What is the time complexity of inserting an element into a binary heap?
Practice Questions
Q1
What is the time complexity of inserting an element into a binary 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 binary heap?
Step 1: Understand what a binary heap is. A binary heap is a complete binary tree that satisfies the heap property, meaning each parent node is greater than (or less than, depending on max or min heap) its child nodes.
Step 2: Know that when you insert an element into a binary heap, you first add the new element at the end of the heap (the next available position).
Step 3: After adding the new element, you need to maintain the heap property. This is done by 'bubbling up' the new element. You compare it with its parent and swap them if the new element is greater (or less for a min heap).
Step 4: The bubbling up process continues until the new element is in the correct position, which may take several swaps.
Step 5: The maximum number of swaps needed is proportional to the height of the heap. Since a binary heap is a complete binary tree, its height is log(n), where n is the number of elements in the heap.
Step 6: Therefore, the time complexity for inserting an element into a binary heap is O(log n).
