# lec-6 - Administration Account forms. I I have some and...

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Unformatted text preview: Administration Account forms. I I have some and will hand out after class. I Sign in to class account and register, or else!!! CS70: Lecture 6. Outline. 1. Induction/Recursion 2. Stable Marriage Problem (Notes 4.) Tournament has a cycle of length 3 if at all. Tournament has a cycle of length 3 if at all. Assume the the smallest cycle is of length k . Tournament has a cycle of length 3 if at all. Assume the the smallest cycle is of length k . Case 1: Of length 3. Done. Tournament has a cycle of length 3 if at all. Assume the the smallest cycle is of length k . Case 1: Of length 3. Done. Case 2: Of length larger than 3. p 1 p 2 p 3 p 4 p k Tournament has a cycle of length 3 if at all. Assume the the smallest cycle is of length k . Case 1: Of length 3. Done. Case 2: Of length larger than 3. p 1 p 2 p 3 p 4 p k p 3 p 1 = 3 cycle Contradiction. Tournament has a cycle of length 3 if at all. Assume the the smallest cycle is of length k . Case 1: Of length 3. Done. Case 2: Of length larger than 3. p 1 p 2 p 3 p 4 p k p 3 p 1 = 3 cycle Contradiction. p 1 p 3 = k- 1 length cycle! Contradiction! Program to produce a 3 cycle from a tournamant and a cycle. 3Cycle(T,C) p1 = C[1] p2 = C[2] p3 = C[3] Program to produce a 3 cycle from a tournamant and a cycle. 3Cycle(T,C) p1 = C[1] p2 = C[2] p3 = C[3] if beats?(p3,p1,T) return [p1,p2,p3] Program to produce a 3 cycle from a tournamant and a cycle. 3Cycle(T,C) p1 = C[1] p2 = C[2] p3 = C[3] if beats?(p3,p1,T) return [p1,p2,p3] else 3Cycle(T, append([p1,p3],C[4,..])) Induction/Recursion: Cycle in dense graph. Proof outline for cycle in n nodes, n edge graph. Induction/Recursion: Cycle in dense graph. Proof outline for cycle in n nodes, n edge graph. Base Case: A three node three edge simple graph is a cycle. Induction/Recursion: Cycle in dense graph. Proof outline for cycle in n nodes, n edge graph. Base Case: A three node three edge simple graph is a cycle. Induction Step: 1. if vertex incident to one edge, then remove and use induction hypothesis. Induction/Recursion: Cycle in dense graph. Proof outline for cycle in n nodes, n edge graph. Base Case: A three node three edge simple graph is a cycle. Induction Step: 1. if vertex incident to one edge, then remove and use induction hypothesis. 2. Otherwise. Construct a cycle .. walking along unvisited edges until one cycles. This outline can be converted to recursive procedure that finds a cycle. Find-Cycle(G) This outline can be converted to recursive procedure that finds a cycle. Find-Cycle(G) if nVertices(G) = nEdges(G) = 3 return vertices(G) Base Case. This outline can be converted to recursive procedure that finds a cycle....
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## This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.

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lec-6 - Administration Account forms. I I have some and...

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