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# Assignment 1 – choose ONE exercise each from Chapters 2 and 3
## Chapter 2: Exercises
1. Write pseudocode instructions to carry out each of the following
computational operations:
* Determine the area of a triangle given values for the base `b` and the height `h`.
* Compute the interest earned in 1 year given the starting account balance B
and the annual interest rate / and assuming simple interest, that is, no
compounding. Also determine the final balance at the end of the year.
* Determine the flying time between two cities given the mileage M between
them and the average speed of the airplane.
2. Using only the sequential operations described in Section 2.2.2, write an
algorithm that gets values for the starting account balance B, annual
interest rate I, and annual service charge S. Your algorithm should output
the amount of interest earned during the year and the final account balance
at the end of the year. Assume that interest is compounded monthly and the
service charge is deducted once, at the end of the year.
3. Using only the sequential operations described in Section 2.2.2, write an
algorithm that gets four numbers corresponding to scores received on three
semester tests and a final examination. Your algorithm should compute and
display the average of all four tests, weighting the final exam twice as
heavily as a regular test.
4. Write an algorithm that gets the price for item A plus the quantity
purchased. The algorithm prints the total cost, including 6% sales tax.
5. Write an if/then/else primitive to do each of the following operations:
* a. Compute and display the value `x / y` if the value of `y` is not `0`. if
`y` does have the value `0`, then display the message `Unable to perform the
division.`
* b. Compute the area and circumference of a circle given the radius `r` if
the radius is greater than or equal to `1.0`; otherwise, you should compute
only the circumference.
6. Modify the algorithm of Exercise 2 to include the annual service charge only
if the starting account balance at the beginning of the year is less than
$1,000. If it is greater than or equal to $1,000, then there is no annual
service charge.
7. Write an algorithm that uses the `loop` (1) to input 10 pairs of numbers,
where each pair represents the score of a football game with the Computer
State University (CSU) score listed first, and (2) for each pair of numbers,
determine whether CSU won or lost. After reading in these 10 pairs of values,
print out the won/lost/tie record of CSU. In addition, if this record is
perfect 10-0, then print out the message `Congratulations on your undefeated
season.`
8. Modify the test-averaging algorithm of Exercise 3 so that it reads in 15 test
scores rather than 4. There are 14 regular tests and a final examination,
which counts twice as much as a regular test. Use a loop to input and sume
the scores.
9. Modify the sales computation algorithm of Exercise 4 so that after finishing
the computation for one item, it starts on the computation for the next. This
iterative process is repeated until the total cost exceeds $1,000.
10. Write an algorithm that is given your electric meter readings (in
kilowatt-hours) at the beginning and end of each month of the year. The
algorithm determines your annual cost of electricity on the basis of a
charge of 6 cents per kilowatt-hour for the first 1,000 kilowatt-hours of
each month and 8 cents per kilowatt-hour beyond 1,000. After printing out
your total annual charge, the algorithm also determines whether you used
less than 500 kilowatt-hours for the entire year and, if so, prints out a
message thank you for conserving electricity.
11. Develop an algorithm to compute gross pay. The inputs of your algorithm are
the hours worked per week and the hourly pay rate. The rule for determining
gross pay is to pay the regular pay rate for all hours worked up to 40,
time-and-a-half for all hours over 40 up to 54, and double time for all
hours over 54. Compute and display the value for gross pay using this rule.
After displaying one value, ask the user whether he or she wants to do
another computation. Repeat the entire set of operations until the user says
no.
12. Develop a formal argument that "proves" that the sequential search algorithm
shown in Figure 2.13 cannot have an infinite loop; that is, prove that it
will always stop after a finite number of operations.
13. Modify the sequential search algorithm of Figure 2.13 so that it works
correctively even if the names in the directory are not unique, that is, if
the desired name occurs more than once. Your modified algorithm should find
every occurrence of NAME in the directory and print out the telephone number
corresponding to every match. In addition, after all the numbers have been
displayed, your algorithm should print out how many occurrences of NAME were
located. For example, if NAME occurred three times, the output of the
algorithm might look something like this:
528-5638
922-7874
488-2020
14. Use the Find Largest algorithm of Figure 2.14 to help you develop an
algorithm to find the median value in a list containing `N` unique numbers.
The median of `N` numbers is defined as the value in the list in which
approximately half the values are larger than it and half the values are
smaller than it. For example, consider the following list of seven number:
25, 50, 83, 44, 91, 20, 55
The median value is 50 because three values (20, 26, 44) are smaller and
three values (55, 83, and 91) are larger. if `N` is an even value, then the
number of values larger than the median will be one greater than the number
of values smaller than the median.
15. With regard to the Find Largest algorithm of Figure 2.14, if the numbers in
our list were not unique and therefore the largest number could occur more
than once, would the algorithm find the first occurrence? The last
occurrence? Every occurrence? Explain precisely how this algorithm would
behave when presented with this new condition.
16. On the sixth line of the Find Largest algorithm of Figure 2.14, there is an
instruction that reads, `while(i<=n) do`. Explain exactly what would happen
if we changed that instruction to read as follows:
* a. `while(i>=n) do`
* b. `while(i<n) do`
* c. `while(i==n) do`
17. On the seventh line of the Find Largest algorithm of Figure 2.14, there is
an instruction that reads `if A > largest so far then ...`. Explain exactly
what would happen if we changed that instruction to rea as follows:
* a. `if A >= largest so far then...`
* b. `if A < largest so far then...`
Looking back at your answers in Exercises 16 and 17, what do they say about
the importance of using the correct relational operations (<,==,>,>=,<=,!=)
when writing out either an iterative or conditional algorithmic primitive?
18. Refer to the pattern-matching algorithm in Figure 2.16.
* a. What is the output of the algorithm as it currently stands if our text is
`We must band together and handle adversity` and we search for `and`?
* b. How could we modify the algorithm so that it finds only the complete word
`and` rather than the occurrence of the character sequance `a`, `n` and `d`
that is contained within another word, such as `band`?
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