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| Purdom R.W., Brown C.A. — The analysis of algorithms |
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| Предметный указатель |
Noetherian, induction 55
nondeterministic 425
Nonredundant equations 370—374
Nonrepeating Hashing 109
Nonrepeating Hashing, average time 95—96 109—112
Nonterminal symbol 325
Norm of a partition 449
Normal distribution for probabilities 454
Normalization condition 242
NP problems 422
NP-complete 422
NP-hard 438
Null hypothesis 445
Number of elements obeying conditions 146
Ofman, Yu. 213 501
Olver, F.W.J. 98 328 498
One-tailed test 447
Operator 67—69 261 333
Operator method for solving recurrences 346
Optimal algorithm 409
Optimization problem 437
Or (logical) 172 417—418
Oracle 414
Order of a recurrence 202
Ordering 42
Orszag, Steven A. 204 235 239 254 256 259 261 268 301 328 496
Out-degree 362
Papadimitriou, Christos H. 392 440 442 496
Parallel computer 2 403
Parallel Or Algorithm 331
Parallel, Parallel Or 331
Parse Algorithm 326
Parser size 479—480
Parsing 325—328
Parsing, Parse 326
Partial derivative 488
Partial fractions 85—88 220 223 235—237
Partial order 42 54
Partial solution 169
Particular solution 201 346
Partition 145 449
Path 363
Path of positive probability 343
Path, directed 363
Path, length in a tree 316
Path, simple 363
Path, undirected 363
Pattern matching 375
Pattern Matching, Fast Pattern Match 377
Pattern Matching, Pattern Preprocessing 378
Pattern Matching, Simple Pattern Match 375
Pattern Preprocessing Algorithm 378
Patterson, M. 249 502
Pearl, Judea 271 501
Pearson, Carl E. 301 498
Peck, Elizabeth A. 480 498
Permutation 92
Peterson, W.W. 78 502
Pigeon-hole principle 147
Pipelined computer 5 400
Pippenger, N. 249 502
Poisson process 240
Polar coordinates 97
Pole of a function 491
Polish prefix notation 46
Polynomial 6
Polynomial binomial sums 102—103
Polynomial exponential sums 80
Polynomial sums 69
Polynomial time 2—3 422
Polynomial, Horner's Method 7
Polynomially equivalent 422
Polynomials, use of in proofs 128
Polyphase merge 229
Polyphase merge, Algorithm 231
Postorder 283
Potential 375
Power convention 100
Power of a statistical test 446
Power series 158—160
Practical advice 8 26 62 95 106 163 459
Pratt, Vaughan 249 379 499 501
Predicate 55 172 293
Predominator 366
Predominator, immediate 366
Preorder 283
Primitive recursive function 392
Principal root of unity 123
probability 28
probability density see “Density function”
Probability generating function 268
Problem instance 410
Problem set 410
Product, consecutive integers 91
Product, conventions 90—91
Product, notation 90
Product, polynomials 27
Productions of a grammar 325
Proof by induction see “Induction”
Pseudo-random number generation 4 481
Purdom, Paul Walton, Jr. 107 180 296 299 366 432 447 448 453 461 468 475 479 480 500 502
Pure literal rule 299
Pure literal rule, Algorithm 299
Quadratic sum 61 70
Queue, infinite servers 254
Queue, multiple server 344
Queue, single server 240
Quicksort, Algorithm 72
Quicksort, average time 278 297
Quicksort, best-case time 215
Quicksort, Median-of-Three Algorithm 299
Quotient 11
Radian 123
Radius of convergence 158
Radix conversion 9—10
Radix conversion, modular 406
Ramus, Christian 126
Random event see “Event”
Random hashing 77 191
Random hashing, Algorithm 77
Random hashing, average time 77 191—192
Random hashing, variance 84
random number generation 4 481
Random predicate 294
Random problem set 173
Random variable 444
Random variable, independent 173
Rank 153 245 390
Rao, Ramamohan K. 400 497
Ratio test of convergence 139
Rational functions 274
Rational number 9
Real number 9
Real part 123
Recurrence equation 200—360
Recurrence equation,  order 202
Recurrence equation, almost linear 303—306
Recurrence equation, binomial coefficients 292
Recurrence equation, break-even points 214—215
Recurrence equation, constant coefficient 234—243
Recurrence equation, divide and conquer 210—212 243—244 314
Recurrence equation, elimination of history 277—278
Recurrence equation, extended order 202
Recurrence equation, extended first order 202 205
Recurrence equation, factoring 261—264
Recurrence equation, finding 136 354—355
Recurrence equation, first order 202
Recurrence equation, full-history 202 277—299
Recurrence equation, homogeneous 202 344
Recurrence equation, integer part 309—314
| Recurrence equation, linear 202
Recurrence equation, linear first order 204—219
Recurrence equation, linear second order 219 221
Recurrence equation, min and max 314—328
Recurrence equation, multidimensional 345—360
Recurrence equation, nonhomogeneous 264—268
