CSCI-1200 Computer Science II — Spring 2006
Lab 7 — Recursion II
Checkpoint 1
Study the recursive definition below which computes the nth Fibonacci number. Draw the complete acti-
vation record hierarchy that results from the function call fib a(4). This problem is complex to analyze
exactly, but find a reasonable upper bound on the number of calls to fib a as a function of n.
int fib_a(int n) {
assert (n >= 0);
if (n == 0) return 1;
if (n == 1) return 1;
return fib_a(n-1) + fib_a(n-2);
}
To complete this checkpoint: Show a TA your diagram and analysis.
Checkpoint 2
Complete the implementation of the driver function for this alternate recursive definition for Fibonacci:
int fib_b_helper(int n, int count, int prev_fib, int current_fib) {
if (n == count) return current_fib;
return fib_b_helper(n, count+1, current_fib, current_fib+prev_fib);
}
int fib_b(int n) {
assert (n >= 0);
return fib_b_helper( /* COMPLETE THIS FUNCTION CALL */ );
}
Draw the activation record hierarchy for a call to fib b(4) and give the order notation for the number of
operations. Using this second version as a guide, write Fibonacci iteratively (that is, using a for or while
loop instead of recursion).
Note: The differences between the activation record hierarchies of the recursive versions of Fibonacci illus-
trate the fact that not all recursive functions can be easily re-written as iterative functions.
To complete this checkpoint: Show a TA your diagram, analysis and iterative function.
Checkpoint 3
Checkpoint 3 will be available in lab. To prepare, study the Merge Sort and Nonlinear Word Search code
we developed in Lecture 10 which has been posted on the webpage.