GATE1994-1.17, UGCNET-Sep2013-II: 32

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Linked lists are not suitable data structures for which one of the following problems?

1. Insertion sort

2. Binary search

4. Polynomial manipulation

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How is it helpful in case of other algorithms?
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Insertion sort: No need to swap here just find appropriate place and join the link

Polynomial manipulation: Linked List is a natural solution for polynomial manipulation

Radix sort: Here we are putting digits according to same position(unit,tens) into  buckets; which can be effectively handled by linked lists.

Not Suitable for:

Binary search: Because finding mid element itself takes $O(n)$ time.

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B also because Binary Search requires random access which isn't possible in case of Binary Search.
B. Because in binary search we need to have access to the mid of the list in constant time. and finding the mid itself in a linked list takes $O(n)$ time which makes no sense to Binary search which otherwise takes $O(\log n)$.

The binary search algorithm is based on the logic of reducing your input size by half in every step until your search succeeds or input  gets exhausted. The important point here is "the step to reduce input size should take constant time". In a case of an array, it's always a simple comparison based on array indexes that take O(1) time.

But in a case of Linked list, you don't have indexes to access items. To perform any operation on a list item, you first have to reach it by traversing all items before it. So to divide list by half you first have to reach the middle of the list then perform a comparison. Getting to the middle of the list takes O(n/2)[you have to traverse half of the list items] and comparison takes O(1).
Total = O(n/2) + O(1) = O(n/2)

So the input reduction step does not take constant time. It depends on list size. hence violates the essential requirement of Binary search.

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