Heap (data structure)

In computer science, a heap is a type of tree (data structure) that satisfies the heap property. Heaps are useful when you need to remove the item with the highest (or lowest) value.^[1] A common implementation of a heap is the binary heap in which the tree is a complete binary tree.

Example of a binary max-heap containing items between 1 and 100.

Heap property

• In a max-heap, the value of each item is less than or equal to the value of its parent, with the maximum-value item at the root.^[1]
• In a min-heap, the value of each item is greater than or equal to the value of its parent, with the minimum-value item at the root.^[1]

Operations

• find: return a maximum item of a max-heap or a minimum item of a min-heap.
• insert: add a new item to the heap.
• extract: returns the maximum item from a max-heap (or minimum item from a min-heap) after removing it.
• delete: removes the root of a max-heap (or min-heap).
• size: return the number of items in the heap.
• is-empty: return true if the heap is empty, false otherwise.

Maintaining the heap property

• insert: insert the item at the bottom rightmost location; swap the item with its parent until the heap property is preserved.
• delete: remove the root; swap it with the item at the bottom rightmost location; swap the new root downwards with the smaller of its children (for a min-heap) until the heap property is preserved.