Space Complexity with no variables defined
Question:
Suppose I had some code:
def foo(forest: list[list[int]]) -> int:
return sum([1 for tree in forest for leaf in tree])
In this code, no variables are defined. Everything is evaluated in one line, which means to my knowledge the data isn’t being stored anywhere. Does that mean this program has a space complexity of O(1)?
Thanks for your time.
Answers:
First, what is the n here?
I think there are two different variables of importance here, I’ll call them M = len(forest) and K = max(len(tree) for tree in forest).
Then the time complexity would be O(MK).
Next, the list you are constructing has a length of O(MK), so its space complexity is the same as the time complexity.
You can avoid that by using a generator expression instead of a list comprehension, like so:
return sum(1 for tree in forest for leaf in tree if leaf < 0)
This avoids having to store every value, only generating a single value at a time when calculating the sum, so its additional space complexity would be O(1).
Suppose I had some code:
def foo(forest: list[list[int]]) -> int:
return sum([1 for tree in forest for leaf in tree])
In this code, no variables are defined. Everything is evaluated in one line, which means to my knowledge the data isn’t being stored anywhere. Does that mean this program has a space complexity of O(1)?
Thanks for your time.
First, what is the n here?
I think there are two different variables of importance here, I’ll call them M = len(forest) and K = max(len(tree) for tree in forest).
Then the time complexity would be O(MK).
Next, the list you are constructing has a length of O(MK), so its space complexity is the same as the time complexity.
You can avoid that by using a generator expression instead of a list comprehension, like so:
return sum(1 for tree in forest for leaf in tree if leaf < 0)
This avoids having to store every value, only generating a single value at a time when calculating the sum, so its additional space complexity would be O(1).