INTRODUCTION TO ALGORITHMS 3rd phần 8 pptx
INTRODUCTION TO ALGORITHMS 3rd phần 8 pptx
... 907
11
i
i
!
0
8
D !
8
8
!
1
8
!
2
8
!
3
8
!
4
8
!
5
8
!
6
8
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7
8
Figure 30.2 The values of !
0
8
;!
1
8
;:::;!
7
8
in the complex plane, where !
8
D e
2i =8
is the prin-
cipal 8th root of unity.
!
n
D ... 941
012345
0
1
2
3
4
5
012345
012345
012345
012345
012345
012345
(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...
INTRODUCTION TO ALGORITHMS 3rd phần 1 docx
... Operations 81 3
28. 1 Solving systems of linear equations 81 3
28. 2 Inverting matrices 82 7
28. 3 Symmetric positive-definite matrices and least-squares approximation
83 2
29 Linear Programming 84 3
29.1 ... 954
31.7 The RSA public-key cryptosystem 9 58
? 31 .8 Primality testing 965
? 31.9 Integer factorization 975
32 String Matching 985
32.1 The naive string-matching algorithm 988...
INTRODUCTION TO ALGORITHMS 3rd phần 2 pdf
... wish to hire.
1 58 Chapter 6 Heapsort
1
23
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1
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4
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(a)
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4
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(b)
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14 ... (k)
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982 1
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9
83
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8...
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
the...
INTRODUCTION TO ALGORITHMS 3rd phần 4 ppt
... Greedy Algorithms
0123456 789 1011121314
time
235
306
457
539
659
7610
88 11
981 2
10214
11 12 16
114
k s
k
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1
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6
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1
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1
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8
a
1
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4
a
8
a
9
a
1
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8
a
10
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1
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8
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RECURSIVE-ACTIVITY-SELECTOR(s, ... s
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INTRODUCTION TO ALGORITHMS 3rd phần 5 pdf
... 23
26
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30
2423
26
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7 21
18 52 38
39 41
(a) 3 (b)
(f)
(g) 21 18 52 38
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(h)
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7 ... 7
21
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(b)
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21...
INTRODUCTION TO ALGORITHMS 3rd phần 6 pdf
... ı.s; u/ when 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
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13
7
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(f)
6432
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7
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(b)
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(d)
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Figure ... there is at
least one path, there is...
INTRODUCTION TO ALGORITHMS 3rd phần 7 pps
... equa-
tion ( 28. 4) by P
1
gives P
1
PA D P
1
LU ,sothat
A D P
1
LU : ( 28. 7)
Hence, the vector x is our solution to Ax D b:
Ax D P
1
LUx (by equation ( 28. 7))
D P
1
Ly (by equation ( 28. 6))
D P
1
Pb ... bottom n 1 rows of this matrix must have row rank strictly less
than n 1. The row rank of the entire matrix, therefore, is strictly less than n.
Applying Exercise D.2 -8 to...
INTRODUCTION TO ALGORITHMS 3rd phần 9 docx
... 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 ... all three together do also, and
so we have a way to decide on ˛ in polynomial time. In other words, by “reducing”
solving problem A to solving problem B, we use the “easines...
INTRODUCTION TO ALGORITHMS 3rd phần 10 pps
... published in 185 4. Modern set theory was created
by G. Cantor during the period 187 4– 189 5. Cantor focused primarily on sets of
infinite cardinality. The term “function” is attributed to G. W. Leibniz, ... bound
1 188 Appendix C Counting and Probability
C.1-5
Prove the identity
n
k
!
D
n
k
n 1
k 1
!
(C .8)
for 0<kÄ n.
C.1-6
Prove the identity
n
k
!
D
n
n k
n 1
k
!
for 0 Ä...
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