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DESIGN AND ANALYSIS OF ALGORITHMS - Duke University

CPS 230 DESIGN AND ANALYSISOF ALGORITHMSFall 2008 Instructor:Herbert EdelsbrunnerTeaching Assistant:Zhiqiang GuCPS 230 Fall Semester of 2008 Table of Contents1 Introduction3 IDESIGNTECHNIQUES42 Divide-and-Conquer53 Prune-and-Search84 Dynamic Programming115 Greedy Algorithms14 First Homework Assignment17 IISEARCHING186 Binary Search Trees197 Red-Black Trees228 Amortized Analysis269 Splay Trees29 Second Homework Assignment33 IIIPRIORITIZING3410 Heaps and Heapsort3511 Fibonacci Heaps3812 Solving Recurrence Relations41 Third Homework Assignment44 IVGRAPHALGORITHMS4513 Graph Search4614 Shortest Paths5015 Minimum Spanning Trees5316 Union-Find56 Fourth Homework Assignment60 VTOPOLOGICALALGORITHMS6117 Geometric Graphs6218 Surfaces6519 Homology68 Fifth Homework Assignment72 VIGEOMETRICALGORITHMS7320 Plane-Sweep7421 Delaunay Triangulations7722 Alpha Shapes81 Sixth Homework Assignment84 VIINP-COMPLETENESS8523 Easy and Hard Problems8624NP-Complete Problems8925 Approximation Algorithms92 Seventh Homework

The behavior of this version of quick-sort depends on p, which is producedby a random number generator. Average analysis. We assume that the items in A[0..n− 1] are pairwise different. The pivot splits Ainto A[0..m−1], A[m], A[m+1..n−1]. By assumption on function RSPLIT, the probability for each m ∈ [0,n− 1] is 1 n. Therefore the ...

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