CIS 9615. Analysis of Algorithms

Algorithms on Trees


1. Data structures

terms: tree, root, leaf, path, level, depth, height, linear DS as tree

shape: binary tree, full binary tree, complete binary tree

order: heap, binary search tree (BST), balanced BST (AVL tree, Red-Black tree, applet), B-Tree (applet)

storage: tree as linked nodes, heap in array


2. Operations and their efficiency

traversal (walk, search): recursive, depth-first and breadth-first, backtracking, Θ(n)

search: order? shape? Θ(n) or Θ(lg n)

insertion and deletion: shape and order, Θ(n) or Θ(lg n)

sorting: tree building (with order/shape) followed by deletion or traversal (e.g., heap, BST), Θ(n2) or Θ(n lg n)


3. Usages and Augmentations

Heap as priority queue

BST with size information for dynamic order statistics

Efficiency of operations (search, insert, delete, traversal, sorting) in various data structures (shape, order)