Homework 20

(OPTIONAL) If time permits, here is more practice on recursion:

(from the textbook) We have n people in a room, where n is an integer greater than or equal to 1. Each person shakes hands once with every other person. What is the total number, h(n), of handshakes? Write a recursive function to solve this problem.

Consider this to get you started. If there are only one or two people in the room, then

handshake(1) = 0
handshake(2) = 1

If a third person enters the room, she must shake hands with each of the two people already there. This is two handshakes in addition to the number of handshakes that would be made in a room of two people (1), or a total of three handshakes.

If a fourth person enters the room, she must shake hands with each of the three people already there. This is three handshakes in addition to the number of handshakes that would be made in a room of three people (3), or a total of six handshakes.

If you can generalize this to n handshakes, you should be able to write the recursive solution.

Write a program that tests your function by taking in a  `n` from the user and printing out the result of `handshake(n)`.

Turn In a printout of your program and a screen capture showing your program run on `n = 5`.