#!/usr/bin/perl

use strict;
use warnings;

my $n = 1e4;  # number of runs for the statistics
my $N = 32;
my @sum;
my @max = (0)x($N+1);

for (1..$n) {
    my @have_num = ();
    
    for my $i (1..$N) {
        my $attempts = 0;
        while(1) {
            my $rand = int(rand($N));
            #print ".";
            $attempts++;
            unless ($have_num[$rand]) {
                #print " $i: $rand\n";
                $have_num[$rand] = 1;
                last;
            }
        }
        $sum[$i] += $attempts;
        $max[$i]  = $attempts if $attempts > $max[$i];
    }
}

for my $i (1..$N) {
    my $avg = $sum[$i]/$n;
    my $bar = "*" x int($avg+0.5);
    printf "%2d: %6.3f [%6.3f] %s max=%d\n",
            $i,  $avg, $N/($N-$i+1), $bar, $max[$i];
}

__END__

 1:  1.000 [ 1.000] * max=1
 2:  1.033 [ 1.032] * max=4
 3:  1.065 [ 1.067] * max=4
 4:  1.104 [ 1.103] * max=5
 5:  1.142 [ 1.143] * max=7
 6:  1.186 [ 1.185] * max=7
 7:  1.230 [ 1.231] * max=8
 8:  1.283 [ 1.280] * max=8
 9:  1.334 [ 1.333] * max=8
10:  1.392 [ 1.391] * max=10
11:  1.453 [ 1.455] * max=10
12:  1.521 [ 1.524] ** max=11
13:  1.601 [ 1.600] ** max=13
14:  1.684 [ 1.684] ** max=13
15:  1.779 [ 1.778] ** max=14
16:  1.882 [ 1.882] ** max=16
17:  1.999 [ 2.000] ** max=19
18:  2.137 [ 2.133] ** max=17
19:  2.283 [ 2.286] ** max=23
20:  2.462 [ 2.462] ** max=20
21:  2.674 [ 2.667] *** max=26
22:  2.904 [ 2.909] *** max=29
23:  3.198 [ 3.200] *** max=31
24:  3.551 [ 3.556] **** max=37
25:  3.996 [ 4.000] **** max=48
26:  4.554 [ 4.571] ***** max=47
27:  5.331 [ 5.333] ***** max=55
28:  6.400 [ 6.400] ****** max=79
29:  8.026 [ 8.000] ******** max=95
30: 10.597 [10.667] *********** max=140
31: 15.983 [16.000] **************** max=211
32: 32.092 [32.000] ******************************** max=343