Creating random numbers with no duplicates

Question

In this case, the MAX is only 5, so I could check the duplicates one by one, but how could I do this in a simpler way? For example, what if the MAX has a value of 20? Thanks

Answer 1

Your problem seems to reduce to choose k elements at random from a collection of n elements. The Collections.shuffle answer is thus correct, but as pointed out inefficient: its O(n).

Wikipedia: Fisher–Yates shuffle has a O(k) version when the array already exists. In your case, there is no array of elements and creating the array of elements could be very expensive, say if max were 10000000 instead of 20.

The shuffle algorithm involves initializing an array of size n where every element is equal to its index, picking k random numbers each number in a range with the max one less than the previous range, then swapping elements towards the end of the array.

You can do the same operation in O(k) time with a hashmap although I admit its kind of a pain. Note that this is only worthwhile if k is much less than n. (ie k ~ lg(n) or so), otherwise you should use the shuffle directly.

You will use your hashmap as an efficient representation of the backing array in the shuffle algorithm. Any element of the array that is equal to its index need not appear in the map. This allows you to represent an array of size n in constant time, there is no time spent initializing it.

1. Pick k random numbers: the first is in the range 0 to n-1, the second 0 to n-2, the third 0 to n-3 and so on, thru n-k.

2. Treat your random numbers as a set of swaps. The first random index swaps to the final position. The second random index swaps to the second to last position. However, instead of working against a backing array, work against your hashmap. Your hashmap will store every item that is out of position.

int getValue(i)
{
    if (map.contains(i)) 
        return map[i];
    return i;
}

void setValue(i, val)
{   
    if (i == val)
        map.remove(i);
    else
        map[i] = val;
}

int[] chooseK(int n, int k)
{
    for (int i = 0; i < k; i++)
    {
        int randomIndex = nextRandom(0, n - i); //(n - i is exclusive)
        int desiredIndex = n-i-1;

        int valAtRandom = getValue(randomIndex);
        int valAtDesired = getValue(desiredIndex);

        setValue(desiredIndex, valAtRandom);
        setValue(randomIndex, valAtDesired);
    }

    int[] output = new int[k];
    for (int i = 0; i < k; i++)
    {
        output[i] = (getValue(n-i-1));
    }

    return output;
}