Generate k distinct numbers less than n

Question

The task is this: generate k distinct positive numbers less than n without duplication.

My method is the following.

First create array size of k where we should write these numbers:

int a[] = new int[k];

//Now I am going to create another array where I check if (at given number
//position is 1 then generate number again, else put this number in an
//array and continue cycle.

I put a piece here of code and explanations.

int a[]=new int[k];
int t[]=new int[n+1];
Random r=new Random();
for (int i==0;i<t.length;i++){
    t[i]=0;//initialize it to zero
}

int m=0;//initialize it also
for (int i=0;i<a.length;i++){
    m=r.nextInt(n);//random element between  0 and  n
    if (t[m]==1){
        //I have problems with this. I want in case of duplication element
        //occurs repeat this steps afain until there will be different number.
    else{
        t[m]=1;
        x[i]=m;
    }
}

So I fill concret my problem: if t[m]==1. It means that this element occurs already so I want to generate a new number, but problem is that number of generated numbers will not be k because if i==0 and occurs duplicate element and we write continue then it will switch at i==1. I need like goto for the repeat step. Or:

for (int i=0;i<x.length;i++){
    loop:
        m=r.nextInt(n);

    if ( x[m]==1){
        continue loop;
    }
    else{
        x[m]=1;
        a[i]=m;
        continue; //Continue next step at i=1 and so on.
    }
}

I need this code in Java.

Answer 1

Create an array arr with n elements (1..n);
for i=1 to k {
  result[i] = arr[rand]
  delete arr[result[1]]
}

Answer 2

It seems that you need a random sampling algorithm. You want to be able to choose m random items from the set {0,1,2,3...,n-1}.

See this post, where I wrote about 5 efficient algorithms for random sampling.

Following is Floyd's implementation, which can be useful in your case:

private static Random rnd = new Random();
...
public static Set<Integer> randomSample(int n, int m){
    HashSet<Integer> res = new HashSet<Integer>(m);
    for(int i = n - m; i < n; i++){
        int item = rnd.nextInt(i + 1);
        if (res.contains(item))
            res.add(i);
        else
            res.add(item); 
    }
    return res;
}