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Random Numbers
Most computer programs do the same thing every time they are executed, so they are said to be deterministic. Usually, determinism is a good thing, since we expect the same calculation to yield the same result. For some applications, though, we would like the computer to be unpredictable. Games are an obvious example. Making a program truly nondeterministic turns out to be not so easy, but there are ways to make it at least seem nondeterministic. One of them is to generate {pseudorandom} numbers and use them to determine the outcome of the program. Pseudorandom numbers are not truly random in the mathematical sense, but for our purposes, they will do. C++ provides a function called random that generates pseudorandom numbers. It is declared in the header file stdlib.h, which contains a variety of "standard library" functions, hence the name. The return value from random is an integer between 0 and RAND_MAX, where RAND_MAX is a large number (about 2 billion on my computer) also defined in the header file. Each time you call random you get a different randomlygenerated number. To see a sample, run this loop: for (int i = 0; i < 4; i++) {int x = random (); cout << x << endl; } On my machine I got the following output: 1804289383846930886 1681692777 1714636915 You will probably get something similar, but different, on yours. Of course, we don't always want to work with gigantic integers. More often we want to generate integers between 0 and some upper bound. A simple way to do that is with the modulus operator. For example: int x = random ();int y = x % upperBound; Since y is the remainder when x is divided by upperBound, the only possible values for y are between 0 and upperBound  1, including both end points. Keep in mind, though, that y will never be equal to upperBound. It is also frequently useful to generate random floatingpoint values. A common way to do that is by dividing by RAND_MAX. For example: int x = random ();double y = double(x) / RAND_MAX; This code sets y to a random value between 0.0 and 1.0, including both end points. As an exercise, you might want to think about how to generate a random floatingpoint value in a given range; for example, between 100.0 and 200.0.


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