Practice Problems

1. Write a recursive function void factors(int n) that prints out the factorization of n.
   • What's the base case?
   • How could a recursive call to factors with a smaller n-value help solve the problem?
   Use firstfactor(int) that you guys defined for me in a previous homework (see below).

   
   // Returns the smallest factor of n
   int firstfactor(int n)
   {
     int i = 2;
     while(n % i != 0)
       i++;
   
     return i;
   }
   

   Take a look at a solution
2. Make change

   ~$ ./change
   Enter amount: 134
   Change to give is: QQQQQNPPPP
   
   ~$ ./change
   Enter amount: 32
   Change to give is: QNPP
   

   Solution.
3. Any thoughts on how you could modify to print out coins in increasing value?
4. Printing in binary

   ~$ ./binary
   Enter non-negative integer: 127
   In binary that's 1111111
   
   ~$ ./binary
   Enter non-negative integer: 11
   In binary that's 1011
   
   ~$ ./binary
   Enter non-negative integer: 65536
   In binary that's 10000000000000000
   

   Solution
5. Fibonacci Numbers
6. Computing Continued Fractions
7. Writing Continued Fractions in HTML