Advanced Fibonacci Problem Set in MATLAB
This booklet extends the basic Fibonacci example by adding five related programming problems. Each section gives:
- The MATLAB function or script to save in a file (.m)
- Exact commands to run in the Command Window
- A short explanation or expected output
>> How to use this guide
1. Copy each code block into its own .m file (use the suggested file name).
2. Save the file in your current MATLAB folder.
3. In the Command Window, type the test commands exactly as shown.
4. For plotting examples, a new Figure window will pop up automatically.
Problem 1 - Count the Number of Recursive Calls
Modify the recursive function so it also returns how many times it was invoked.
Save as fibonacci_count.m:
function [result, count] = fibonacci_count(n)
% Counted recursive Fibonacci
if n == 0 || n == 1
result = n;
count = 1; % this call
else
[r1, c1] = fibonacci_count(n-1);
[r2, c2] = fibonacci_count(n-2);
result = r1 + r2;
count = c1 + c2 + 1; % +1 for this call
end
end
Run in Command Window:
%% Command window test
n = 5;
[fib, calls] = fibonacci_count(n);
fprintf('Fibonacci(%d) = %d, recursive calls = %d\n', n, fib, calls);
Expected output:
Fibonacci(5) = 5, recursive calls = 15
Problem 2 - Compare Recursive vs Iterative Timing
First, create an iterative Fibonacci function (save as fibonacci_basic.m):
function fib = fibonacci_basic(n)
if ~isscalar(n) || n < 0 || n ~= fix(n)
error('n must be a non-negative integer');
end
fib = zeros(1,n+1);
fib(1) = 0;
if n >= 1, fib(2) = 1; end
for k = 3:n+1
fib(k) = fib(k-1) + fib(k-2);
end
fib = fib(end); % return F(n) only
end
