time complexity when working with python string

Question

I’m analysing the complexity of string concatination for different methods and what I notice.

%%time
sent = ""
word = "hello "
num = 100000
for _ in range(num):
    sent += word

this method takes 20ms

%%time
sent_1 = "".join([word] * num)

the second method takes 4 ms and

%%time
sent_2 = ""
for _ in range(num//5):
    sent_2 = sent_2 + word + word + word + word + word

the third method takes 208 ms

sent==sent_1==sent_2
gives me True

can someone explain why I get such results

Asked By: Влад Лещук

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Source

Answer 1

sent2 + word + word + word + word + word creates multiple temporary str objects, roughly equivalent to

t1 = sent2 + word
t2 = t1 + word
t3 = t2 + word
t4 = t3 + word
sent_2= t4 + word

Creating all these objects (and copying the ever-growing values of one temporary value into another) results in a quadratic runtime.

''.join([word] * num), on the other hand, gets all the strings to concatenate at once in a single list, so it can allocate one result string and copy the substring in place in linear time.

The first example,

for _ in range(num):
    sent += word

should be equivalent to repeated concatenation. But, CPython in particular optimizes this by recognizing that nobody can access the value of sent while sent + word is being computed, so it "cheats" and updates sent in place, with no new string being allocated to assign back to sent. This means you still have a linear-time operation, like ''.join, but with extra overhead due to iterating over the string in Python rather than at the C level of the interpreter.

Answered By: chepner

time complexity when working with python string

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