Why it matters

Balanced trees are common but complex. Treap provides simple correct implementation.

Advertisement

The architecture

Insertion: BST insert; rotate to restore heap property.

Delete: rotate leaf down; remove.

Treap invariantsBST propertyon valueHeap propertyon priorityRandom priorityexpected balanceRandomization avoids adversarial inputs; expected O(log n) operations
Treap balance.
Advertisement

How it works end to end

Split / merge: primary treap operations. Enable set-like operations in O(log n).

Implicit treap: implicit keys enable dynamic array with O(log n) operations.

Applications: dynamic set, order statistics, sequence with modifications.