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3-dimensional matching, 527–531 Ω, 61 ω, 88 , 107 operations using, 65–67 abstraction, 5 properties, 59–60, 62–64, 91, accessor operations, 116 97–103 Ackermann’s function, 304 recurrences and, 67, 73–79 Adel’son-Vel’ski˘ı, G. M, 205, 242 summations and, 68 ADT, 107 Θ, 62 Aho, A. V., 145, 288 Aigner, M., 373 Bachman, P. G. H., 103 aliasing, 145 Bayer, R., 242, 243 Amdahl, G. M, 288 Bellman, R. E., 412 amortized analysis, 121–123, 129–139 Bentley, J. L., 24, 373 Andersson, A., 242 Berge, C., 468 approximation ratio, 563 big-Oh, 58 Apt, K. R., 55 big-Omega, 61 arbitrary precision arithmetic big-Theta, 62 exponentiation, 369 bin packing problem, 558, 570–574, 585 radix conversion, 369 binary search, 149–152 arbitrary-precision arithmetic, 145, binomial coefficients, 241 350–364 binomial theorem, 241 division, 350–359, 368 bitonic tour, 411 exponentiation, 369 Blum, M., 373 multiplication, 366, 481–482, Boehme, E. M., 288 485–504 Bool, 124 radix conversion, 369 boolean expressions reciprocal, 357–364, 368 conjunctive normal form, 517 arithmetic series, 49 DeMorgan’s laws, 518 asymptotic notation k-conjunctive normal form, 522 O, 58 literal, 517 limits and, 91–93 satisfiability, 508–523, 539–553 multiple variables, 81–88 not all equal, 554 o, 88 validity, 509

597 INDEX 598 boolean satisfiability Dinic, E. A., 468 conjunctive normal form discrete Fourier transform, 471 clauses, 517 discrete space, 170 Bor ˙uvka, O, 391 disjoint set, 289 Brassard, G., 103–104, 308, 412, 559 disjoint set structures, 289–308 Bratley, P., 308, 412, 559 divide-and-conquer, 74, 150, 332–373 Burnikel, C., 372 Dumey, A. I., 288 Burrus, C. S., 506 Dutch national flag, 37–43, 52, 54–55, 337 Carter, J. L, 288 dynamic programming, 392–412 change-making problem, 392–395 Cheriton, D., 391 Eckert, J. P., 372 Chinese Remainder Theorem, 498 Edmonds, J., 391, 468 chirp transform, 505 Euler, L., 330 Chiu-Shao, C., 506 Even, S., 330 Chvatal, V., 412 event, 172 clique, 555, 586 independence of, 176 clique problem, 555 pairwise, 230 cloning, 123 events shallow, 123 independence of Collatz problem, 33, 55 mutual, 231 Collatz, L., 55 eventually nondecreasing, 67, 87 collision, see hashing, collision eventually positive, 68, 87 compression map, see hashing, Expand function, 150 compression map expandable array, 121 conditional probability, 176 expected value, 171 ConsList, 124 expected-case analysis, 170 constructive induction, 347 convolution, 469–481 factorial, 50 negative wrapped, 488 Fast Fourier Transform, 469–506 positive wrapped, 480 Fibonacci sequence, 50 Cook, S. A., 372, 559 Fischer, M. J., 412 Cooley, J. W., 506 Fisher, M. J., 308 Cormen, T. H., 55, 104, 288, 308, 468 floor, 69 correctness Floyd, R. W., 194, 412 algorithms, 55 for loops, 32 data structures, 112 Ford, L. R., 468 countable set, 170 Francez, N., 55 Crane, C. A., 194 Fredman, M. L., 194, 288, 391 craps, 193–194 Fulkerson, D. R., 468 cut, 579 fully polynomial approximation scheme, 567 Demers, A., 586 design patterns, 20, 106 Galler, B. A., 308 Dijkstra, E. W., 24, 55, 391 Gambin, A., 194 INDEX 599

