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...
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...
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....
INTRODUCTION TO ALGORITHMS 3rd phần 2 pdf
... (k)
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158 Chapter 6 Heapsort
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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...
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
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2 0.05 0.15
d
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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
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4 wŒi;i 1 D q
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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...
INTRODUCTION TO ALGORITHMS 3rd phần 5 pdf
... 14,15
u
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Figure...
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)
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5
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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...
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...