What is the time complexity of building a heap from an array of n elements?
Practice Questions
Q1
What is the time complexity of building a 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 heap from an array of n elements?
Step 1: Understand what a heap is. A heap is a special tree-based data structure that satisfies the heap property, where the parent node is either greater than or equal to (max-heap) or less than or equal to (min-heap) its children.
Step 2: Know that we can build a heap from an array of elements. This means we want to rearrange the elements in the array to satisfy the heap property.
Step 3: Learn about the 'heapify' process. Heapify is a method used to maintain the heap property. It can be applied to each element in the array starting from the last non-leaf node down to the root.
Step 4: Realize that the last non-leaf node is at index n/2 - 1, where n is the number of elements in the array. We will apply heapify to each node from this index down to 0.
Step 5: Understand that the time complexity of heapifying a single node is O(log n) in the worst case, but since we are heapifying nodes from the bottom up, the overall time complexity for building the heap is O(n).
Step 6: Conclude that building a heap from an array of n elements can be done in O(n) time using the heapify process.
