Python dictionary vs list, which is faster?

Question

I was coding a Euler problem, and I ran into question that sparked my curiosity. I have two snippets of code. One is with lists the other uses dictionaries.

using lists:

n=100000
num=[]
suma=0
for i in range(n,1,-1):
    tmp=tuple(set([n for n in factors(i)]))
    if len(tmp) != 2: continue
    if tmp not in num:
       num.append(tmp)
           suma+=i

using dictionaries:

n=100000
num={}
suma=0
for i in range(n,1,-1):
   tmp=tuple(set([n for n in factors(i)]))
   if len(tmp) != 2: continue
   if tmp not in num:
      num[tmp]=i
      suma+=i

I am only concerned about performance. Why does the second example using dictionaries run incredibly fast, faster than the first example with lists. the example with dictionaries runs almost thirty-fold faster!

I tested these 2 code using n=1000000, and the first code run in 1032 seconds and the second one run in just 3.3 second,,, amazin'!

Answer 1

In Python, the average time complexity of a dictionary key lookup is O(1), since they are implemented as hash tables. The time complexity of lookup in a list is O(n) on average. In your code, this makes a difference in the line if tmp not in num:, since in the list case, Python needs to search through the whole list to detect membership, whereas in the dict case it does not except for the absolute worst case.

For more details, check out TimeComplexity.

Answer 2

If it's about speed, you should not create any lists:

n = 100000
factors = ((frozenset(factors(i)), i) for i in range(2, n+1))
num = {k:v for k,v in factors if len(k)==2}
suma = sum(num.values())

Answer 3

In a list, the code if tmp not in num: is O(n), while it is O(lgn) in dict.

Edit: The dict is based on hashing, so it is much quicker than liner list search. Thanks @user2357112 for point this.