe[v].extend(noeuds)
for w in graphe[v]:
if w > v:
graphe[w].append(v)
return graphe

[docs]def is_eulerian_tour(graph, tour):
"""Eulerian tour on an undirected graph

:param graph: directed graph in listlist format, cannot be listdict
:param tour: vertex list
:returns: test if tour is eulerian
:complexity: O(|V|*|E|) under the assumption that
set membership is in constant time
"""
m = len(tour)-1
arcs = set((tour[i], tour[i+1]) for i in range(m))
if len(arcs) != m:
return False
for (u, v) in arcs:
if v not in graph[u]:
return False
return True