INTRODUCTION TO ALGORITHMS 3rd phần 5 pdf

... deleting a node 52 1 17 30 24 23 26 35 15 7 21 18 52 38 39 41 (b) 17 30 24 23 26 51 5 7 21 18 52 38 39 41 (c) 17 30 24 23 2 651 5 7 21 18 52 38 39 41 (d) 17 30 24 23 2 651 5 7 21 18 52 38 39 41 (e) 17 30 24 ... 41 (h) 17 30 2423 26 35 46 7 21 18 52 38 39 41 17 30 2423 26 35 46 7 21 18 52 38 39 41 17 30 2423 26 35 46 7 21 18 52 38 39 41 17 30 2423 26 35 46 7 21 18 52 3...

Ngày tải lên: 13/08/2014, 18:20

... returns the index of the candidate we wish to hire. 158 Chapter 6 Heapsort 1 23 456 7 8910 1 23 456 7 8910 1 23 456 7 8910 1 23 456 7 8910 1 23 456 7 8910 1 23 456 7 8910 4 13 2910 14 8 7 (a) 16 41 23 ... must we toss until every bin contains at least one ball? Let us call a toss in which a ball falls into an empty bin a “hit.” We want to know the expected number n of tosses requir...

Ngày tải lên: 13/08/2014, 18:20

... it is added to S,wehadx:d D ı.s; x/ when x was added 24.3 Dijkstra’s algorithm 659 0 ∞∞ ∞∞ 0 ∞ ∞ 1 2 10 5 (c) 10 5 0 8 5 14 7 0 8 5 13 7 0 8 5 9 7 0 5 9 7 8 6432 9 7 s tx yz 1 2 10 5 (f) 6432 9 7 s tx yz 1 2 10 5 (b) 6432 9 7 s tx yz 1 2 10 5 (e) 6432 9 7 s tx yz 1 2 10 5 (a) 6432 9 7 s tx yz 1 2 10 5 (d) 6432 9 7 s tx yz Figure ... difference constraints: x 1  x 2 Ä...

Ngày tải lên: 13/08/2014, 18:20

... Techniques Introduction 357 15 Dynamic Programming 359 15. 1 Rod cutting 360 15. 2 Matrix-chain multiplication 370 15. 3 Elements of dynamic programming 378 15. 4 Longest common subsequence 390 15. 5 Optimal ... Disjoint-set forests 56 8 ? 21.4 Analysis of union by rank with path compression 57 3 VI Graph Algorithms Introduction 58 7 22 Elementary Graph Algorithms 58 9 22...

Ngày tải lên: 13/08/2014, 18:20

... key k not already stored in the table is equally likely to hash to any of the m slots. The expected time to search unsuccessfully for a key k is the expected time to search to the end of list ... keys) K (actual keys) 0 m–1 k 1 k 2 k 3 k 4 k 5 h(k 1 ) h(k 4 ) h(k 3 ) h(k 2 ) = h(k 5 ) Figure 11.2 Using a hash function h to map keys to hash-table slots. Because keys k 2 and k...

Ngày tải lên: 13/08/2014, 18:20

... contribution k 1 1 0. 15 0.30 k 2 0 0.10 0.10 k 3 2 0. 05 0. 15 k 4 1 0.10 0.20 k 5 2 0.20 0.60 d 0 2 0. 05 0. 15 d 1 2 0.10 0.30 d 2 3 0. 05 0.20 d 3 3 0. 05 0.20 d 4 3 0. 05 0.20 d 5 3 0.10 0.40 Total 2.80 For ... probabilities: i 0123 45 p i 0. 15 0.10 0. 05 0.10 0.20 q i 0. 05 0.10 0. 05 0. 05 0. 05 0.10 (a) A binary search tree with expected search cost 2.80. (b) A bin...

Ngày tải lên: 13/08/2014, 18:20

... defined by  120 344 56 3  x D  3 7 8  ; where A D  120 344 56 3  ; b D  3 7 8  ; and we wish to solve for the unknown x. The LUP decomposition is L D  100 0:2 1 0 0:6 0 :5 1  ; U D  56 3 00:80:6 002 :5  ; P ... temporary array T with n elements to store the results of the recursive merge sorting. Line 5 calculates the index q of AŒp : : r to divide the elements into...

Ngày tải lên: 13/08/2014, 18:20

... .a 0 ;a 1 ;:::;a n1 /,wheren is a power of 2. 31.3 Modular arithmetic 941 0123 45 0 1 2 3 4 5 0123 45 0123 45 0123 45 0123 45 0123 45 0123 45 (a) 1 2 4 7 8 11 13 14 1 2 4 7 8 11 13 14 1 2 4 7 8 11 13 14 2 4 8 ... multiple of p in the list. For example, since the prime divisors of 45 are 3 and 5, . 45/ D 45 Â 1  1 3 ÃÂ 1  1 5 Ã D 45 Â 2 3 ÃÂ 4 5 Ã D 24 : If p is prime, th...

Ngày tải lên: 13/08/2014, 18:20

...  is a tautology if it evaluates to 1 for every assignment of 1 and 0 to the input variables. Define TAUTOLOGY as the language of boolean formulas that are tautologies. Show that TAUTOLOGY 2 co-NP. 34.2-9 Prove ... scheme that allows the closest-pair algorithm to check only 5 points following each point in array Y 0 . The idea is always to place points on line l into set P L . Then,...

Ngày tải lên: 13/08/2014, 18:20

... each professor shook hands. 1202 Appendix C Counting and Probability 0. 05 0.10 0. 15 0.20 0. 25 123 456 7891011121314 15 0.30 0. 35 k  2 3 à k1  1 3 à Figure C.1 A geometric distribution with probability ... 0. B.4 Graphs 1171 12 3 45 6 uvwxyz (a) 12 3 4 5 uvwxy (b) G G′ Figure B.3 (a) A pair of isomorphic graphs. The vertices of the top graph are mapped to the vertices of the...

Ngày tải lên: 13/08/2014, 18:20