import java.util.Random;

public class Test {
        
    public static void main(String args[]) {
        int[] n = getRandomSeries(20);
        for(int a : n) {
            System.out.print(a + " ");
        }
    }
    
    public static int[] getRandomSeries(int size) {
        int[] series = new int[size];
        for(int i = 0; i < size; i++) {
            series[i] = i + 1;
        }
        Random ran = new Random();
        for(int i = 0, k = size * 2; i < k; i++) {
            int index1 = ran.nextInt(size);
            int tmp = series[index1];
            int index2 = ran.nextInt(size);
            series[index1] = series[index2];
            series[index2] = tmp;
        }
        return series;
    }
}

------解决方案--------------------
Java code

        List<Integer> list = new ArrayList<Integer>();
        Random rnd = new Random();
        for (int i = 0; i < 20; i++) {
            int j = rnd.nextInt(21);
            if (!list.contains(j) && j != 0) {
                list.add(j);
            } else {
                --i;
            }
        }
        Integer[] ii = list.toArray(new Integer[20]);
        Arrays.sort(ii);
        for (Integer i : ii) {
            System.out.println(i);
        }