1. Using domain and range transformations, solve the following
recurrence relations:
a) T(1) = 1, T(n) = 2T(n/2) + 6n - 1
b) T(1) = 1, T(n) = 3T(n/2) + n^2 - n
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
Solve the following recurrence relations. a. x(n) = x(n − 1) + 3
for n > 1, x(1) = 0 b. x(n) = 5x(n − 1) for n > 1, x(1) = 6
c. x(n) = x(n/5) + 1 for n > 1, x(1) = 1 (solve for n = 5k )
Using the backward substitution method, solve the following
recurrence relations: a.T(n)= T(n−1)+3forn>1 ,T(1)=0
b.T(n)=3T(n−1) forn>1 ,T(1)=7 c.T(n)= T(n−1)+n for n>0
,T(0)=0 d.T(n)= T(n/2)+n for n>1 ,T(1)=1(solve for n=2k) e.T(n)=
T(n/3)+1forn>1 ,T(1)=1(solve for n=3k)
What are Big-O expressions for the following runtine
functions?
a) T(n)= nlog n + n log (n2
)
b) T(n)= (nnn)2
c) T(n)= n1/3 +
n1/4 + log n
d) T(n)= 23n +
32n
e) T(n)= n! + 2n
Write algorithm and program : Find the sum of the integers from
1 through n.
a)Use iterative
algorithm and program
b) Use recursive
algorithm and program.
Order the following functions by growth rate:...
Using the following data create a log-log plot. What is the
slope and resulting y-intercept? Show calculations.
Mass
Current
0.02
0
0.15
0.1
0.161
0.2
0.199
0.3
0.298
0.4
0.522
0.5
0.84
0.6
1.298
0.7
1.801
0.8
2.372
0.9
2.571
1
how do i find a peak in time complexity of O(log(n)) in a
list?
input: a list of numbers or integers
output: a possible local peak in the list
for an example:
calling function [2,3,8,9,5] would return 3
im thinking about using binary search but it would require a
sorted list.