Generating Unique Random Numbers in Java

Question

I\'m trying to get random numbers between 0 and 100. But I want them to be unique, not repeated in a sequence. For example if I got 5 numbers, they should be 82,12,53,64,32

Answer 1

One clever way to do this is to use exponents of a primitive element in modulus.

For example, 2 is a primitive root mod 101, meaning that the powers of 2 mod 101 give you a non-repeating sequence that sees every number from 1 to 100 inclusive:

2^0 mod 101 = 1
2^1 mod 101 = 2
2^2 mod 101 = 4
...
2^50 mod 101 = 100
2^51 mod 101 = 99
2^52 mod 101 = 97
...
2^100 mod 101 = 1

In Java code, you would write:

void randInts() {
int num=1;
for (int ii=0; ii<101; ii++) {
    System.out.println(num);
    num= (num*2) % 101;
    }
}

Finding a primitive root for a specific modulus can be tricky, but Maple's "primroot" function will do this for you.