Implementing a Min Heap in JavaScript

Min heaps are fundamental data structures used in various algorithms, including priority queues and heap sort. This challenge asks you to implement a min heap data structure in JavaScript, allowing you to efficiently manage and retrieve the smallest element. A min heap ensures that the root node always holds the smallest value, making it ideal for scenarios where you need to repeatedly access the minimum element.

Problem Description

You are tasked with creating a MinHeap class in JavaScript. This class should support the following operations:

• insert(value): Inserts a new value into the heap, maintaining the min-heap property.
• extractMin(): Removes and returns the minimum value (root) from the heap, re-heapifying to maintain the min-heap property. Returns null if the heap is empty.
• peek(): Returns the minimum value (root) without removing it. Returns null if the heap is empty.
• size(): Returns the number of elements in the heap.
• isEmpty(): Returns true if the heap is empty, false otherwise.

The min-heap property dictates that for every node i in the heap, the value of the node is less than or equal to the value of its children. You should use an array to represent the heap internally.

Examples

Example 1:

Input:
Initial Heap: []
insert(5)
insert(3)
insert(8)
extractMin()
insert(1)
extractMin()
extractMin()
extractMin()
extractMin()

Output:
5
3
1
8
null

Explanation: The heap starts empty. 5, 3, and 8 are inserted, resulting in a heap structure. extractMin() removes 3. 1 is inserted, and then 3, 1, 5, and 8 are extracted in that order, leaving the heap empty.

Example 2:

Input:
Initial Heap: []
peek()
insert(10)
peek()
insert(5)
peek()
extractMin()
peek()

Output:
null
10
5
5
null

Explanation: peek() on an empty heap returns null. 10 is inserted, peek() returns 10. 5 is inserted, peek() returns 5. extractMin() removes 5, and peek() returns 10.

Example 3: (Edge Case - Empty Heap)

Input:
Initial Heap: []
size()
isEmpty()
extractMin()

Output:
0
true
null

Explanation: The heap is initially empty. size() returns 0, isEmpty() returns true, and extractMin() returns null.

Constraints

• The heap will contain numbers only.
• The number of elements inserted will be between 0 and 1000 (inclusive).
• The values inserted will be integers between -1000 and 1000 (inclusive).
• The extractMin() and peek() operations should be efficient, ideally with a time complexity of O(log n), where n is the number of elements in the heap.

Notes

• Consider using an array to represent the heap. The index of a node's children can be calculated as 2i + 1 (left child) and 2i + 2 (right child), where i is the index of the parent node.
• The insert operation involves adding the new element to the end of the array and then "heapifying up" by swapping the element with its parent until the min-heap property is satisfied.
• The extractMin operation involves replacing the root with the last element in the array, removing the last element, and then "heapifying down" by swapping the root with the smaller of its children until the min-heap property is satisfied.
• Pay close attention to edge cases, such as inserting into an empty heap or extracting from an empty heap.