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Suppose each set is represented as a linked list with elements in arbitrary order. Which of the operations among Union, intersection,membership,cardinality will be the slowest?
- a)Union only
- b)intersection membership
- c)membership, cardinality
- d)Union, intersection
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Suppose each set is represented as a linked list with elements in arbi...
membership is linear search 
cardinality is linear - 
for union we need to ensure no duplicate elements should be present 
for each element we need to check if
that element exists in other set for intersection also for every element in set1 we need to scan set2
for each element we need to check ifthat element exists in other set for intersection also for every element in set1 we need to scan set2
Most Upvoted Answer
Suppose each set is represented as a linked list with elements in arbi...
Explanation:
When sets are represented as linked lists, certain operations may take longer than others due to the nature of linked lists. The slowest operations among Union, intersection, membership, and cardinality are explained below:
1. Union and Intersection:
- Union: To perform a union operation on two linked lists, we need to iterate through each element of one list and check if it exists in the other list. If it does not, we add that element to the final list. This process takes O(n^2) time.
- Intersection: To perform an intersection operation on two linked lists, we need to iterate through each element of one list and check if it exists in the other list. If it does, we add that element to the final list. This process takes O(n^2) time.
Since both Union and Intersection operations require iterating through each element of both lists, they take the same amount of time and are slower than the other operations.
2. Membership:
To check if an element exists in a linked list, we need to iterate through each element of the list until we find the element or reach the end of the list. This process takes O(n) time.
3. Cardinality:
To find the number of elements in a linked list, we need to iterate through each element of the list and increment a counter variable for each element. This process takes O(n) time.
Conclusion:
Based on the above explanations, we can conclude that Union and Intersection operations are slower than Membership and Cardinality operations when sets are represented as linked lists. Therefore, option D, Union and Intersection, is the correct answer.
When sets are represented as linked lists, certain operations may take longer than others due to the nature of linked lists. The slowest operations among Union, intersection, membership, and cardinality are explained below:
1. Union and Intersection:
- Union: To perform a union operation on two linked lists, we need to iterate through each element of one list and check if it exists in the other list. If it does not, we add that element to the final list. This process takes O(n^2) time.
- Intersection: To perform an intersection operation on two linked lists, we need to iterate through each element of one list and check if it exists in the other list. If it does, we add that element to the final list. This process takes O(n^2) time.
Since both Union and Intersection operations require iterating through each element of both lists, they take the same amount of time and are slower than the other operations.
2. Membership:
To check if an element exists in a linked list, we need to iterate through each element of the list until we find the element or reach the end of the list. This process takes O(n) time.
3. Cardinality:
To find the number of elements in a linked list, we need to iterate through each element of the list and increment a counter variable for each element. This process takes O(n) time.
Conclusion:
Based on the above explanations, we can conclude that Union and Intersection operations are slower than Membership and Cardinality operations when sets are represented as linked lists. Therefore, option D, Union and Intersection, is the correct answer.
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Suppose each set is represented as a linked list with elements in arbitrary order. Which of the operations among Union, intersection,membership,cardinalitywill be the slowest?a)Union onlyb)intersection membershipc)membership, cardinalityd)Union, intersectionCorrect answer is option 'D'. Can you explain this answer?
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