COMP251: Red-black trees Jérôme Waldispühl School of Computer Science McGill University Based on (Cormen et al., 2002) Based on slides from D. Plaisted (UNC) Red-black trees: Overview • Red-black trees are a variation of binary search trees to ensure that the tree is balanced. – Height is O(lg n), where n is the number of […]
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COMP251: Elementary graph algorithms Jérôme Waldispühl School of Computer Science McGill University Based on (Cormen et al., 2002) Based on slides from D. Plaisted (UNC) Graphs • GraphG=(V,E) – V = set of vertices – E=setofedgesÍ(V ́V) • Typesofgraphs bc a def – Undirected: edge (u, v) = (v, u); for all v, (v, v)
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COMP 251: Recurrences Jérôme Waldispühl School of Computer Science McGill University Based on slides from Hatami, Bailey, Stepp & Martin, Snoeyink. Outline • Introduction: Thinking recursively • Definition • Examples: o Binary search o Fibonacci numbers o Merge sort o Quicksort • Running time • Substitution method Course credits c(x) = total number of credits
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COMP251: Binary search trees, AVL trees & AVL sort Jérôme Waldispühl School of Computer Science McGill University From Lecture notes by E. Demaine (2009) Midterm #1 • Wednesday September 30. • Duration of the exam: o Theory: 1h30 o In practice: 3h30. The latter accounts for technical issues (i.e. internet) and barrier of learning. •
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COMP251: Greedy algorithms Jérôme Waldispühl School of Computer Science McGill University Based on (Cormen et al., 2002) Based on slides from D. Plaisted (UNC) & (goodrich & Tamassia, 2009) Overview • Algorithm design technique to solve optimization problems. • Problems exhibit optimal substructure. • Idea (the greedy choice): – When we have a choice to
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COMP251: Algorithms and Data Structures Jérôme Waldispühl School of Computer Science McGill University About Me • JérômeWaldispühl • AssociateProfessorofComputerScience • ResearchinBioinformatics&Human-Computing • Howtoreachme? o Office hours (TBA; See online schedule) o By appointment (email me to schedule a meeting) o Email: cs251@cs.mcgill.ca (Note: This will be the only email address you should use and from
COMP251: Minimum Spanning Trees Jérôme Waldispühl School of Computer Science McGill University Based on (Cormen et al., 2002) Based on slides from D. Plaisted (UNC) Minimum Spanning Tree (Example) • A town has a set of houses and a set of roads. • A road connects 2 and only 2 houses. • A road connecting
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COMP251: Bipartite graphs Jérôme Waldispühl School of Computer Science McGill University Based on slides fom M. Langer (McGill) & P. Beame (UofW) & K. Wayne (Princeton) Bipartite graphs A B Vertices are partitioned into 2 sets. All edges cross the sets. Examples AB Courses Candidates People registration employment Have read/seen Students Companies Books/Movies Counter-examples Easy
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COMP251: Disjoint sets Jérôme Waldispühl School of Computer Science McGill University Based on slides from M. Langer (McGill) Problem Let G=(V,E) be undirected graph, and A, B Î V two nodes of G. Question: Is there a path between A and B? But we are not interested in knowing the path between A and B.
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COMP251: Topological Sort & Strongly Connected Components Jérôme Waldispühl School of Computer Science McGill University Based on (Cormen et al., 2002) Based on slides from D. Plaisted (UNC) Recap: Breadth-first Search • Input: Graph G = (V, E), either directed or undirected, and source vertex s Î V. • Output: – d[v] = distance (smallest
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