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 = [0] # vertices to be explored, start at 0 R = [] # path from start node next_ = [0] * 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 seen[neighbor].add(node) # mark backward arc 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 = [0] # vertices to be explored, start at 0 R = [] # path from start node next_ = [0] * 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