Recurrence equation, nonlinear 299—328
Recurrence equation, notation 201—204
Recurrence equation, order reduction with a solution 259—261
Recurrence equation, polynomial coefficients 251—256
Recurrence equation, pseudo-nonlinear 300—301
Recurrence equation, Recurrence equation, linear order 219—276
Recurrence equation, repertorie method 296—299
Recurrence equation, secondary 205—210 358
Recurrence equation, simplifying multiple-variable 357—360
Recurrence equation, systems of equations 329—345
Recurrence equation, theory of first order 273—276
Recurrence equation, transforming indices 205—210 347—354
Recurrence equation, transforming to linear 300—301
Recurrence equation, two dimensional 137 272
Recurrence equation, variation of parameters 264—268
Recursive function 442
Recursive Transitive Closure Algorithm 420
REDUCE symbolic algebra system 112
Reflexive relation 41
Reflexive transitive closure 41
Reingold, Edward M. 20 37 54 75 83 121 282 319 388 498 502
Rejecting state of a Turing machine 423—424
Relation 41—42
Relation, closure 41—42 55 385 416
Relation, confluent 55
Relation, minimum extension 368
Relation, reflexive 41
Relation, symmetric 41
Relation, transitive 41
Relative error 193
Relatively prime 14
Remainder 11
Renyi, Alfred 356
Repair of machines 344
Repeated function application 202
Repertoire method for solving recurrences 296—299
Residue of a pole 491
Reynolds, John 479 502
RFFT (Fourier transform) Algorithm 396
Rief, John xv
Riemann, Georg Friedrich Bernhard 488
Riemann, Georg Friedrich Bernhard, integral 450
Riemann, Georg Friedrich Bernhard, sum 450
Right child 279
Rightdelete Algorithm 481
Riordan, John 101 221 283 293 353 498
Rivest, Ronald L. 249 499
Robertson, Edward L., Ill 432 502
Rogers, Hartley, Jr. 442 496
Root 17 304
Root of unity 123 393
Rosser, J. Barkley 55
Run of increasing numbers 353
Running time, assembly code 5
Running time, convention 10
Running time, practical considerations 5
Running time, timing errors 5
Ruzzo, Walter L. 327 500
Saaty, Thomas L. 242 255 498
Sahni, Sartaj 4 16 20 25 37 40 54 75 83 121 157 180 388 495
Salkin, Harvey M. 487 498
Sample mean 456
Sample space 444
Satisfiability 172 293 427
Satisfiability, three 430—432
Sawtooth function 184
Saxe, James B. 212 499
Schonhage, A. 249 502
Schwartz, Arthur J. 337 497
Schwartz, J.I. 327 500
Scope of sums 59
Score 268
Score, composite games 270—271
Score, sum 269—270
Search tree 279—280 315 354—355
Searching (for solution), Backtrack Estimation 465
Searching (for solution), Backtracking 171
Searching (for solution), Pure Literal Rule 299
Searching (for solution), Silly 293
Searching (table), Binary Search 19
Searching (table), Binary Search with Equality Checking 209
Searching (table), Binarysearch 49
Searching (table), Hashing with Chaining 118
Searching (table), Linear Search 64
Searching (table), Move to Front Algorithm 379
Searching (table), Random Hashing 77
Secondary recurrence 205—210 358
Secondary recurrence, starting index 208
Sedgewick, Robert 4 20 25 37 75 83 121 388 480 498
Select Algorithm 245
Select Algorithm, worst-case time 246—250
Selecting, Maximum 136
Selecting, Median 246
Selecting, Select 245
Selection with replacement 30—31
Selection without replacement 30 31
Semi-invariants 453
Sentence 325
Sentential form 325
Sentinel 72
Separation of variables 352—353
Sequence notation for a recurrence 201
Series Matrix Multiplication Algorithm 322
Set (union) Algorithm 386
Set Union with Ranks and Collapsing worst-case time 390—393
Set Union with Ranks worst-case, time 389
Set Union, Find 386
Set Union, Find'with Collapsing (x) 388
Set Union, Is 386
Set Union, Set 386
Set Union, Union 386
Set Union, Union (t, u) with Ranks 387
Set Union, Union {t, u) with Weights 387
Shing, M.T. 323 498 501
Shortest path algorithm 24
Signal processing 400
Signature of an anagram 94
Significance of a statistical test 447
Silly (satisfiability) Algorithm 293
Simonnard, Michel 487 498
Simple loop 6
Simple Merge Sort Algorithm 227
Simple Merge Sorting 337
Simple path 363
Simple Pattern Match Algorithm 375
Simplex algorithm 411
Singular point 256 491
Singular solutions 203
Sink node 364
Slater, Lucy Joan 142 145 498
Sleator, Daniel Sleator 384 502
Sloane, N.J.A. 306 499
Slow Algorithm (multiplying series of matrices) 323
Snedecor, George W. 444 449 498
Sorting 297 409 “Quicksort” “Mergesort “Heapsort
Sorting, Binary Merge 49
Sorting, Distribute 229
Sorting, Heap 82
Sorting, Heapsort 82
Sorting, Insertion Sort 35
Sorting, lower bounds 412 414
Sorting, Merge 228
Sorting, Polyphase Merge 231
Sorting, Quicksort 72
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