What Is a Min Heap?
Explore the concept of a min heap as a complete binary tree where the smallest element is always at the root. Understand key operations such as insertion, extraction, peeking, and size determination, along with the time complexity of each. This lesson helps you grasp how min heaps maintain order and efficiency, essential for priority queues and graph algorithms.
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Min heap
A min heap is a complete binary tree where every parent node is smaller than or equal to its children, meaning the smallest element in the entire heap is always sitting at the root and is instantly accessible at any time.
Example: Consider a min heap containing the values: [2, 5, 8, 10, 14].
The root is 2 because it is the smallest element. Its children are 5 and 8, both of whom are greater than 2. Similarly, 5's children are 10 and 14, both of whom are greater than 5. This ordering holds at every level of the tree, which makes it a valid min heap.
In array form, this heap is stored as [2, 5, 8, 10, 14], with the root at index 0.
Understanding the index formulas
For any element at index i, its parent and children can be located using simple arithmetic:
Parent:
Left child:
Right child:
This works because the array representation ...