1 / 5

Review for Final Exam

Review for Final Exam. Non-cumulative, covers material since exam 2 Data structures covered: Treaps Hashing Disjoint sets Graphs For each of these data structures Basic idea of data structure and operations Be able to work out small example problems Prove related theorems

vteresa
Download Presentation

Review for Final Exam

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Review for Final Exam • Non-cumulative, covers material since exam 2 • Data structures covered: • Treaps • Hashing • Disjoint sets • Graphs • For each of these data structures • Basic idea of data structure and operations • Be able to work out small example problems • Prove related theorems • Advantages and limitations • Asymptotic time performance • Comparison • Review questions are available on the web.

  2. Treaps • Definition • It is both a BST and a binary min heap (heap is not a CBT) • Each node has a key/priority pair (priority is a random number) • It obeys BST order according to key value • It obeys heap order according to priority value • Treap operations • find: same as BST (no change) • insert: first insert as in BST, then rotate until heap order is restored • remove: first find the item, then rotate it down until it becomes leaf • Why rorate? • What to do if item is not there or if it is a duplicate • Performance analysis • Height is almost always O(log n) • Why? • Comparison to BST, RBT, Splay tree

  3. Hashing • Hash table • Table size (primes) • Trading space for time • Hashing functions • Properties making a good hashing function • Examples of division and multiplication hashing functions • Operations (insert/remove/find/) • Collision management • Separate chaining • Open addressing (different probing techniques, clustering problem) • Worst case time performance: • O(1) for find/insert/delete if  is small and hashing function is good • Limitations • Hard to answer order based queries (successor, min/max, etc.)

  4. Disjoint Sets • Equivalence relation and equivalence class • definitions and examples • Disjoint sets and up-tree representation • representative of each set • direction of pointers • Union-find operations • basic union and find operation • path compression (for find) and union by weight heuristics • time performance when the two heuristics are used: O(m lg* n) for m operations (what does lg* n mean) O(1) amortized time for each operation

  5. Graphs • Graph definitions • G = (V, E), directed and undirected graphs, DAG • path, path length (with/without weights), cycle, simple path • connectivity, connected component, connected graph, complete graph, strongly and weakly connectedness. • Adjacency and representation • adjacency matrix and adjacency lists, when to use which • time performance with each • Graph traversal: DF and BF • Single source shortest path • Breadth first (with unweighted edges) • Dijkstra’s algorithm (with weighted edges) • Topological order (for DAG) • What is a topological order (definitions of predecessor, successor, partial order) • Algorithm for topological sort

More Related