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Study Guide

COMP 251- Final Exam Guide - Comprehensive Notes for the exam ( 196 pages long!) Premium

196 Pages
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Department
Computer Science (Sci)
Course Code
COMP 251
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Description
[COMP 251] Comprehensive Winter guide including any lecture notes, textbook notes and exam guides.COMP 251 Course Overview Created by: Daniil Lisus Table of Contents Algorithm Analysis ................................................................................................................3 Time Complexity Notations + Examples..........................................................................................3 Graphs ..................................................................................................................................4 Adjacency Matrix Representation...................................................................................................4 Adjacency List Representation........................................................................................................4 Breadth First Search Traversal........................................................................................................4 Breadth First Search Traversal........................................................................................................4 Testing Bipartiteness......................................................................................................................5 Strongly Connected Graphs............................................................................................................5 Directed Acyclic Graphs + Topological Order...................................................................................5 Greedy Algorithms ................................................................................................................6 Interval Scheduling ........................................................................................................................6 Interval Partitioning.......................................................................................................................6 Scheduling to Minimize Lateness....................................................................................................6 Optimal Caching.............................................................................................................................6 DijkstraÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â€ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â™s Algorithm.......................................................................................................................7 Minimum Spanning Trees......................................................................................................7 Kruskal Algorithm..........................................................................................................................7 Reverse Deletion Algorithm ...........................................................................................................7 PriÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â€ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â™s AlgorithÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯............................................................................................................................7 Cut Property..................................................................................................................................7 Cycle Property ...............................................................................................................................8 Clustering Problem ........................................................................................................................8 Huffman Coding ....................................................................................................................8 Simple...........................................................................................................................................8 Prefix Codes as Binary Trees...........................................................................................................8 Divide and Conquer...............................................................................................................9 Masters Theorem...........................................................................................................................9 Mergesort......................................................................................................................................9 Counting Inversions .......................................................................................................................9 Closest Pair of Points......................................................................................................................9 Integer Multiplication: Recursive..................................................................................................10 IÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯teger MultipliÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯atioÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯: KaratsuÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯aÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â€ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â™s AlgorithÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¢ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â–ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚ÂƒÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚ÂƒÃƒÂ‚Ã‚Â‚ÃƒÂƒÃ‚Â‚ÃƒÂ‚Ã‚Â¯...............................................................................10 Matrix Multiplication: Simple Algorithm.......................................................................................11 Matrix Multiplication: Divide and Conquer Slow...........................................................................11 Matrix Multiplication: Strassen Algorithm ....................................................................................11 Dynamic Programming........................................................................................................ 12 Weighted Interval Scheduling.......................................................................................................12 Knapsack Problem .......................................................................................................................12 RNA Secondary Structure.............................................................................................................13
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