Functions: Chap 3

1. Mid Val: User enters three doubles; they're sent to a func, which returns the middle value (in terms of size). 5 points

2. Caps: Enter a lower case letter, send it to a func, and return the capital version of that letter. 5 points

3. d-v-t program: Prompt the user for a distance traveled, average speed, and travel time. The user will enter 2 of the 3, entering a zero for the quantity that is unknown. Call one of three functions (depending on the unknown) to compute the unknown. 5 points

4. Prime numbers: The user enters two numbers, n1 and n2, and a function is called that prints all the prime numbers, p, such that n1 <= p <= n2. Determine if a number is prime using a loop and a test for divisibility. For full credit the program must be efficient. 10 points

5. Voting program: Create at least four candidates for whom an unlimited number of voters can cast ballots. To cast a ballot for a particular candidate, a certain number or letter should be entered. After each vote, call a tally function that updates the vote count for the candidates. Enter D or ten to display the current status of each candidate via a function call. When Q or zero is entered another function should be called that tells us that the polls have closed. This function should also call the display function so we can see the final results, and it should declare a winner. Note: Although it is not considered a good programming practice, you may use global variables to represent the # of votes for each candidate. 20 points

6. Sum of squares: Make an iterative (normal) func with a loop that prints it for all even #'s from 1 to an input val. Make another func (without a loop) that does this recursively (pg 172). 10 points

7. Peanut butter: Enter the size of the pb jar in ounces and right next to it the price in dollars. On the next line the user enters the same data for another brand. Do this until the user enters zero for size or price. After each pair of numbers is entered a unit price func should be called that contains a static var (pg 169). The static var will contain the price per ounce and will only be overwritten if the new price per ounce is the lowest so far. Print which brand is the best deal. 10 points

8. Guessing game: Computers thinks of a rand num from 1 up to some max that the human chooses. Human guesses. Computer says too high or too low, AND hot or cold (hot means within 10% of right answer), and counts how many guesses the human needs. 15 pts.

9. Free throw simulation: Human tells computer how good a free throw shooter he is (as a %). Computer estimates the probability of human making at least N free throws out of ten, where human enters N. It should do so by calling a trial function that generates 10 rand #'s, one for each shot. Each shot should be tested to see whether it is a basket or a miss, based on the human's shooting %. The trial func counts the # of baskets & returns a value that represents whether the trial was successful or not (based on N). Using a loop, run about 10 thousand trials. The approx probability is the # of successful trials over the total # of trials. Note: This technique, called the Monte Carlo method, is very powerful, especially in highly complex situations in which calculating the theoretical probability is extremely difficult. Good math students should calculate the theoretical probability and compare it to their simulated results (see me for help). 25 pts.