1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
# Authors: William Mill (bill@billmill.org)
# License: BSD 3 clause
import numpy as np
class DrawTree:
def __init__(self, tree, parent=None, depth=0, number=1):
self.x = -1.0
self.y = depth
self.tree = tree
self.children = [
DrawTree(c, self, depth + 1, i + 1) for i, c in enumerate(tree.children)
]
self.parent = parent
self.thread = None
self.mod = 0
self.ancestor = self
self.change = self.shift = 0
self._lmost_sibling = None
# this is the number of the node in its group of siblings 1..n
self.number = number
def left(self):
return self.thread or len(self.children) and self.children[0]
def right(self):
return self.thread or len(self.children) and self.children[-1]
def lbrother(self):
n = None
if self.parent:
for node in self.parent.children:
if node == self:
return n
else:
n = node
return n
def get_lmost_sibling(self):
if not self._lmost_sibling and self.parent and self != self.parent.children[0]:
self._lmost_sibling = self.parent.children[0]
return self._lmost_sibling
lmost_sibling = property(get_lmost_sibling)
def __str__(self):
return "%s: x=%s mod=%s" % (self.tree, self.x, self.mod)
def __repr__(self):
return self.__str__()
def max_extents(self):
extents = [c.max_extents() for c in self.children]
extents.append((self.x, self.y))
return np.max(extents, axis=0)
def buchheim(tree):
dt = first_walk(DrawTree(tree))
min = second_walk(dt)
if min < 0:
third_walk(dt, -min)
return dt
def third_walk(tree, n):
tree.x += n
for c in tree.children:
third_walk(c, n)
def first_walk(v, distance=1.0):
if len(v.children) == 0:
if v.lmost_sibling:
v.x = v.lbrother().x + distance
else:
v.x = 0.0
else:
default_ancestor = v.children[0]
for w in v.children:
first_walk(w)
default_ancestor = apportion(w, default_ancestor, distance)
# print("finished v =", v.tree, "children")
execute_shifts(v)
midpoint = (v.children[0].x + v.children[-1].x) / 2
w = v.lbrother()
if w:
v.x = w.x + distance
v.mod = v.x - midpoint
else:
v.x = midpoint
return v
def apportion(v, default_ancestor, distance):
w = v.lbrother()
if w is not None:
# in buchheim notation:
# i == inner; o == outer; r == right; l == left; r = +; l = -
vir = vor = v
vil = w
vol = v.lmost_sibling
sir = sor = v.mod
sil = vil.mod
sol = vol.mod
while vil.right() and vir.left():
vil = vil.right()
vir = vir.left()
vol = vol.left()
vor = vor.right()
vor.ancestor = v
shift = (vil.x + sil) - (vir.x + sir) + distance
if shift > 0:
move_subtree(ancestor(vil, v, default_ancestor), v, shift)
sir = sir + shift
sor = sor + shift
sil += vil.mod
sir += vir.mod
sol += vol.mod
sor += vor.mod
if vil.right() and not vor.right():
vor.thread = vil.right()
vor.mod += sil - sor
else:
if vir.left() and not vol.left():
vol.thread = vir.left()
vol.mod += sir - sol
default_ancestor = v
return default_ancestor
def move_subtree(wl, wr, shift):
subtrees = wr.number - wl.number
# print(wl.tree, "is conflicted with", wr.tree, 'moving', subtrees,
# 'shift', shift)
# print wl, wr, wr.number, wl.number, shift, subtrees, shift/subtrees
wr.change -= shift / subtrees
wr.shift += shift
wl.change += shift / subtrees
wr.x += shift
wr.mod += shift
def execute_shifts(v):
shift = change = 0
for w in v.children[::-1]:
# print("shift:", w, shift, w.change)
w.x += shift
w.mod += shift
change += w.change
shift += w.shift + change
def ancestor(vil, v, default_ancestor):
# the relevant text is at the bottom of page 7 of
# "Improving Walker's Algorithm to Run in Linear Time" by Buchheim et al,
# (2002)
# https://citeseerx.ist.psu.edu/doc_view/pid/1f41c3c2a4880dc49238e46d555f16d28da2940d
if vil.ancestor in v.parent.children:
return vil.ancestor
else:
return default_ancestor
def second_walk(v, m=0, depth=0, min=None):
v.x += m
v.y = depth
if min is None or v.x < min:
min = v.x
for w in v.children:
min = second_walk(w, m + v.mod, depth + 1, min)
return min
class Tree:
def __init__(self, label="", node_id=-1, *children):
self.label = label
self.node_id = node_id
if children:
self.children = children
else:
self.children = []
|
