Fernando Fernando - 1 year ago 51
Python Question

Counting word strokes while parsing Trie tree

I'm trying to solve the keyboard autocompletion problem described here.
The problem is to calculate how many keystrokes a word requires, given some dictionary and autocomplete rules. For example, for the dictionary:

data = ['hello', 'hell', 'heaven', 'goodbye']

We get the following results (please refer to the link above for further explanations):

{'hell': 2, 'heaven': 2, 'hello': 3, 'goodbye': 1}

Quick explanation: if the user types
, then
is autocompleted because all words starting with
also have
as second letter. Now if the user types in
, the other
is filled, giving 2 strokes for the word
. Of course,
would require one more stroke. Please, see the link above for more examples.

code is the following, and it works fine (taken from https://en.wikipedia.org/wiki/Trie). The
code is to parse the tree from root (see edit below):

class Stack(object):
def __init__(self, size):
self.data = [None]*size
self.i = 0
self.size = size

def pop(self):
if self.i == 0:
return None
item = self.data[self.i - 1]
self.i-= 1
return item

def push(self, item):
if self.i >= self.size:
return None
self.data[self.i] = item
self.i+= 1
return item

def __str__(self):
s = '# Stack contents #\n'
if self.i == 0:
for idx in range(self.i - 1, -1, -1):
s+= str(self.data[idx]) + '\n'
return s

class Trie(object):
def __init__(self, value, children):
self.value = value #char
self.children = children #{key, trie}

class PrefixTree(object):
def __init__(self, data):
self.root = Trie(None, {})
self.data = data

for w in data:
self.insert(w, w)

def insert(self, string, value):
node = self.root
i = 0
n = len(string)

while i < n:
if string[i] in node.children:
node = node.children[string[i]]
i = i + 1

while i < n:
node.children[string[i]] = Trie(string[:i], {})
node = node.children[string[i]]
i = i + 1

node.value = value

def find(self, key):
node = self.root
for char in key:
if char in node.children:
node = node.children[char]
return None
return node

I couldn't figure it out how to count the number of strokes:

data = ['hello', 'hell', 'heaven', 'goodbye']
tree = PrefixTree(data)
strokes = {w:1 for w in tree.data} #at least 1 stroke is necessary

And here's the code to parse the tree from the root:

stack = Stack(100)
stack.push((None, pf.root))
print 'Key\tChilds\tValue'
print '--'*25

strokes = {}

while stack.i > 0:
key, curr = stack.pop()

# if something:
#update strokes

print '%s\t%s\t%s' % (key, len(curr.children), curr.value)
for key, node in curr.children.items():
stack.push((key, node))

print strokes

Any idea or constructive comment would help, thanks!

Answer Source

The trie for your example can look like this

 ' '
|    \
H     G
|     |
E     O
| \   |
L  A  O
|  |  |
L$ V  D
|  |  |
O  E  B
   |  |
   N  Y

What nodes in the trie can be seen as markers for user key strokes? There are two types of such nodes:

  1. Inner nodes with more than one child, because the user has to choose among multiple alternatives.
  2. Nodes that represent the last letter of a word, but are not leaves (marked with $), because the user has to type the next letter if the current word is not what is needed.

While traversing the trie recursively one counts how many of these marker nodes were encountered before the last letter of a word was reached. This count is the number of strokes needed for the word.

For the word "hell" it is two marker nodes: ' ' and E (2 strokes).
For the word "hello" it is three marker nodes: ' ', E, L$ (3 strokes).
And so on...

What needs to be changed in your implementation:

The end of a valid word needs to be marked in the tree, so that the second condition can be checked. Therefore, we change the last line of the PrefixTree.insert() method from

node.value = value


node.value = value + '$'

Now we add a stroke counter for each stack item (the last value in the triple pushed to the stack) and the checks that increase the counter:

stack = Stack(100)
stack.push((None, tree.root, 0)) # We start with stroke counter = 0

strokes = {}

while stack.i > 0:
    key, curr, stroke_counter = stack.pop()

    if curr.value is not None and curr.value.endswith('$'):
        # The end of a valid word is reached. Save the word and the corresponding stroke counter.
        strokes[curr.value[:-1]] = stroke_counter

    if len(curr.children) > 1:
        # Condition 2 is true. Increase the stroke counter.
        stroke_counter += 1
    if curr.value is not None and curr.value.endswith('$') and len(curr.children) > 0:
        # Condition 1 is true. Increase the stroke counter.
        stroke_counter += 1

    print('%s\t%s\t%s' % (key, len(curr.children), curr.value))
    for key, node in curr.children.items():
        stack.push((key, node, stroke_counter)) # Save the stroke counter



Key Childs  Value
None    2   None
h   1   
e   2   h
a   1   he
v   1   hea
e   1   heav
n   0   heaven$
l   1   he
l   1   hell$
o   0   hello$
g   1   
o   1   g
o   1   go
d   1   goo
b   1   good
y   1   goodb
e   0   goodbye$
{'heaven': 2, 'goodbye': 1, 'hell': 2, 'hello': 3}
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