Problem 1
Write pseudocode instructions to carry out each of the following computational operations: a. Determine the area of a triangle given values for the base \(b\) and the height \(h\). b. 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. c. Determine the flying time between two cities given the mileage \(M\) between them and the average speed of the airplane.
Problem 5
Write an if/then/else primitive to do each of the following operations: a. Compute and display the value \(x \div y\) 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.
Problem 7
Write an algorithm that uses a 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, to determine whether CSU won or lost. After reading in these 10 pairs of values, print the won/lost/tie record of CSU. In addition, if this record is a perfect \(10-0\), then print the message 'Congratulations on your undefeated season'.
Problem 11
Develop an algorithm to compute gross pay. The inputs to 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.
Problem 20
Design an algorithm that is given a positive integer \(N\) and determines whether \(N\) is a prime number, that is, not evenly divisible by any value other than 1 and itself. The output of your algorithm is either the message 'not prime', along with a factor of \(N\), or the message 'prime'.
Problem 21
Write an algorithm that generates a Caesar cipher-a secret message in which each letter is replaced by the one that is \(k\) letters ahead of it in the alphabet, in a circular fashion. For example, if \(k=5\), then the letter a would be replaced by the letter \(f\), and the letter \(x\) would be replaced by the letter c. We'll talk more about the Caesar cipher and other encryption algorithms in Chapter 8.) The input to your algorithm is the text to be encoded, ending with the special symbol " \(\$$ ", and the value \)k$. (You may assume that, except for the special ending character, the text contains only the 26 letters a ... z.) The output of your algorithm is the encoded text.
Problem 22
Design and implement an algorithm that is given as input an integer value \(k \geq 0\) and a list of \(k\) numbers \(N_{1}, N_{2}, \ldots, N_{k}\). Your algorithm should reverse the order of the numbers in the list. That is, if the original list contained: $$ N_{1}=5, N_{2}=13, N_{3}=8, N_{4}=27, N_{5}=10 $$ then when your algorithm has completed, the values stored in the list will be: $$ N_{1}=10, N_{2}=27, N_{3}=8, N_{4}=13, N_{5}=5 $$
Problem 23
Design and implement an algorithm that gets as input a list of \(k\) integer values \(N_{1}, N_{2}, \ldots, N_{k}\) as well as a special value SUM. Your algorithm must locate a pair of values in the list \(N\) that sum to the value SUM. For example, if your list of values is \(3,8,13,2,17,18,10\), and the value of SUM is 20, then your algorithm would output either of the two values \((2,18)\) or \((3,17)\). If your algorithm cannot find any pair of values that sum to the value SUM, then it should print the message 'Sorry, there is no such pair of values'.
Problem 24
Instead of reading in an entire list \(N_{1}, N_{2}\), ... all at once, some algorithms (depending on the task to be done) read in only one element at a time and process that single element completely before inputting the next one. This can be a useful technique when the list is very big (e.g., billions of elements) and there might not be enough memory in the computer to store it in its entirety. Write an algorithm that reads in a sequence of values \(V \geq 0\), one at a time, and computes the average of all the numbers. You should stop the computation when you input a value of \(V=-1\). Do not include this negative value in your computations; it is not a piece of data but only a marker to identify the end of the list.
Problem 25
Write an algorithm to read in a sequence of values \(V \geq 0\), one at a time, and determine if the list contains at least one adjacent pair of values that are identical. The end of the entire list is marked by the special value \(V=-1\). For example, if you were given the following input: \(14,3,7,7,9,1,804,22,-1\) the output of your algorithm should be a 'Yes' because there is at least one pair of adjacent numbers that are equal (the 7s). However, given the following input: \(14,3,7,77,9,1,804,22,-1\) the output of your algorithm should be a 'No' because there are no adjacent pairs that are
