# A time complexity question

Cheryl Scodario

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posted 5 years ago

- 1

What's the time complexity to remove an element from a sorted and unsorted linked list? I have heard different answers. I mean for remove, do we need to concern with the "find" part? Because in an unsorted linked list, you need to find it first, which takes O(n), though the remove action itself just takes 1. So do we say N or 1? Sorted and unsorted have the same time complexity I think. Insert also has to do with "find".

Thanks!

Thanks!

Campbell Ritchie

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Posts: 50687

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posted 5 years ago

In an ArrayList, however, it would be O(log

*n*) if it is already sorted and O(*n*) if not sorted. If you already know the index, it would be constant time. To obtain the logarithmic time you would need a binary search to find the element to remove.
posted 5 years ago

Actually, no. Removing an element from an ordered array or ArrayList takes

Removing from a linked list does, indeed, always take constant time.

Campbell Ritchie wrote:In an ArrayList, however, it would be O(logn) if it is already sorted and O(n) if not sorted. If you already know the index, it would be constant time. To obtain the logarithmic time you would need a binary search to find the element to remove.

Actually, no. Removing an element from an ordered array or ArrayList takes

*linear*time, because after you remove the element, you then have to move an average of N/2 elements down to fill the "hole". If order doesn't matter, then you can just move the last element, and that does take constant time; of course, then you might as well have been using a Set rather than a List in the first place.

Removing from a linked list does, indeed, always take constant time.

Cheryl Scodario

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Posts: 69

posted 5 years ago

Hi Ernest, why removing from a linked list always takes constant time? Because I kinda agree with Jesper that it will have to find the element to remove first, then actually do the remove action.

Ernest Friedman-Hill wrote:

Removing from a linked list does, indeed, always take constant time.

Hi Ernest, why removing from a linked list always takes constant time? Because I kinda agree with Jesper that it will have to find the element to remove first, then actually do the remove action.

posted 5 years ago

Removing does not always imply finding. For example, consider removing the first element of a list. For a linked list, it's done in constant time, and for an array or ArrayList, it takes linear time.

Cheryl Scodario wrote:Ernest Friedman-Hill wrote:

Removing from a linked list does, indeed, always take constant time.

Hi Ernest, why removing from a linked list always takes constant time? Because I kinda agree with Jesper that it will have to find the element to remove first, then actually do the remove action.

*Finding*an object takes linear time; subsequently

*removing*it takes constant time. For an array,

*finding*takes linear time for unsorted, and logarithmic time for a sorted list; and

*removing*takes linear time.

Removing does not always imply finding. For example, consider removing the first element of a list. For a linked list, it's done in constant time, and for an array or ArrayList, it takes linear time.

Campbell Ritchie

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Cheryl Scodario

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Posts: 69

posted 5 years ago

I see...How about insert in a sorted list? I always think of remove and insert very similar. But is insert implying find for sure? Because you need to find the right position to insert it. Then it would be N, linear time?

Ernest Friedman-Hill wrote:Cheryl Scodario wrote:Ernest Friedman-Hill wrote:

Removing from a linked list does, indeed, always take constant time.

Hi Ernest, why removing from a linked list always takes constant time? Because I kinda agree with Jesper that it will have to find the element to remove first, then actually do the remove action.

Findingan object takes linear time; subsequentlyremovingit takes constant time. For an array,findingtakes linear time for unsorted, and logarithmic time for a sorted list; andremovingtakes linear time.

Removing does not always imply finding. For example, consider removing the first element of a list. For a linked list, it's done in constant time, and for an array or ArrayList, it takes linear time.

I see...How about insert in a sorted list? I always think of remove and insert very similar. But is insert implying find for sure? Because you need to find the right position to insert it. Then it would be N, linear time?

Cheryl Scodario

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Posts: 69