binary-search-trees

Binary search tree invariants are verified by proving that every node satisfies the left-smaller, right-greater ordering property after operations. You must document duplicate policies and track height bounds to ensure the structure remains valid.

Use a balanced binary search tree over library containers when your workload demands strict height bounds, specific duplicate policies, or complex predecessor and successor queries that standard library structures do not natively support.

Reason about object identity during tree rotations by separating invariant logic from implementation details. Analyze how pointer reassignments affect node relationships and iterator validity while maintaining strict structural balance.

Transplant operations replace one subtree with another during deletion to maintain the binary search tree structure. This preserves the in-order traversal sequence required for accurate predecessor and successor queries.

Limitations of custom binary search trees include the overhead of manually implementing rotation and transplant logic, the risk of breaking invariants during edge cases, and the maintenance burden compared to using optimized library containers.

Your binary search tree height grows uncontrollably without balance factors because standard insertion does not prevent degenerate linked-list shapes. Applying rotation techniques enforces height bounds to maintain logarithmic performance.