Garey, M. R., 559, 560, 586 transitively closed, 329 Gauss, C. F., 506 universal sink detection, 311–313 generalization, 39–43 universal sink in, 311 geometric series, 49 vertex cover, 523–527, 586 Gilbert, E. N., 412 greatest common divisor, 369 Godbole, S. S., 412 group, 482 Goldberg, A. V., 468 abelian, 482 golden ratio, 50 Gubias, L. J., 242 Gonzalez, T., 587 Graham, R. L., 104, 586 harmonic series, 342 graphs, 309–330 hashing, 248–288 acyclic, 313 c-universal, 272 adjacency list, 319–322, 327 collision, 248 adjacency matrix, 316–319, 327 compression map, 258 articulation points, 429–434 division method, 254–259, 284 biconnected, 442 load factor, 254 bipartite, 444 perfect, 274–283 breadth-first search, 389 polynomial, 259–260, 284 bridges, 442 rehashing, 254 coloring, 443–444, 557 universal, 260–274, 284 connected components of, 377 heaps, 152–186 connected undirected, 329 binary, 178–186 cycle in, 313 leftist, 159–165 edge connectivity, 468 Heideman, M. T., 506 Euler paths in, 329 Hell, P., 559 Hamiltonian cycle, 555 Hirschberg, D. S., 391 Hamiltonian path, 372 Hoare, C. A. R., 55, 373 independent set, 526–527 Hopcroft, J. E., 288, 308, 330, 444, 468 induced subgraph, 421 Huffman, D. A., 391 isomorphic, 555 matching, 455–465, 527 Ibarra, O. H., 587 path cover, 467 immutable structure, 123 reachability, 420–429 indicator random variable, 234 semiconnected, 443 induction, 27–29 shortest paths, 381–383, 389, constructive, 347 398–401 insecure data structure, 117 simple cycle in, 313 , see sorting, insertion sort simple path in, 447 Int, 38 singly connected, 443 interface, 107 sink in, 311 internal function, 115 sparse, 322 invariant strongly connected components, loop, 11 437–439 structural, 110 topological sort, 313–316, 434–436 inversion, 103 transitive closure, 406 InvertedPriorityQueue, 148 INDEX 600 iteration operator, 300 chained, 397–398 Jarn´ık, V., 391 Mauchly, J. W., 372 Jiushao, Q., 506 maximum cut problem, 579–584 Johnson, D. B., 391 maximum subsequence sum, 12–19, 24, Johnson, D. H., 506 29–32, 50–52, 59–61, 63–65, Johnson, D. S., 559, 560, 586 67, 69–78, 94, 332, 374 McCreight, E. M., 243 k-cut, 579 McIlroy, M. D., 308, 373 Karatsuba, A., 372 Micali, S., 468 Karp, R. M., 468, 559 minimum cluster problem, 579–584, 586 Keyed type, 148 mod, 33 Kim, C. E., 587 modular multiplicative inverse, 370 Kirkpatrick, D. G., 559 Moore, E. F., 412 Klarner, D. A., 412 Morris, 308 knapsack problem, 390, 401–403, 405, most significant bit, 351 563–570, 585 most significant digit, 351 Knuth, D. E., 104, 194, 288, 308, 330, 372, 412 Muchnick, S. S., 145 Koml´os, J., 288 multigraphs, 323–325, 327 Kozen, D. C., 308, 412 multiset, 148 Kruskal, J. B., Jr., 391 Nat, 4 L’Hˆopital’s rule, 92 natural number, 3 Landis, E. M., 205, 242 network flow, 445–455, 465 Lawler, E. L., 391 augmenting path, 447 Lelewer, D. A., 391 residual network, 448 lg, 69 Newton’s method, 359–364 limit, 91 nondestructive updates, 123 linearity of expectation, 177 NP-complete problem, 516 linked list, 129 strong sense, 535 little-oh, 88 NP-hard problem, 516 little-omega, 88 non-decision problem, 562 load factor, see hashing, load factor strong sense, 535 null path length, 159 base e, 93 Number, 4 base 2, 69 natural, 93 object-oriented design, 24 Lovasz, L., 559 object-oriented programming, 24 Lucas, E., 444 Ofman, Y., 372 Luhn, H. P., 288 Olderog, E.-R., 55 optimization problem, 374 Malinowski, A., 194 Markov’s Inequality, 194 palindrome, 22, 406 matching Papadimitriou, C. H., 391 bipartite, 455–465 partition problem, 532–539 INDEX 601

