# Path: tryalgo/graph.py
# def write_graph(dotfile, graph, directed=False,
#                 node_label=None, arc_label=None, comment="",
#                 node_mark=set(), arc_mark=set()):
#     """Writes a graph to a file in the DOT format
# 
#     :param dotfile: the filename.
#     :param graph: directed graph in listlist or listdict format
#     :param directed: true if graph is directed, false if undirected
#     :param weight: in matrix format or same listdict graph or None
#     :param node_label: vertex label table or None
#     :param arc_label: arc label matrix or None
#     :param comment: comment string for the dot file or None
#     :param node_mark: set of nodes to be shown in gray
#     :param arc_marc: set of arcs to be shown in red
#     :complexity: `O(|V| + |E|)`
#     """
#     with open(dotfile, 'w') as f:
#         if directed:
#             f.write("digraph G{\n")
#         else:
#             f.write("graph G{\n")
#         if comment:
#             f.write('label="%s";\n' % comment)
#         V = range(len(graph))
#         #                              -- vertices
#         for u in V:
#             if node_mark and u in node_mark:
#                 f.write('%d [style=filled, color="lightgrey", ' % u)
#             else:
#                 f.write('%d [' % u)
#             if node_label:
#                 f.write('label="%u [%s]"];\n' % (u, node_label[u]))
#             else:
#                 f.write('shape=circle, label="%u"];\n' % u)
#         #                              -- edges
#         if isinstance(arc_mark, list):
#             arc_mark = set((u, arc_mark[u]) for u in V)
#         for u in V:
#             for v in graph[u]:
#                 if not directed and u > v:
#                     continue   # don't show twice the edge
#                 if arc_label and arc_label[u][v] is None:
#                     continue   # suppress arcs with no label
#                 if directed:
#                     arc = "%d -> %d " % (u, v)
#                 else:
#                     arc = "%d -- %d " % (u, v)
#                 if arc_mark and ((v, u) in arc_mark or
#                                  (not directed and (u, v) in arc_mark)):
#                     pen = 'color="red"'
#                 else:
#                     pen = ""
#                 if arc_label:
#                     tag = 'label="%s"' % arc_label[u][v]
#                 else:
#                     tag = ""
#                 if tag and pen:
#                     sep = ", "
#                 else:
#                     sep = ""
#                 f.write(arc + "[" + tag + sep + pen + "];\n")
#         f.write("}")


import random
from tryalgo.graph import write_graph
        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}


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

# Path: tryalgo/graph.py
# def write_graph(dotfile, graph, directed=False,
#                 node_label=None, arc_label=None, comment="",
#                 node_mark=set(), arc_mark=set()):
#     """Writes a graph to a file in the DOT format
# 
#     :param dotfile: the filename.
#     :param graph: directed graph in listlist or listdict format
#     :param directed: true if graph is directed, false if undirected
#     :param weight: in matrix format or same listdict graph or None
#     :param node_label: vertex label table or None
#     :param arc_label: arc label matrix or None
#     :param comment: comment string for the dot file or None
#     :param node_mark: set of nodes to be shown in gray
#     :param arc_marc: set of arcs to be shown in red
#     :complexity: `O(|V| + |E|)`
#     """
#     with open(dotfile, 'w') as f:
#         if directed:
#             f.write("digraph G{\n")
#         else:
#             f.write("graph G{\n")
#         if comment:
#             f.write('label="%s";\n' % comment)
#         V = range(len(graph))
#         #                              -- vertices
#         for u in V:
#             if node_mark and u in node_mark:
#                 f.write('%d [style=filled, color="lightgrey", ' % u)
#             else:
#                 f.write('%d [' % u)
#             if node_label:
#                 f.write('label="%u [%s]"];\n' % (u, node_label[u]))
#             else:
#                 f.write('shape=circle, label="%u"];\n' % u)
#         #                              -- edges
#         if isinstance(arc_mark, list):
#             arc_mark = set((u, arc_mark[u]) for u in V)
#         for u in V:
#             for v in graph[u]:
#                 if not directed and u > v:
#                     continue   # don't show twice the edge
#                 if arc_label and arc_label[u][v] is None:
#                     continue   # suppress arcs with no label
#                 if directed:
#                     arc = "%d -> %d " % (u, v)
#                 else:
#                     arc = "%d -- %d " % (u, v)
#                 if arc_mark and ((v, u) in arc_mark or
#                                  (not directed and (u, v) in arc_mark)):
#                     pen = 'color="red"'
#                 else:
#                     pen = ""
#                 if arc_label:
#                     tag = 'label="%s"' % arc_label[u][v]
#                 else:
#                     tag = ""
#                 if tag and pen:
#                     sep = ", "
#                 else:
#                     sep = ""
#                 f.write(arc + "[" + tag + sep + pen + "];\n")
#         f.write("}")


# Path: tryalgo/eulerian_tour.py
import random
from tryalgo.graph import write_graph

        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}


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)