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Go Deh: Indent datastructure for trees

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Article:

(published: Oct. 20, 2019, 5:46 p.m.)

I was browsing StackOverflow and came across a question that mentioned a new-to-me format for a datatructure for holding a tree of data.I am well used to the (name, list_of_children) set of interconnected node datastructures way of doing things, but this mentioned where you
  1. Create an empty list
  2.  then for each node starting at the root which has a depth of zero:
    1. add the (depth, name) tuple of the node to the list
    2. visit all this nodes child node.
It is a preorder traversal of the conceptual tree, aggregating (depth,  name) tuples into a list to form what I am calling the indent tree datastructure as it captures all the information of the tree but in a different datastructure than normal, and can be extended to allow data at each node and might be a useful alternative for DB storage of trees.

An example tree:





Its indent format:

[(0, 'R'),
(1, 'a'),
(2, 'c'),
(3, 'd'),
(3, 'h'),
(1, 'b'),
(2, 'e'),
(3, 'f'),
(4, 'g'),
(2, 'i')]

Indented representation:

If you print out successive names from the indent format list above, one per line, with indent from the left of the indent value, then you get a nice textual regpresentation of the tree; expanded left-to-right rather than the top-down representation of the graphic:


R
a
c
d
h
b
e
f
g
i


Code

I wrote some code to manipulate and traverse this kind of tree datastructure, as well as to use graphviz to draw graphical representations.


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import graphviz as gv
from collections import defaultdict
import re
from pprint import pprint as pp


#%%
node_attr = {at: val for at, val in
(line.strip().split() for line in '''
shape record
fontsize 12
height 0.1
width 0.1
rankdir LR
ranksep 0.25
nodesep 0.25
'''.strip().split('\n'))}
edge_attr = {at: val for at, val in
(line.strip().split() for line in '''
arrowhead none
minlen 1
'''.strip().split('\n'))}
root_attr = {at: val for at, val in
(line.strip().split() for line in '''
fontcolor green
color brown
fontname bold
'''.strip().split('\n'))}
#%%


def _pc2indent(pc, root=None, indent=None, children=None):
"parent-child dependency dict to indent format conversion"
if root is None:
parents = set(pc)
kids = set(sum(pc.values(), []))
root = parents - kids
assert len(root) == 1, f"Need exactly one root: {root}"
root = root.pop()
if indent is None:
indent = 0
if children is None:
children = []
children.append((indent, root))
if root in pc:
for child in pc[root]:
pc2indent(pc, child, indent+1, children)
return children

def dot2indent(tree):
"simple dot format to indent format translator"
depends = defaultdict(list)
for matchobj in re.finditer(r'\s+(\S+)\s*->\s*(\S+)\s', tree.source):
parent, child = matchobj.groups()
depends[parent].append(child)
parent2child = dict(depends)
return _pc2indent(parent2child)

#%%
def _highlight(txt):
return f'#{txt}#'

def pp_indent(data, hlight=None, indent=' '):
"simple printout of indent format tree with optional node highlighting"
if hlight is None:
hlight = set()
for level, name in data:
print(indent * level
+ (_highlight(name) if name in hlight else name))

#%%
def indent2dot(lst):
tree = gv.Digraph(name='indent2dot', node_attr=node_attr)
tree.edge_attr.update(**edge_attr)
levelparent = {}
for level, name in lst:
levelparent[level] = name
if level - 1 in levelparent:
tree.edge(levelparent[level-1], name)
else:
tree.node(name, _attributes=root_attr)
return tree

#%%
def printwithspace(i):
print(i, end=' ')

def preorder(tree, visitor=printwithspace):
for indent, name in tree:
visitor(name)

def levelorder(tree, reverse_depth=False, reverse_in_level=False,
visitor=printwithspace):
if not tree:
return
indent2name = defaultdict(list)
mx = -1
for indent, name in tree:
if indent > mx:
mx = indent
indent2name[indent].append(name)
if reverse_in_level:
for names in indent2name.values():
names.reverse()
if not reverse_depth:
for indent in range(0, mx + 1):
for name in indent2name[indent]:
visitor(name)
else:
for indent in range(mx, -1, -1):
for name in indent2name[indent]:
visitor(name)


#%%
# Example tree
ex1 = [(0, '1'),
(1, '2'),
(2, '4'),
(3, '7'),
(2, '5'),
(1, '3'),
(2, '6'),
(3, '8'),
(3, '9'),
(3, '10'),
]

#%%
if __name__ == '__main__':
print('A tree in indent datastructure format:')
pp(ex1)
print('\nSame tree, printed as indented list:')
pp_indent(ex1)
print('\nSame tree, drawn by graphviz:')
display(indent2dot(ex1)) # display works in spyder/Jupyter

print('\nSame tree, preorder traversal:')
preorder(ex1)
print()
print('Same tree, levelorder traversal:')
levelorder(ex1)
print()
print('Same tree, reverse_depth levelorder traversal:')
levelorder(ex1, True)
print()
print('Same tree, reverse_depth, reverse_in_level levelorder traversal:')
levelorder(ex1, True, True)
print()
print('Same tree, depth_first, reverse_in_level levelorder traversal:')
levelorder(ex1, False, True)
print()

Output:



A tree in indent datastructure format:
[(0, '1'),
(1, '2'),
(2, '4'),
(3, '7'),
(2, '5'),
(1, '3'),
(2, '6'),
(3, '8'),
(3, '9'),
(3, '10')]

Same tree, printed as indented list:

1
    2
        4
            7
        5
    3
        6
            8
            9
            10

Same tree, drawn by graphviz:


Same tree, preorder traversal:
1 2 4 7 5 3 6 8 9 10
Same tree, levelorder traversal:
1 2 3 4 5 6 7 8 9 10
Same tree, reverse_depth levelorder traversal:
7 8 9 10 4 5 6 2 3 1
Same tree, reverse_depth, reverse_in_level levelorder traversal:
10 9 8 7 6 5 4 3 2 1
Same tree, depth_first, reverse_in_level levelorder traversal:
1 3 2 6 5 4 10 9 8 7

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