In a priority queue implemented with a binary heap, what is the time complexity
Practice Questions
Q1
In a priority queue implemented with a binary heap, what is the time complexity of inserting an element?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
In a priority queue implemented with a binary heap, what is the time complexity of inserting an element?
Step 1: Understand what a binary heap is. A binary heap is a special tree structure that maintains a specific order (either min-heap or max-heap).
Step 2: Know that a priority queue is a data structure that allows you to insert elements and retrieve the highest (or lowest) priority element quickly.
Step 3: When you insert an element into a binary heap, you first add it to the end of the heap (the last position in the array representation).
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: Bubbling up involves comparing the new element with its parent and swapping them if the new element has a higher (or lower, depending on the type of heap) priority.
Step 6: This bubbling up process can take at most log(n) steps, where n is the number of elements in the heap, because the height of the binary heap is log(n).
Step 7: Therefore, the time complexity for inserting an element into a priority queue implemented with a binary heap is O(log n).
