What is the time complexity of inserting an element into a priority queue implem
Practice Questions
Q1
What is the time complexity of inserting an element into a priority queue implemented with 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 priority queue implemented with a binary heap?
Step 1: Understand what a priority queue is. A priority queue is a data structure that allows you to store elements with priorities, where the highest (or lowest) priority element can be accessed quickly.
Step 2: Know that a binary heap is a common way to implement a priority queue. It is a complete binary tree that maintains a specific order (heap property).
Step 3: When you insert an element into a binary heap, you first add it to the end of the heap (the last position).
Step 4: After adding the new element, you need to ensure that the heap property is maintained. This is done by 'bubbling up' the new element to its correct position.
Step 5: The 'bubbling up' process involves comparing the new element with its parent and swapping them if the new element has a higher (or lower) priority, depending on whether it's a max-heap or min-heap.
Step 6: The maximum number of swaps needed to maintain the heap property is proportional to the height of the heap. In a binary heap, the height 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).
