**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(n^{2}) 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)