INTRODUCTION TO ALGORITHMS 3rd phần 3 potx
INTRODUCTION TO ALGORITHMS 3rd phần 3 potx
... 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 ... the elements that hash to the same slot into the same linked list, as Figure 11 .3 shows. Slot j contains a pointer to the head of the list of all stored elements that hash to j ; if...
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INTRODUCTION TO ALGORITHMS 3rd phần 1 docx
... 289 12 .3 Insertion and deletion 294 ? 12.4 Randomly built binary search trees 299 13 Red-Black Trees 30 8 13. 1 Properties of red-black trees 30 8 13. 2 Rotations 31 2 13. 3 Insertion 31 5 13. 4 Deletion 32 3 14 ... polynomials 900 30 .2 The DFT and FFT 906 30 .3 Efficient FFT implementations 915 31 Number-Theor etic Algorithms 926 31 .1 Elementary number-theoretic notions...
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INTRODUCTION TO ALGORITHMS 3rd phần 2 pdf
... (k) 1 234 789101416 10 2 13 4789 1614 1 23 4789 161410 3 21 9874 10 14 16 4 23 9871 10 14 16 8 37 4219 161410 7 43 9821 10 14 16 9 83 2174 161410 10 89 31 74 16142 14 810 39 74 1612 16 14 10 39 78 142 A i i i ii ii i i Figure ... candidate we wish to hire. 158 Chapter 6 Heapsort 1 23 4567 8910 1 23 4567 8910 1 23 4567 8910 1 23 4567 8910 1 23 4567 8910 1 23 4567...
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INTRODUCTION TO ALGORITHMS 3rd phần 4 ppt
... measures of its pixels. 15 .3 Elements of dynamic programming 38 5 1 4 1 1 2 4 1 2 3 4 1 3 4 4 2 2 3 4 2 3 4 4 1 1 2 2 3 3 4 4 1 1 2 3 1 2 3 3 3 3 4 4 2 2 3 3 2 2 3 3 1 1 2 2 Figure 15.7 The recursion ... 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...
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INTRODUCTION TO ALGORITHMS 3rd phần 5 pdf
... 41 17 30 24 23 26 35 46 7 21 18 52 38 39 41 17 30 24 23 26 35 46 7 21 18 52 38 39 41 17 30 24 23 26 35 46 7 21 18 52 38 39 41 17 30 24 23 26 35 46 7 21 18 52 38 39 41 17 30 24 23 26 35 46 7 21 18 52 38 39 ... Heaps A 01 23 A 01 23 A 01 23 A 01 23 A 01 23 A 01 23 (c) (d) (e) 17 30 24 23 26 35 46 7 17 30 24 23 26 35 46 7 21 18 52 38 39 41 (...
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INTRODUCTION TO ALGORITHMS 3rd phần 6 pdf
... Single-Source Shortest Paths (a) (b) (c) 0 6 6 7212 4 3 5 3 s tx yz 39 511 0 6 6 7212 4 3 5 3 s tx yz 39 511 0 6 6 7212 4 3 5 3 s tx yz 39 511 Figure 24.2 (a) A weighted, directed graph with ... ∞ 7–1–2 2 (a) xtsryz 25 16 34 7–1–2 2 (c) xtsryz 25 16 34 7–1–2 2 (e) xtsryz 25 16 34 7–1–2 2 (g) xtsryz 2 5 16 34 7–1–2 2 (b) xtsryz 25 16 34 7–1–2 2 (d) xtsryz 25 16 34...
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INTRODUCTION TO ALGORITHMS 3rd phần 7 pps
... defined by 120 34 4 5 63 x D 3 7 8 ; where A D 120 34 4 5 63 ; 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 00:80:6 002:5 ; P ... equa- tion (28.5) as y 1 D b Œ1 ; l 21 y 1 C y 2 D b Œ2 ; l 31 y 1 C l 32 y 2 C y 3 D b 3 ; : : : l n1 y 1 C l n2 y 2 C l n3 y 3 C C y n D b...
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INTRODUCTION TO ALGORITHMS 3rd phần 8 pptx
... 2. 31 .3 Modular arithmetic 941 01 234 5 0 1 2 3 4 5 01 234 5 01 234 5 01 234 5 01 234 5 01 234 5 01 234 5 (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 14 1 7 11 13 481 132 14711 714 134 112 ... one -to- one correspondence ˛ between their elements such that a C b Á c.mod 4/ if and only if ˛.a/ ˛.b/ Á ˛.c/ .mod 5/. 31 .3- 2 List all subgroups of Z 9 and of Z ...
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INTRODUCTION TO ALGORITHMS 3rd phần 9 docx
... in Figure 34 .8(b) is unsatisfiable. 34 .3- 2 Show that the Ä P relation is a transitive relation on languages. That is, show that if L 1 Ä P L 2 and L 2 Ä P L 3 ,thenL 1 Ä P L 3 . 34 .3- 3 Prove that ... inputs, then we would have to check up to 2 k possible assignments. When 33 .4 Finding the closest pair of points 10 43 Section 2 .3. 1: we are splitting a sorted array into two...
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INTRODUCTION TO ALGORITHMS 3rd phần 10 pps
... likely: Pr f s g D 1 =36 . Define the random variable X to be the maximum of the two values showing on the dice. We have Pr f X D 3 g D 5 =36 ,sinceX assigns a value of 3 to 5 of the 36 possible elementary ... and Probability 0.05 0.10 0.15 0.20 0.25 1 234 56789101112 131 415 0 .30 0 .35 k  2 3 à k1  1 3 à Figure C.1 A geometric distribution with probability p D 1 =3 of succ...
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