6.001 Structure and Interpretation of Computer Programs
Recitation #3


Student Name: ____________________

Friday, September 17, 2004

Topics

Practice

(alt-sum low high) returns an alternating sum of the integers from low to high inclusive.  For example, (alt-sum 0 5) = 0 - 1 + 2 - 3 + 4 - 5.

1. Write a recursive version of alt-sum.  Show a substitution model evaluation for (alt-sum 1 4).








2. Write an iterative version of alt-sum.  Show a substitution model evaluation for (alt-sum 1 4).








(pow a n) = an for integers n >= 0

3. Write a recursive version of pow.  Show a substitution model evaluation for (pow 3 4).













4. Write an iterative version of pow.  Show a substitution model evaluation for (pow 3 4).












(fib n) computes the nth Fibonacci number F(n), where F(0)=0, F(1)=1, and for all n>1, F(n)=F(n-1)+F(n-2).

5. Write a recursive version of fib.  Show a substitution model evaluation for (fib 4).












6. Write an iterative version of fib.  Show a substitution model evaluation for (fib 4).