Question
In: Computer Science
Solve the following recurrences by assuming T(n) is constant for sufficiently small values of n and...
Solve the following recurrences by assuming T(n) is constant for sufficiently small values of n and find time complexity
?(?) = ?(? − 1) + ? (?/2) + ?
?(?) = 4? (?/3) + ???(?)
?(?)=?(?−2)+ 1/ lg(?)
Solutions
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venereology answered 1 year agoRelated Solutions
Give asymptotic tight bounds for T(n) in each of the following recurrences using recursion tree. a....
Give asymptotic tight bounds for T(n) in each of the following
recurrences using recursion tree.
a. T(n) = 2T(n − 1) + 1
b. T(n) = t(n − 1) + n
c. T(n) = 2T (n/4) + √n
Use the substitution method to prove the solutions for the following recurrences: Recurrence Solution 1 T(n)...
Use the substitution method to prove the solutions for the
following recurrences:
Recurrence
Solution
1
T(n) = T(n-1) + n
O(n2)
2
T(n) = T(n/2) + 1
O(lgn)
3
T(n) = T(n/2) + n
ϴ(nlgn)
4
T(n) = 3T(n/2) + n
O(nlg(3)).
5
T(n) = 2T(n/2) + n2
O(n2)
6
T(n) = 4T(n/2 + 2) + n
O(n2)
7
T(n) = 2T(n – 1) + 1
O(2n)
8
T(n) = T(n – 1) + T(n/2) + n
O(2n)
9
T(n)...
- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n
- Solve the following recurrence relation :
T(n) = T(αn) + T((1 − α)n) + n
What are the critical values of t for each of the following values of N and...
What are the critical values of t for each of the
following values of N and alpha using a nondirectional
hypothesis?
N
a
a.
12
0.05
b.
20
0.01
c.
2
0.05
d.
5
0.02
e.
19
0.01
Now using a directional hypothesis?
N
a
f.
13
0.025
g.
17
0.005
h.
8
0.05
i.
15
0.01
j.
10
0.05
6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0...
6. Solve the following recurrence relations
t(n) = t(n-1) + 3 for n>1
t(1) = 0
t(n) = t(n-1) + n for n>1
t(1) = 1
t(n) = 3t(n/2) + n for n>1, n is a power
of 2
t(1) = ½
t(n) = 6t(n-1) – 9t(n-2) for n>1
t(0) = 0 t(1) = 1
Solve for the new pressure in each of the following, with n and V constant: aA...
Solve for the new pressure in each of the following, with
n and V constant:
aA gas with a pressure of 1.25
atm at 60 ∘C is cooled to -24 ∘C.
b. A sample of
N2 with a pressure of 760 mmHg at -70 ∘C is heated to 34 ∘C.
Give asymptotic upper and lower bounds for T(n). Assume that T(n) is constant for n <=...
Give asymptotic upper and lower bounds for T(n). Assume that
T(n) is constant for n <= 2.
Make your bounds as tight as possible, and justify your
answers.
T(n) = T(n-2) + n^2
Introduction to Algorithms - Analysis of Algorithms Solve the following recurrence relation: T(n) = T(an) +...
Introduction to Algorithms - Analysis of Algorithms
Solve the following recurrence relation: T(n) = T(an) + T((1 -
a)n) + n
Solve the recurrence equations by Substitution a) T(n) = 4T (n/2) + n, T (1) =...
Solve the recurrence equations by Substitution
a) T(n) = 4T (n/2) + n, T (1) = 1
b) T(n) = 4T (n/2) + n2 , T (1) = 1
c) T(n) = 4T (n/2) + n3 , T (1) = 1
Use recursion tree to solve the recurrence: T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)
Use recursion tree to solve the recurrence:
T(n) = T(n/15) + T(n/10) + 2T(n/6) + n^(1/2)
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