What is the time complexity of inserting an element into a binary heap used as a
Practice Questions
Q1
What is the time complexity of inserting an element into a binary heap used as a priority queue?
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 used as a priority queue?
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 either greater than or equal to (max-heap) or less than or equal to (min-heap) its child nodes.
Step 2: Know that a binary heap is often used to implement a priority queue, where elements are inserted with a priority level.
Step 3: When you insert a new element into a binary heap, you first add it to the end of the heap (the next available position in the tree). This takes O(1) time.
Step 4: After adding the new element, you need to ensure the heap property is maintained. This is done by 'bubbling up' the new element to its correct position in the heap.
Step 5: The 'bubbling up' process involves comparing the new element with its parent and swapping them if the new element has a higher priority (in a max-heap) or lower priority (in a min-heap).
Step 6: In the worst case, the new element may need to be compared and swapped all the way up to the root of the heap. The height of a binary heap 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 binary heap is O(log n) because of the potential number of swaps needed to maintain the heap property.
