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Extra resources for Algorithms: Design Techniques and Analysis (Lecture Notes Series on Computing)
163 6. three Mergesort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred sixty five 6. three. 1 How the set of rules vorks . . . . . . . . . . . . . . . . . 166 6. three. 2 AnalyGs of the merg~sorta~gorithm . . . . . . . . . . . 167 6. four The Divide and triumph over Paradigm . . . . . . . . . . . . . . . . 169 172 6. five choice: discovering the Median and the kth Sm~lIestElement 6. five. 1 research of the choice set of rules . . . . . . . . . . . . a hundred seventy five 6. 6 Quicksort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6. 6. 1 A partitioning set of rules . . . . . . . . . . . . . . . . . . 177 6. 6. 2 The sorting ~ g o r i t h m. . . . . . . . . . . . . . . . . . . 179 6. 6. three research of the quicksort set of rules . . . . . . . . . . . . 181 6. 6. three. 1 The worst case habit . . . . . . . . . . . . 181 6. 6. three. 2 the typical case habit . . . . . . . . . . . 184 6. 6. four comparability of sorting algorithms . . . . . . . . . . . . . 186 i oLarge n Integers . . . . . . . . . . . . . . . . . . 187 6. 7 ~ u l ~ i ~ l i c a tof 6. eight Matrix Mu~tip~cation. . . . . . . . . . . . . . . . . . . . . . . 188 6. eight. 1 the conventional set of rules . . . . . . . . . . . . . . . . . 188 6. eight. 2 Recursive model . . . . . . . . . . . . . . . . . . . . . . 188 6. eight. three Strassen’s set of rules . . . . . . . . . . . . . . . . . . . . a hundred ninety 6. eight. four Comparisons of the 3 algorithms . . . . . . . . . . . 191 6. nine The Ciosest Pair challenge . . . . . . . . . . . . . . . . . . . . . 192 6. nine. 1 Time complexity . . . . . . . . . . . . . . . . . . . . . . 194 . Contents xv 6. 10 workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. eleven Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 195 202 bankruptcy 7 Dynamic Programming 203 203 205 208 214 215 217 220 226 7. 1 7. 2 7. three 7. four 7. five 7. 6 7. 7 7. eight creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Longest universal Subsequence challenge . . . . . . . . . . Matrix Chain Multiplication . . . . . . . . . . . . . . . . . . . . The Dynamic Programming Paradigm . . . . . . . . . . . . . . The All-Pairs Shortest direction challenge . . . . . . . . . . . . . . . The Knapsack challenge . . . . . . . . . . . . . . . . . . . . . . workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ibliograph~c Notes . . . . . . . . . . . . . . . . . . . . . . . . . half three First-Cut ideas 227 bankruptcy eight The grasping strategy 231 231 232 237 239 242 246 248 251 255 eight. 1 advent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. 2 The Shortest course challenge . . . . . . . . . . . . . . . . . . . . eight. 2. 1 A linear time set of rules for dense graphs . . . . . . . . eight. three minimal rate Spanning bushes (Kruskal’s set of rules) . . . . . eight. four minimal expense Spanning timber (Prim’s set of rules) . . . . . . . eight. four. 1 A linear time set of rules for dense graphs . . . . . . . . eight. five dossier Compression . . . . . . . . . . . . . . . . . . . . . . . . . . eight. 6 workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. 7 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . bankruptcy nine nine. 1 nine. 2 nine. three nine. four nine. five Graph Traversal 257 advent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Depth-First seek . . . . . . . . . . . . . . . . . . . . . . . . . 257 nine. 2. 1 Time complexity of depth-first seek . . . . . . . . . . 261 purposes of Depth-First seek . . . . . . . . . . . . . . . . 262 262 nine. three. 1 Graph ~ y c l j c i t y . . . . . . . . . . . . . . . . . . . . . . nine. three. 2 Topological sorting . . . . . . . . . . . . . . . . . . . . . 262 nine. three. three discovering articulation issues in a graph . . . . . . . . . . 263 nine. three. four Strongly hooked up elements . . . . . . . . . . . . . . 266 Breadth-First seek . . . . . . . . . . . . . . . . . . . . . . . . 267 purposes of Breadth-First seek . . . . . . . . . . . . . . . 269 xvi Contents nine. 6 workouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. 7 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . .