Can you explain what is meant by the data structure binary heap?

A binary heap is a data structure that represents a complete binary tree satisfying the heap property:

• For a min-heap: the value in each node is less than or equal to the values of its children.
• For a max-heap: the value in each node is greater than or equal to the values of its children.

Main properties:

• Complete binary tree: all levels are fully filled, except possibly the last, which is filled from left to right.
• Fast insertion and deletion of the minimum (or maximum) element in O(log n).

Applications:

• Implementation of priority queues.
• Sorting algorithms (heapsort).

Example: a min-heap with elements [2, 3, 5, 7, 8, 10]

       2
      / \
     3   5
    / \  / 
   7  8 10

Insertion and deletion operations maintain the heap structure and property through "sifting" up or down.