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The concatenation of two lists is to be performed in O(1) time. Which of the following implementations of a list could be used?
- a)Singly linked list
- b)Doubly linked list
- c)Circular doubly linked list
- d)Array implementation of list
Correct answer is option 'C'. Can you explain this answer?
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The concatenation of two lists is to be performed in O(1) time. Which ...
In circular doubly linked list, one does not need to traverse the whole list to find the end of the list.
The second list can be concatenated at any location. Only fixed number of pointers need to be changed. Hence can be done in O(1) time.
The second list can be concatenated at any location. Only fixed number of pointers need to be changed. Hence can be done in O(1) time.
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The concatenation of two lists is to be performed in O(1) time. Which ...
Concatenation of Two Lists in O(1) Time
To perform concatenation of two lists in O(1) time, we need a data structure that supports constant time insertion and deletion at both ends of the list. Let's analyze each option given in the question:
a) Singly linked list: In a singly linked list, we can insert or delete a node at the beginning of the list in O(1) time, but we need to traverse the entire list to insert or delete a node at the end of the list, which takes O(n) time. Therefore, concatenation of two singly linked lists takes O(n) time.
b) Doubly linked list: In a doubly linked list, we can insert or delete a node at both ends of the list in O(1) time. Therefore, concatenation of two doubly linked lists takes O(1) time if we maintain a pointer to the last node of the first list and a pointer to the first node of the second list.
c) Circular doubly linked list: A circular doubly linked list is similar to a doubly linked list, but the last node points to the first node, forming a circular structure. This means that we can maintain a pointer to the last node of the first list and a pointer to the first node of the second list without any extra overhead. Therefore, concatenation of two circular doubly linked lists takes O(1) time.
d) Array implementation of list: In an array implementation of a list, we need to allocate a new array and copy the elements of both lists to the new array, which takes O(n) time. Therefore, concatenation of two arrays takes O(n) time.
Conclusion
The correct option for concatenation of two lists in O(1) time is a circular doubly linked list as it supports constant time insertion and deletion at both ends of the list, and maintains a circular structure to concatenate two lists without any extra overhead.
To perform concatenation of two lists in O(1) time, we need a data structure that supports constant time insertion and deletion at both ends of the list. Let's analyze each option given in the question:
a) Singly linked list: In a singly linked list, we can insert or delete a node at the beginning of the list in O(1) time, but we need to traverse the entire list to insert or delete a node at the end of the list, which takes O(n) time. Therefore, concatenation of two singly linked lists takes O(n) time.
b) Doubly linked list: In a doubly linked list, we can insert or delete a node at both ends of the list in O(1) time. Therefore, concatenation of two doubly linked lists takes O(1) time if we maintain a pointer to the last node of the first list and a pointer to the first node of the second list.
c) Circular doubly linked list: A circular doubly linked list is similar to a doubly linked list, but the last node points to the first node, forming a circular structure. This means that we can maintain a pointer to the last node of the first list and a pointer to the first node of the second list without any extra overhead. Therefore, concatenation of two circular doubly linked lists takes O(1) time.
d) Array implementation of list: In an array implementation of a list, we need to allocate a new array and copy the elements of both lists to the new array, which takes O(n) time. Therefore, concatenation of two arrays takes O(n) time.
Conclusion
The correct option for concatenation of two lists in O(1) time is a circular doubly linked list as it supports constant time insertion and deletion at both ends of the list, and maintains a circular structure to concatenate two lists without any extra overhead.
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The concatenation of two lists is to be performed in O(1) time. Which of the following implementations of a list could be used?a)Singly linked listb)Doubly linked listc)Circular doubly linked listd)Array implementation of listCorrect answer is option 'C'. Can you explain this answer?
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