Final answer:
To build a binary heap with keys D A T A S T R U C T U R E, we start by inserting elements one by one into a min-heap or max-heap. In a min-heap, elements 'bubble up' if they are less than their parents, while in a max-heap, they 'bubble up' if they are larger. The process is efficient but can have O(log n) complexity for each insert.
Step-by-step explanation:
Building a Min-Heap and Max-Heap
To answer the question of how to create a binary heap with the keys D A T A S T R U C T U R E, let's start by understanding the heap structure. A binary heap is a complete binary tree that satisfies the heap property. For a min-heap, every parent node is less than or equal to its child nodes. Conversely, in a max-heap, every parent node is greater than or equal to its child nodes.
When inserting elements successively starting from 'D', the min-heap would be built by placing each new element in the next available position to maintain the complete tree property and then 'bubbling up' the element if it is smaller than its parent. This would continue until all elements are inserted and the heap property is maintained.
The resulting min-heap after inserting the elements D A T A S T R U C T U R E in that order would look like this:
For the max-heap, the process is similar, but instead of 'bubbling up' for smaller elements, we 'bubble up' for larger elements until the heap property is achieved.
The resulting max-heap would look like this:
Building a heap using successive insertions is efficient because it ensures that the complete tree property is maintained at each step, and the heap property is re-established as needed. However, this process can have a complexity of O(log n) for each insertion due to the potential of 'bubbling up' operations.