Patashnik, O., 104 Sch¨onhage, A., 506 Paulson, L. C., 147 scheduling, 289–291, 375–377 Perl, Y., 560 Sedgewick, R., 242 polynomial approximation scheme, 567 selection problem, 2–5, 25–27, 37–39, fully, 567 45–46, 72, 343–350 polynomial multiplication, 333–336, , see sorting, selection sort 469–481 self-adjusting, 214 polynomial-time algorithm, 512 sentinel element, 180 postcondition, 3 Sethi, R., 145 precondition, 3 Sharir, M., 444 Prim, R. C., 391 significant bit, 351 , 258 significant digit, 351 principal roots of unity, 471 SizeOf, 23 principle of optimality, 395 skip lists, 223–237 priority queue, 148–194 Sleator, D., 147, 194, 242 PriorityQueue, 148 smooth function, 68, 87, 104 probability, 170 sorting probability space, 170 heap sort, 178–186, 336 pseudopolynomial, 534 insertion sort, 5–12, 27–29, 32–37, Pugh, W., 243 71–72 , 336, 337, 372 queue, 143 quick sort, 54, 337–343, 372 quick sort, see sorting, quick sort selection sort, 22–23 stable, 192, 336 RAM, 540 specification, 2 random access machine, 540 of an algorithm, 3 random variable, discrete, 171 state of a data structure, 110 Rao, S., 468 Steiglitz, K., 391 recurrence, 67 Strassen, V., 373, 506 asymptotic solution to, see String, 143–145 asymptotic notation, summations recurrences and arithmetic series, 49 reduction, 5 asymptotic solution to, see polynomial asymptotic notation, many-one, 514 summations and Turing, 561–562 geometric series, 49 pseudopolynomial, 536 Szermer´edi, E., 288 rehashing, see hashing, rehashing ring, 483 tail recursion, 9 commutative, 483 Tarjan, R. E., 147, 194, 242, 308, 330, unit element, 483 391, 444 Rochester, N., 288 ToArray, 256 Toeplitz matrix, 505 Sahni, S., 586 top-down, 2, 5, 6, 24 Samuel, A. L., 288 topological sort, 316–322 INDEX 602

Tr´emaux, 444 universal sink detection, 316 transformation, 9 traveling salesperson problem, 558, van Leeuwen, J., 559 574–579 Vazirani, V. V., 468 metric, 575–579 virtual initialization, 244–248 trees, 329, 377 Visitor interface, 195 AVL, 205–214, 294 visitor pattern, 195 binary, 155 von Neumann, J., 372 binary search, 198–223 Vuillemin, J., 194 leftist, 160–165 Wagner, R. A., 412 red-black, 240 Warshall, S., 412 rooted, 153 Wegman, M. N., 288 height of, 154 Weisstein, E., 55 leaf, 154 Whitney, H., 391 size of, 154 Williams, J., 194 traversals, 201, 415–420 Wirth, N., 24 spanning, 377 worst case, 57 depth-first, 423 Wright, J. W., 412 minimum-cost, 377–381 splay, 214–223 Yao, A. C., 586 Tritter, A. L., 308 Yao, A. C.-C., 391 Ts˘u,S., 506 Yao, F. F., 412 Tukey, J. W., 506 Zaks, S., 412, 560 Ullman, J. D., 145, 288, 308, 586 Zi, S., 506 universal family, 261, 284 Ziegler, J., 372

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