Question

Insert the following integers, one at a time and in the order given, to a binary min heap. (Do not use the buildHeap operation.)

50, 10, 25, 44, 36,7
The integer items are stored in a basic array, according to the implicit representation presented in the lecture videos. Assume that the root item is stored at index 1. To indicate the state of the binary min heap after all items have been inserted, fill in the blank by providing the integer item stored at each array index.
Index 1:_____

Answer 1

To insert the integers into a binary min heap, each number is inserted one by one while maintaining the heap property. After all insertions, the root of the heap stored at index 1 is the integer 7.

Step-by-step explanation:

The process of inserting integers into a binary min heap requires us to maintain the heap property, where the parent node is always smaller than its child nodes. Here's how we insert the integers 50, 10, 25, 44, 36, and 7 one by one:

• Insert 50: [50]
• Insert 10: [10, 50] - 10 becomes the new root as it is smaller than 50.
• Insert 25: [10, 50, 25]
• Insert 44: [10, 50, 25, 44]
• Insert 36: [10, 50, 25, 44, 36]
• Insert 7: We insert 7 at the end, then it bubbles up to become the new root as it is the smallest. Any intermediate steps observe the heap order property.

After all insertions, the heap would look like:

• Index 1: 7 (root)
• Index 2: 10
• Index 3: 25
• Index 4: 44
• Index 5: 36
• Index 6: 50