def path_large_unjumble(n):
d = defaultdict(list)
for t in listAllFreeTrees(n):
g, edge_lbls = gen_tree_edge_list_from_list(t)
d[path_f({}, g).expand()].append(tuple(t))
# d[path_f({}, g).expand()] += 1
return d
def max_path_small_unjumble_with_weighted(n, weights=(1, 2)):
d = defaultdict(list)
for t in listAllFreeTrees(n):
# print t
g, edge_lbls = gen_tree_edge_list_from_list(t)
mp = find_maximal_paths(g)
# print mp
for lbl in get_labeled_graphs(t, 2, True):
coloring = []
# sc = []
for mpindex in xrange(len(mp)):
p = mp[mpindex]
w = 0
for i in xrange(1, len(p)):
x, y = min(p[i], p[i - 1]), max(p[i], p[i - 1])
w += weights[lbl[edge_lbls[(x, y)]]]
# if mpindex > 0 and len(mp[mpindex]) > len(mp[mpindex - 1]):
# coloring += sorted(sc)
# coloring.append("|")
# sc = []
# sc.append(str(w))
coloring.append(w)
# coloring += sorted(sc)
# print lbl, str(coloring)
# d[tuple(sorted(coloring))] += 1
d[tuple(sorted(coloring))].append((tuple(t), lbl))
# d[tuple(sorted(coloring))] += 1
return d
def path_small_unjumble_weights(n):
monomials = [[x**k * y**(i - k) for k in xrange(i + 1)] for i in xrange(1, n)]
monomials_weights = [[1 * k + 2 * (i - k) for k in xrange(i + 1)] for i in xrange(1, n)]
# d = defaultdict(int)
d = defaultdict(list)
for t in listAllFreeTrees(n):
g, edge_lbls = gen_tree_edge_list_from_list(t)
for lbl in get_labeled_graphs(t, 2, True):
f = path_labeled_f({}, edge_lbls, lbl, g).expand()
# wl = [] #[0] * (4 * (n + 1) + 1)
# for term in str(f).split("+"):
# term = term.strip()
# if term.find("x") != -1 and term.find("y") != -1:
# if term.count("*") > 1:
# ii = term.find("*")
# term1 = term[: ii]
# term2 = term[ii + 1 :].replace("x", "1").replace("y", "2").replace("*", "+").replace("^", "*")
# # print term, "t1", eval(term1 + "*(%s)"%term2)
# val = eval(term2)
# if val >= len(wl):
# wl += [0] * (val - len(wl) + 1)
# wl[val] += int(term1)
# else:
# # print term, "t2", eval(term.replace("x", "1").replace("y", "2").replace("*", "+").replace("^", "*"))
# val = eval(term.replace("x", "1").replace("y", "2").replace("*", "+").replace("^", "*"))
# if val >= len(wl):
# wl += [0] * (val - len(wl) + 1)
# wl[val] += 1
# elif not term.isdigit():
# # print term, "t3", eval(term.replace("x", "1").replace("y", "2").replace("^", "*"))
# ii = term.find("*")
# if ii != -1:
# term1 = term[: ii]
# term2 = term[ii + 1:]
# val = eval(term2.replace("x", "1").replace("y", "2").replace("^", "*"))
# if val >= len(wl):
# wl += [0] * (val - len(wl) + 1)
# wl[val] += int(term1)
# else:
# val = eval(term.replace("x", "1").replace("y", "2").replace("^", "*"))
# if val >= len(wl):
# wl += [0] * (val - len(wl) + 1)
# wl[val] += 1
# print tuple([wl[k] for k in sorted(wl)])
wl = [0] * (sum(i + 1 for i in lbl) + 1)
for i in xrange(len(monomials)):
for j in xrange(i + 2):
amonomial = f.coefficient(monomials[i][j])(x=0, y=0)
if amonomial != 0:
wl[monomials_weights[i][j]] += amonomial
# print t, lbl, f, wl
d[tuple(wl)].append((f, t, lbl))
# d[str(wl)] += 1
return d
def path_small_unjumble_labeled(n):
d = defaultdict(list)
for t in listAllFreeTrees(n):
g, edge_lbls = gen_tree_edge_list_from_list(t)
# d[path_labeled_f({}, g).expand()] += 1
for lbl in get_labeled_graphs(t, 2, True):
d[path_labeled_f({}, edge_lbls, lbl, g).expand()].append((tuple(t), lbl))
# d[path_labeled_f({}, edge_lbls, lbl, g).expand()] += 1
return d
def max_path_small_unjumble(n):
d = defaultdict(list)
for t in listAllFreeTrees(n):
# print t
g, edge_lbls = gen_tree_edge_list_from_list(t)
mp = find_maximal_paths(g)
# print mp
for lbl in get_labeled_graphs(t, 2, True):
coloring = []
for mpindex in xrange(len(mp)):
p = mp[mpindex]
colorcnt = [0, 0]
for i in xrange(1, len(p)):
x, y = min(p[i], p[i - 1]), max(p[i], p[i - 1])
colorcnt[lbl[edge_lbls[(x, y)]]] += 1
# print "".join(map(str, get_smaller_color(acoloring))), lbl
coloring.append(tuple(colorcnt))
d[tuple(sorted(coloring))].append((tuple(t), lbl))
# d[tuple(sorted(coloring))] += 1
# print lbl, str(coloring)
# print d
return d
def max_path_large_unjumble(n):
d = defaultdict(list)
for t in listAllFreeTrees(n):
g, edge_lbls = gen_tree_edge_list_from_list(t)
d[tuple([len(p) for p in find_maximal_paths(g)])].append(tuple(t))
return d