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Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is
- a)Ω(logn)
- b)Ω(n)
- c)Ω(nlogn)
- d)Ω(n2)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider a complete binary tree where the left and the right subtrees ...
The answer to this question is simply max-heapify function. Time complexity of max-heapify is O(Log n) as it recurses at most through height of heap.
// A recursive method to heapify a subtree with root at given index
// This method assumes that the subtrees are already heapified
void MinHeap::MaxHeapify(int i)
{
int l = left(i);
int r = right(i);
int largest = i;
if (l < heap_size && harr[l] < harr[i])
largest = l;
if (r < heap_size && harr[r] < harr[smallest])
largest = r;
if (largest != i)
{
swap(&harr[i], &harr[largest]);
MinHeapify(largest);
}
}
// This method assumes that the subtrees are already heapified
void MinHeap::MaxHeapify(int i)
{
int l = left(i);
int r = right(i);
int largest = i;
if (l < heap_size && harr[l] < harr[i])
largest = l;
if (r < heap_size && harr[r] < harr[smallest])
largest = r;
if (largest != i)
{
swap(&harr[i], &harr[largest]);
MinHeapify(largest);
}
}
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Community Answer
Consider a complete binary tree where the left and the right subtrees ...
The lower bound for the number of operations to convert the tree to a heap is the number of nodes in the tree.
In a complete binary tree, the number of nodes is given by 2^h - 1, where h is the height of the tree. Since the tree is complete, the height is equal to the number of levels in the tree.
In a max-heap, the maximum element is at the root and the maximum element in each subtree is greater than or equal to the elements in its children. Therefore, to convert the tree to a max-heap, we need to ensure that the maximum element is at the root and the maximum element in each subtree is greater than or equal to the elements in its children.
To achieve this, we need to perform operations such as swapping elements and comparing elements to ensure that the heap property is satisfied. Each operation involves accessing and modifying elements in the tree.
Therefore, the lower bound for the number of operations to convert the tree to a heap is equal to the number of nodes in the tree, which is 2^h - 1.
In a complete binary tree, the number of nodes is given by 2^h - 1, where h is the height of the tree. Since the tree is complete, the height is equal to the number of levels in the tree.
In a max-heap, the maximum element is at the root and the maximum element in each subtree is greater than or equal to the elements in its children. Therefore, to convert the tree to a max-heap, we need to ensure that the maximum element is at the root and the maximum element in each subtree is greater than or equal to the elements in its children.
To achieve this, we need to perform operations such as swapping elements and comparing elements to ensure that the heap property is satisfied. Each operation involves accessing and modifying elements in the tree.
Therefore, the lower bound for the number of operations to convert the tree to a heap is equal to the number of nodes in the tree, which is 2^h - 1.
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Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap isa)Ω(logn)b)Ω(n)c)Ω(nlogn)d)Ω(n2)Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap isa)Ω(logn)b)Ω(n)c)Ω(nlogn)d)Ω(n2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap isa)Ω(logn)b)Ω(n)c)Ω(nlogn)d)Ω(n2)Correct answer is option 'A'. Can you explain this answer?.
Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap isa)Ω(logn)b)Ω(n)c)Ω(nlogn)d)Ω(n2)Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap isa)Ω(logn)b)Ω(n)c)Ω(nlogn)d)Ω(n2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a complete binary tree where the left and the right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap isa)Ω(logn)b)Ω(n)c)Ω(nlogn)d)Ω(n2)Correct answer is option 'A'. Can you explain this answer?.
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