What is the time complexity of building a binary heap from an array of n element
Practice Questions
Q1
What is the time complexity of building a binary heap from an array of n elements?
O(n)
O(log n)
O(n log n)
O(n^2)
Questions & Step-by-Step Solutions
What is the time complexity of building a binary heap from an array of n elements?
Step 1: Understand what a binary heap is. A binary heap is a complete binary tree that satisfies the heap property (either max-heap or min-heap).
Step 2: Know that we can build a binary heap from an array of n elements using a process called 'heapify'.
Step 3: The heapify process involves adjusting the positions of elements to maintain the heap property, starting from the last non-leaf node and moving upwards to the root.
Step 4: Realize that the heapify operation for each node takes time proportional to the height of the tree, which is log(n).
Step 5: However, not all nodes require the same amount of work. Most nodes are near the bottom of the tree, where the height is small.
Step 6: When you sum the work done for all nodes, it turns out that the total time complexity for building the heap is O(n), not O(n log n).
Step 7: Therefore, the time complexity of building a binary heap from an array of n elements is O(n).
