Tamamlanmış

Algorithm, Big-Oh

A framework for Θ- simplifications:

As a kind of reminder and reference, here are the basic rules for Θ-simplifications, where a, b stand for arbitrary terms, and n ≥ 1:

(EQ) If a = b, then a = Θ(b). For example (n+5)^2 = θ(n^2 +10n+25).

(IQ) If a≤b,then a=O(b). E.g.,2^n =O(3^n).

(F) For a (constant!) factor α > 0, we have α · a = Θ(a). E.g., 5n^2 = Θ(n^2).

(LO) Lower-order terms: if a = O(b), then a + b = Θ(b). E.g., n^2 + n^3 = Θ(n^3).

(L1) logb(n) = Θ(lg(n)) for any (constant) b > 1. E.g., log10(n) = Θ(lg(n)).

(L2) lg(n) = O(n^α) for any (constant) α > 0.

E.g., lg(n) = O(n^2).

(P)For(constant)α≥β>0,wehavenβ ≤ n^α. E.g., n^2 = O(n^3).

(E) n^α = O(β^n) for any (constant) α > 0, β > 1. E.g., n^3 = O(2^n).

Questions

[url removed, login to view] Θ-expressions which are as simple as possible, and state the rules you applied:

4n^8 = Θ(?)

2n^6+8n^3+n^7 = Θ(?)

4·2^n+n^1000 = Θ(?)

5√n + log4(n) = Θ(?)

(n+2)^4 = Θ(?)

lg(n)+3^n+n^3 = Θ(?)

2. After Θ-simplifications one sees, that each of the following expression is either (asymp- totically) a logarithm (L), a power (P), or an exponential (E) — say which applies:

(a) log10 n+5lgn

(b) 1.6^n

(c) 10n+n^2

(d)4 √n+logn

(e) 2n/10^1000 + n^5 + lg n

3. Mark each of the following assertions “true” or “false”:

(a) All logarithms are asymptotically equal.

(b) Some exponentials are asymptotically smaller than some powers.

(c) Every power is asymptotically smaller than every exponential.

(d) Some powers are asymptotically smaller than some logarithms.

(e) Every logarithm is asymptotically smaller than any power.

(f) All powers are asymptotically equal.

(g) All exponentials are asymptotically equal.

4. Solve the following recurrences, using the simplified Master Theorem, where you need to show the (small) computation, and state the case applied:

(a) T (n) = 16T (n/2) + n^4 .

(b) T(n) = 4T(n/2) + n^4.

(c) T(n) = T(n/2) + T(n/2) + 2.

(d) T(n) = 5T(n/3) + n.

(e) T(n) = 7T(n/3) + n^2.

(f) T(n) = 7T(n/7) + n^2.

Beceriler: Algoritma

Daha fazlasını gör: the big o 1, simple algorithm example, recurrences, o logn, o 1 algorithm, lo p, l2, give an example of an algorithm, example of an algorithm, example of algorithm, example of a algorithm, example for algorithm, example algorithm, c algorithm questions, big oh, big o 2, an example of an algorithm, algorithm example, algorithm big o, algorithm b

İşveren Hakkında:
( 12 değerlendirme ) Swansea, United Kingdom

Proje NO: #8827450

Seçilen:

madhur0912

A proposal has not yet been provided

1 gün içinde %selectedBids___i_sum_sub_4%%project_currencyDetails_sign_sub_5% GBP
(6 Değerlendirme)
3.9

Bu iş için 4 freelancer ortalamada £113 teklif veriyor

Calleus

Hi, I have strong background in Algorithms and experience in Complexity. Let me help you. I am ready to start.

£50 GBP in 3 gün içinde
(34 Değerlendirme)
5.2
szymszteinsl

Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !Ready !

£100 GBP in 2 gün içinde
(2 Değerlendirme)
3.2
klimkolyvanov

Hi! I graduated with the degree in Applied Mathematics and Computer Science. For sure I will finish this project today. :) We can discuss the price because normally I adjust the price to the amount of hours spen Daha Fazla

1 gün içinde %bids___i_sum_sub_32%%project_currencyDetails_sign_sub_33% GBP
(0 Değerlendirme)
0.0