Loops - Multimedia Introduction to Programming Using Java - page 263

ple, these two sequences are complements of each other:
sequence 1: ACGTTAC
sequence 2: TGCAATG
Notice how the A's and T's line up with each other, as do the C's and G's. Write
a loop to determine if two String s s1 and s2 representing DNA sequences are
complements of each other. What do you need to assume about the lengths of
those String s?
E8. Write a loop to produce the DNA complement of a String s .
E9. The Fibonacci numbers are the numbers 0 , 1 , 1 , 2 , 3 , 5 , 8 , … . Each number is
the sum of the previous two. This recurrence relation describes the sequence:
f 0 = 0
f 2 = 1
f n = f n-1 + f n-2 for n>1
Write code that finds Fibonacci number n , where n> 1. Use this invariant:
invariant: a= f i and b= f i-1
postcondition: i = n (and, therefore, a = f n )
E10. Write a loop that reads a file containing integers and computes their sum.
E11. Write a loop that reads a file containing integers and computes how many
even integers and how many odd integers it contains.
E12. Compound interest on an account is computed as follows: if an account has
balance balance , and the annual interest rate is rate , the next year's balance is
this:
balance + balance * rate
Write a program segment that reads the initial dollar balance (a double ), the
interest rate (also a double , such as .07 to represent a 7% interest rate), and the
number of years to calculate (an int ), and computes the final balance in the
account.
E13. Write a loop (with initialization) that generates an approximation to e, the
“base of the natural logarithm”, using this formula:
e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... + 1/k! + ...
(You can see what e is by evaluating Math.E .) Here, k! is “ k factorial”, the quan-
tity 1*2*...*k . Use this invariant:
e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... + 1/k! and
tk = 1/k!
Use type double for e and tk . At each iteration, calculate the next term