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An algorithm performs (log N)1/2 find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?
- a)Unsorted array
- b)Min - heap
- c)Sorted array
- d)Sorted doubly linked list
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
An algorithm performs(log N)1/2find operations , N insert operations, ...
The operations given can be performed in any order. So, for Min-heap we cannot do the usual BuildHeap method.
Delete in unsorted array is O(1) as we can just swap the deleted element with the last element in the array and delete the last element.
For sorted-doubly linked-list we cannot do binary search as this would require another array to maintain the pointers to the
nodes.
nodes.
Most Upvoted Answer
An algorithm performs(log N)1/2find operations , N insert operations, ...
Algorithm Analysis:
The algorithm performs the following operations:
1. (log N)^(1/2) find operations
2. N insert operations
3. (log N)^(1/2) delete operations
4. (log N)^(1/2) decrease key operations
To find the most suitable data structure, we need to consider the time complexity of each operation in different data structures.
Unsorted Array:
- Find operation: O(N) - In the worst case, we may need to traverse the entire array to find the desired item.
- Insert operation: O(1) - We can simply append the item to the end of the array.
- Delete operation: O(N) - Similar to the find operation, we may need to traverse the entire array to find the item to be deleted.
- Decrease key operation: Not applicable.
Min-Heap:
- Find operation: O(log N) - We can perform a binary search in the heap to find the desired item.
- Insert operation: O(log N) - We need to maintain the heap property by percolating the inserted item up the tree.
- Delete operation: O(log N) - We need to replace the item to be deleted with the last item in the heap and then percolate it down to maintain the heap property.
- Decrease key operation: O(log N) - We need to percolate the decreased item up the tree to maintain the heap property.
Sorted Array:
- Find operation: O(log N) - We can perform a binary search in the sorted array to find the desired item.
- Insert operation: O(N) - We need to find the correct position in the sorted array and shift all the subsequent elements to make space for the inserted item.
- Delete operation: O(N) - We need to find the item to be deleted and shift all the subsequent elements to fill the gap left by the deleted item.
- Decrease key operation: Not applicable.
Sorted Doubly Linked List:
- Find operation: O(N) - We need to traverse the linked list to find the desired item.
- Insert operation: O(1) - We can insert the item at the beginning or end of the linked list.
- Delete operation: O(1) - We can delete the item by updating the pointers of the adjacent nodes.
- Decrease key operation: O(N) - We need to traverse the linked list to find the item with the decreased key.
Conclusion:
Considering the time complexity of each operation, the unsorted array is the most suitable data structure for the given algorithm. The find and delete operations have a time complexity of O(N), which matches the time complexity of the unsorted array. Additionally, the insert operation has a constant time complexity of O(1), which is the best among all the data structures considered here. Although the decrease key operation is not applicable to the unsorted array, it is not a significant factor in determining the overall asymptotic complexity of the algorithm.
The algorithm performs the following operations:
1. (log N)^(1/2) find operations
2. N insert operations
3. (log N)^(1/2) delete operations
4. (log N)^(1/2) decrease key operations
To find the most suitable data structure, we need to consider the time complexity of each operation in different data structures.
Unsorted Array:
- Find operation: O(N) - In the worst case, we may need to traverse the entire array to find the desired item.
- Insert operation: O(1) - We can simply append the item to the end of the array.
- Delete operation: O(N) - Similar to the find operation, we may need to traverse the entire array to find the item to be deleted.
- Decrease key operation: Not applicable.
Min-Heap:
- Find operation: O(log N) - We can perform a binary search in the heap to find the desired item.
- Insert operation: O(log N) - We need to maintain the heap property by percolating the inserted item up the tree.
- Delete operation: O(log N) - We need to replace the item to be deleted with the last item in the heap and then percolate it down to maintain the heap property.
- Decrease key operation: O(log N) - We need to percolate the decreased item up the tree to maintain the heap property.
Sorted Array:
- Find operation: O(log N) - We can perform a binary search in the sorted array to find the desired item.
- Insert operation: O(N) - We need to find the correct position in the sorted array and shift all the subsequent elements to make space for the inserted item.
- Delete operation: O(N) - We need to find the item to be deleted and shift all the subsequent elements to fill the gap left by the deleted item.
- Decrease key operation: Not applicable.
Sorted Doubly Linked List:
- Find operation: O(N) - We need to traverse the linked list to find the desired item.
- Insert operation: O(1) - We can insert the item at the beginning or end of the linked list.
- Delete operation: O(1) - We can delete the item by updating the pointers of the adjacent nodes.
- Decrease key operation: O(N) - We need to traverse the linked list to find the item with the decreased key.
Conclusion:
Considering the time complexity of each operation, the unsorted array is the most suitable data structure for the given algorithm. The find and delete operations have a time complexity of O(N), which matches the time complexity of the unsorted array. Additionally, the insert operation has a constant time complexity of O(1), which is the best among all the data structures considered here. Although the decrease key operation is not applicable to the unsorted array, it is not a significant factor in determining the overall asymptotic complexity of the algorithm.
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An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer?
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An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer?.
An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An algorithm performs(log N)1/2find operations , N insert operations, (log N)1/2 delete operations, and (log N)1/2 decreasekey operations on a set of data items with keys drawn from a linearly ordered set . For a delete operation, a pointer is provided to the record that must be deleted . For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?a)Unsorted arrayb)Min - heapc)Sorted arrayd)Sorted doubly linked listCorrect answer is option 'A'. Can you explain this answer?.
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