CSE 131 Module 3: Iteration

Practice Problems

Directions: In Lab 2, you wrote recursive procedures to implement several arithmetic functions. In these practice problems, you will implement similar functions using iteration (loops). Provide an iterative implementation for each of the following specifications.

If you are planning to complete the optional extension on loop invariants for this module, you should prepare by additionally:

  1. Write an iterative procedure expt with the following specification. Use repeated multiplication. Do not use the built-in exponentiation method. 
    PARAMETERS:   integers n and k, with k >= 0
RETURN VALUE: the value of n to the power k
EXAMPLES:     expt(3,2) is 9
              expt(5,0) is 1
              expt(2,5) is 32

  2. Write an iterative procedure harmonicSum with the following specification. 
    PARAMETERS:   a positive integer, n
RETURN VALUE: the sum 1 + 1/2 + 1/3 + ... + 1/(n-1) + 1/n

  3. Write an iterative procedure called geometricSum with the following specification. 
    PARAMETERS:   a non-negative integer, k
RETURN VALUE: the sum 1 + 1/2 + 1/4 + 1/8 + ... + 1/(2^k)

  4. Write an iterative procedure mult with the following specification. Use repeated addition. Do not use the multiplication operator. 
    PARAMETERS:   integers j and k
RETURN VALUE: the product j*k

  5. Write an iterative procedure sumDownBy2 with the following specification. 
    PARAMETERS:   a positive integer n
RETURN VALUE: the sum of the positive integers n + (n-2) + (n-4) + ...
EXAMPLES:     sumDownBy2(7) is 7+5+3+1 = 16
              sumDownBy2(8) is 8+6+4+2 = 20

  6. Write an iterative procedure sumOdd1toN with the following specification. 
    PARAMETERS:   a positive integer n
RETURN VALUE: the sum of all the odd integers between 1 and n, inclusive
EXAMPLES:     sumOdd1toN(7) is 1+3+5+7 = 16
              sumOdd1toN(8) is 1+3+5+7 = 16
              sumOdd1toN(1) is 1

  7. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. Write an iterative procedure lcm with the following specification. 
    PARAMETERS:   positive integers j and k
RETURN VALUE: the least common multiple (LCM) of j and k
EXAMPLES:     lcm(3,5) is 15
              lcm(6,8) is 24

Solutions