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Kenneth Rosen Edition 7 Exercise 8.3 Question 16 (Page No. 535)
Solve the recurrence relation for the number of rounds in the tournament described in question $14.$
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152
Kenneth Rosen Edition 7 Exercise 8.3 Question 15 (Page No. 535)
How many rounds are in the elimination tournament described in question $14$ when there are $32$ teams?
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153
Kenneth Rosen Edition 7 Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
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154
Kenneth Rosen Edition 7 Exercise 8.3 Question 13 (Page No. 535)
Give a big-O estimate for the function $f$ given below if $f$ is an increasing function. $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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Kenneth Rosen Edition 7 Exercise 8.3 Question 12 (Page No. 535)
Find $f (n)$ when $n = 3k,$ where $f$ satisfies the recurrence relation $f (n) = 2f (n/3) + 4 \:\text{with}\: f (1) = 1.$
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Combinatory
May 9, 2020
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626
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kenneth-rosen
discrete-mathematics
counting
recurrence-relation
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156
Kenneth Rosen Edition 7 Exercise 8.3 Question 11 (Page No. 535)
Give a big-O estimate for the function $f$ in question $10$ if $f$ is an increasing function.
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May 9, 2020
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admin
355
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kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 8.3 Question 10 (Page No. 535)
Find $f (n)$ when $n = 2^{k},$ where $f$ satisfies the recurrence relation $f (n) = f (n/2) + 1 \:\text{with}\: f (1) = 1.$
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May 9, 2020
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364
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kenneth-rosen
discrete-mathematics
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Kenneth Rosen Edition 7 Exercise 8.3 Question 9 (Page No. 535)
Suppose that $f (n) = f (n/5) + 3n^{2}$ when $n$ is a positive integer divisible by $5, \:\text{and}\: f (1) = 4.$ Find $f (5)$ $f (125)$ $f (3125)$
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May 9, 2020
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admin
393
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kenneth-rosen
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counting
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159
Kenneth Rosen Edition 7 Exercise 8.3 Question 8 (Page No. 535)
Suppose that $f (n) = 2f (n/2) + 3$ when $n$ is an even positive integer, and $f (1) = 5.$ Find $f (2)$ $f (8)$ $f (64)$ $(1024)$
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May 9, 2020
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admin
702
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kenneth-rosen
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counting
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160
Kenneth Rosen Edition 7 Exercise 8.3 Question 7 (Page No. 535)
Suppose that $f (n) = f (n/3) + 1$ when $n$ is a positive integer divisible by $3,$ and $f (1) = 1.$ Find $f (3)$ $f (27)$ $f (729)$
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May 9, 2020
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admin
476
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kenneth-rosen
discrete-mathematics
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161
Kenneth Rosen Edition 7 Exercise 8.3 Question 6 (Page No. 535)
How many operations are needed to multiply two $32 \times 32$ matrices using the algorithm referred to in Example $5?$
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May 9, 2020
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admin
350
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kenneth-rosen
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Kenneth Rosen Edition 7 Exercise 8.3 Question 5 (Page No. 535)
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
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May 9, 2020
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Kenneth Rosen Edition 7 Exercise 8.3 Question 4 (Page No. 535)
Express the fast multiplication algorithm in pseudocode.
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