Randomly generating sequence of ints in a specific range

Question

Hi, I am unsure how to put this and my math skills aren't that strong. But here's what I need.

I want to generate a list of all the 16bit integers (0-65535). But everytime I do so I want to seed the algorithm randomly that each time the list starts with a different integer and all the subsequent integers will be generated once but also in random order.

small example (1-5): ...

1, 5, 3, 2, 4

4, 3, 1, 5, 2

2, 1, 4, 5, 3 ...

Any help?

Answer 1

The easiest way is probably to generate the list of required numbers and then shuffle it.

Answer 2

1. Create a list of integers. In your example from 1 to 5 inclusive;
2. Perform a correct shuffle on it. For example, the Fisher-Yates shuffle. The "correct" part is important as an incorrect shuffle algorithm will yield biased results.

You don't say what language you use but here are two:

PHP

$arr = range(1, 5);
shuffle($arr);

Java

List<Integer> list = new ArrayList<Integer>();
for (int i=1; i<=5; i++) {
  list.add(i);
}
Collections.shuffle(list);

Answer 3

Assuming you have no security requirements, possibly the easiest method is to create a Linear Congruential Generator (LCG) and select a new multiplier and/or increment every time you need to change the sequence. Using the notation from the Wikipedia entry, if you want all k-bit integers, your modulus is m=2^k and conditions 1, 2, and 3 simplify to:
1. c is odd
2. a = 1 + 4*x for any integer x

There are other generators that are similar to LCG that should be just as satisfactory.