CS 361, HW4
Prof. Jared Saia, University of New Mexico
Due: February 17th, 2004
1. Consider the recurrence T(n) = 2T(n/4) + n2
(a) Use the recursion tree method to get a tight upper bound (i.e.
big-O) on the solution to this recurrence
(b) Now use annihilators (and a transformation) to get a tight upper
bound on the solution to this recurrence. Show your work. (Note
that your two bounds should match)
2. Consider the recurrence T(n) = 2T(n/2) + log2n
(a) Use the Master method to get a general solution to this recur-
rence.
(b) Now use annihilators (and a transformation) to get a tight upper
bound on the solution to this recurrence. Show your work. (Note
that your two bounds should match)
3. Consider the following function:
int f (int n){
if (n==0) return 0;
else if (n==1) return 1;
else{
int val = 6*f (n-1);
val = val - 9*f (n-2);
return val;
}
}
(a) Write a recurrence relation for the value returned by f. Solve the
recurrence exactly. (Don’t forget to check it)
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