Question: What is the time complexity of inserting an element into a max-heap?
Options:
O(1)
O(log n)
O(n)
O(n log n)
Correct Answer: O(log n)
Solution:
Inserting an element into a max-heap requires maintaining the heap property, which takes O(log n) time.
What is the time complexity of inserting an element into a max-heap?
Practice Questions
Q1
What is the time complexity of inserting an element into a max-heap?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the time complexity of inserting an element into a max-heap?
Step 1: Understand what a max-heap is. A max-heap is a special tree structure where each parent node is greater than or equal to its child nodes.
Step 2: When you want to insert a new element into a max-heap, you first add the element at the end of the heap (the last position).
Step 3: After adding the new element, you need to check if the heap property is still maintained. This means checking if the new element is greater than its parent.
Step 4: If the new element is greater than its parent, you swap them. This is called 'bubbling up' or 'sifting up'.
Step 5: You continue to bubble up the new element until the heap property is restored or it reaches the top of the heap.
Step 6: The maximum number of swaps you might need to do is equal to the height of the heap, which is log(n) where n is the number of elements in the heap.
Step 7: Therefore, the time complexity for inserting an element into a max-heap is O(log n).
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