INTRODUCTION TO ALGORITHMS 3rd phần 10 pps
INTRODUCTION TO ALGORITHMS 3rd phần 10 pps
... created by G. Cantor during the period 1874–1895. Cantor focused primarily on sets of infinite cardinality. The term “function” is attributed to G. W. Leibniz, who used it to refer to several kinds ... vertices of the top graph are mapped to the vertices of the bottom graph by f.1/ D u; f .2/ D ; f .3/ D w; f.4/ D x;f .5/ D y;f .6/ D ´. (b) Two graphs that are not isomorphic, since th...
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INTRODUCTION TO ALGORITHMS 3rd phần 7 pps
... 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 D 001 100 010 : (You might want to verify that PA D ... comes into the picture, executing instructions 4–6. Processor 2 reads x from memory into register r 2 ; increments it, producing the value 1 in r 2 ; and then stores this value into...
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INTRODUCTION TO ALGORITHMS 3rd phần 1 docx
... convex hull 102 9 33.4 Finding the closest pair of points 103 9 34 NP-Completeness 104 8 34.1 Polynomial time 105 3 34.2 Polynomial-time verification 106 1 34.3 NP-completeness and reducibility 106 7 34.4 ... 220 III Data Structures Introduction 229 10 Elementary Data Structures 232 10. 1 Stacks and queues 232 10. 2 Linked lists 236 10. 3 Implementing pointers and objects 241 10....
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INTRODUCTION TO ALGORITHMS 3rd phần 2 pdf
... (k) 123478 9101 416 10 2 13 4789 1614 1 23 4789 161 410 3 21 9874 10 14 16 4 23 9871 10 14 16 8 37 4219 161 410 7 43 9821 10 14 16 9 83 2174 161 410 10 89 3174 16142 14 810 3974 1612 16 14 10 3978 142 A i i i ii ii i i Figure ... we wish to hire. 158 Chapter 6 Heapsort 1 23 4567 8 910 1 23 4567 8 910 1 23 4567 8 910 1 23 4567 8 910 1 23 4567 8 910 1 23 4567 8 910 4 13 2...
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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 ... interest are pointers to other nodes, and they vary according to the type of tree. Binary trees Figure 10. 9 shows how we use the attributes p, left,andright to store pointers to t...
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INTRODUCTION TO ALGORITHMS 3rd phần 4 ppt
... 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 a given ... tables 2 for i D 1 to n C 1 3 eŒi;i 1 D q i1 4 wŒi;i 1 D q i1 5 for l D 1 to n 6 for i D 1 to n l C 1 7 j D i C l 1 8 eŒi;j D1 9 wŒi;j D wŒi;j 1 C...
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INTRODUCTION TO ALGORITHMS 3rd phần 5 pdf
... 14,15 u 2 0 1 A proto-vEB(2) 1 1 u 2 0 1 A proto-vEB(2) 0 0 u 2 0 1 A proto-vEB(2) 0 1 u 2 0 1 A proto-vEB(2) 0 0 u 2 0 1 A proto-vEB(2) 0 0 u 2 0 1 A proto-vEB(2) 0 0 u 2 0 1 A proto-vEB(2) 0 1 u 2 0 1 A proto-vEB(2) 1 1 u 2 0 1 A proto-vEB(2) 1 1 u 2 0 1 A proto-vEB(2) 1 1 u 2 0 1 A proto-vEB(2) 0 0 u 2 0 1 A proto-vEB(2) 0 1 u 2 0 1 A proto-vEB(2) 0 1 u 2 0 1 A proto-vEB(2) 1 1 u 2 Figure...
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INTRODUCTION TO ALGORITHMS 3rd phần 6 pdf
... there is at least one path, there is a shortest path p from s to u. Prior to adding u to S, path p connects a vertex in S, namely s, to a vertex in V S, namely u.Letus consider the first vertex ... 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...
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INTRODUCTION TO ALGORITHMS 3rd phần 8 pptx
... in binary is 000; 100 ; 010; 110; 001; 101 ; 011; 111, and when we reverse the bits of each value we get the sequence 000; 001; 010; 011; 100 ; 101 ; 110; 111. To see that we want a bit-reversal permutation ... this manner until the vector holds two .n=2/-element DFTs, which we combine using n=2 butterfly operations into the final n-element DFT. To turn this bottom-up approach into code...
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INTRODUCTION TO ALGORITHMS 3rd phần 9 docx
... D f 10; 11; 101 ; 111; 101 1; 1101 ; 100 01; : : : g is the language of binary represen- 105 2 Chapter 34 NP-Completeness polynomial-time reduction algorithm instance β polynomial-time algorithm to ... 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 TAUT...
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