#!/usr/bin/python

# outputs the automaton as a graphviz dot file, arranging the vertices
# in levels according to their distance from the starting vertex
# to convert to a PDF, run:
# ./dot_graph.py | dot -Tpdf > output.pdf

import coxeter_automaton
from collections import deque

coxeter_matrix = [[1, 3, 3],
                  [3, 1, 3],
                  [3, 3, 1]]

# coxeter_matrix = [[1, 2, 0, 0, 0, 2],
#                   [2, 1, 2, 0, 0, 0],
#                   [0, 2, 1, 2, 0, 0],
#                   [0, 0, 2, 1, 2, 0],
#                   [0, 0, 0, 2, 1, 2],
#                   [2, 0, 0, 0, 2, 1]]

#coxeter_matrix = [[1, 0, 0],
#                  [0, 1, 0],
#                  [0, 0, 1]]

graph = coxeter_automaton.generate_automaton_coxeter_matrix(coxeter_matrix, lex_reduced = True)

#graph = coxeter_automaton.even_graph(graph)

colors = {0: "red", 1: "darkgreen", 2: "blue", 3: "orange", 4: "black", 5: "gray"}

todo = deque([0])
distances = [None]*len(graph)
distances[0] = 0

while todo:
    node = todo.pop()
    for newnode in graph[node]:
        if newnode:
            if not distances[newnode] or distances[newnode] > distances[node] + 1:
                distances[newnode] = distances[node] + 1
                todo.appendleft(newnode)

max_distance = max(filter(None, distances))
nodes_by_distance = [[] for _ in range(max_distance+1)]
for n,d in enumerate(distances):
    if d != None:
        nodes_by_distance[d].append(n)

print('digraph test123 {')
for dn in nodes_by_distance:
    print('{rank = same; %s}' % "; ".join([str(x) for x in dn]))

for i,node in enumerate(graph):
    for edge,j in enumerate(node):
        if j:
#            print('{i:d} -> {j:d} [color={color}];'.format(i = i, j = j, color = "black"))
            print('{i:d} -> {j:d} [color={color}];'.format(i = i, j = j, color = colors[edge]))

print('}')