What is the worst-case time complexity for deleting the minimum element from a b
Practice Questions
Q1
What is the worst-case time complexity for deleting the minimum element from a binary min-heap?
O(1)
O(log n)
O(n)
O(n log n)
Questions & Step-by-Step Solutions
What is the worst-case time complexity for deleting the minimum element from a binary min-heap?
Step 1: Understand what a binary min-heap is. A binary min-heap is a complete binary tree where the value of each node is less than or equal to the values of its children.
Step 2: Identify the minimum element in a binary min-heap. The minimum element is always at the root of the heap (the top node).
Step 3: Remove the minimum element (the root). This involves taking the last element in the heap and placing it at the root position.
Step 4: Restore the heap property. After removing the root, the new root may violate the min-heap property, so we need to 'heapify' the tree. This means we compare the new root with its children and swap it with the smaller child until the heap property is restored.
Step 5: Determine the time complexity of the heapify process. Since the height of a binary min-heap is log(n) (where n is the number of elements in the heap), the worst-case time complexity for restoring the heap property is O(log n).
Step 6: Conclude that the worst-case time complexity for deleting the minimum element from a binary min-heap is O(log n).
