CS141 Lab 3
For the labs of the third week:
Review recurrence relations, i.e. how to solve them using the
forward/backforward substitution (also called iteration) method
and the Master Theorem (Levitin Ch 2.4, Ch 4, and Appendix B),
and how to use them to analyze time complexity. Use Ex. 4-1(a,b) on page
85 of CLRS as examples. Refer to the
tutorial on recurrence relations and
my old lecture notes based on CLRS.
Give a recursive algorithm for sequential search in a list
(although it's not natural).
Derive the recurrence relation for its time complexity, and
solve it to obtain O(n).
Continue the in-lab exercise: Calculate the n-th Fibonnaci number;
But this time, emphasize the time complexity analysis.
printFib(n): Given a number n print the nth
Do it in two ways:
1. Recursively using recurrence:
fib(n) = fib(n-1) + fib(n-2)
x = 0
y = 1
for i = 2 to n
z = x + y
x = y
y = z
- Implement both algorithms and count time difference
as a function of n. Create a table and observe the trend.
- Obtain the asymptotic complexity of each algorithm as functions of n,
using a recurrence relation for the recurisve one.
For simplicity, approximate the recurrence
relation with T(n) <= 2*T(n-1).
Compare the complexity functions and correlate with the observed execution times.
TA: Keep track of which students completed the exercise.