How do you implement a min-max heap?

A min-max heap is implemented by maintaining a binary tree with alternating levels of min and max heaps.

A min-max heap is a complete binary tree that satisfies the min-max heap property. This property states that at every level of the tree, the key of each node at an even level is less than or equal to the keys of its children and the key of each node at an odd level is greater than or equal to the keys of its children. The root of the tree is at level 0, which is considered an even level.

To implement a min-max heap, you first need to create a binary tree. Each node in the tree should have a key and two child nodes. The left child should always have a key less than or equal to its parent's key, and the right child should always have a key greater than or equal to its parent's key. This ensures that the tree maintains the min-max heap property.

When inserting a new element into the heap, you should place it at the next available position in the tree to maintain its complete binary tree structure. Then, you should "bubble up" the element to its correct position by comparing it with its parent. If the element is at an even level and it's less than its parent, or if it's at an odd level and it's greater than its parent, you should swap it with its parent. You should continue this process until the element is at its correct position.

Deleting an element from the heap involves removing the root and replacing it with the last element in the tree. Then, you should "bubble down" the element to its correct position by comparing it with its children. If the element is at an even level and it's greater than one of its children, or if it's at an odd level and it's less than one of its children, you should swap it with the smaller or larger child, respectively. You should continue this process until the element is at its correct position.

In summary, implementing a min-max heap involves maintaining a complete binary tree with alternating levels of min and max heaps, and using the "bubble up" and "bubble down" processes to insert and delete elements, respectively.