You didn't calculate (n + p) %p

But ( 0 + x ) % x is just x % x; and is always 0?

Yes you're right.

So your code does something like this :-

     int r = rand();
     int n = r % p;
     while ( a[n] != 0 ) {
         n = (n + n) % p;
     }
     a[n] = r;
[download]

so you get stuck when n =0. But if you add a value to n that's relatively prime to P then it should work.

for example,

say (($_ + 5) % 11 ) for (0..10);

5
6
7
8
9
10
0
1
2
3
4
[download]

if you add a value to n that's relatively prime to P then it should work.

As with my initial thought of adding 1, all that does is move the problem, not fix it, whatever relatively prime constant you use:

for( my $i = 0; $i < 17; ++$i ) { 
    my $j = $i; 
    printf "%2u: %s\n", $i, join' ', map{ sprintf "%2u", $j = ( $j + $
+i + 13 ) % 17 } 0 .. 16; 
};; #                                                                 
+  ##^^##   
 0: 13  9  5  1 14 10  6  2 15 11  7  3 16 12  8  4  0
 1: 15 12  9  6  3  0 14 11  8  5  2 16 13 10  7  4  1
 2:  0 15 13 11  9  7  5  3  1 16 14 12 10  8  6  4  2
 3:  2  1  0 16 15 14 13 12 11 10  9  8  7  6  5  4  3
 4:  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  4  <<<<<<<<< here
 5:  6  7  8  9 10 11 12 13 14 15 16  0  1  2  3  4  5
 6:  8 10 12 14 16  1  3  5  7  9 11 13 15  0  2  4  6
 7: 10 13 16  2  5  8 11 14  0  3  6  9 12 15  1  4  7
 8: 12 16  3  7 11 15  2  6 10 14  1  5  9 13  0  4  8
 9: 14  2  7 12  0  5 10 15  3  8 13  1  6 11 16  4  9
10: 16  5 11  0  6 12  1  7 13  2  8 14  3  9 15  4 10
11:  1  8 15  5 12  2  9 16  6 13  3 10  0  7 14  4 11
12:  3 11  2 10  1  9  0  8 16  7 15  6 14  5 13  4 12
13:  5 14  6 15  7 16  8  0  9  1 10  2 11  3 12  4 13
14:  7  0 10  3 13  6 16  9  2 12  5 15  8  1 11  4 14
15:  9  3 14  8  2 13  7  1 12  6  0 11  5 16 10  4 15
16: 11  6  1 13  8  3 15 10  5  0 12  7  2 14  9  4 16

for( my $i=0; $i < 17; ++$i ) { 
    my $j = $i; 
    printf "%2u: %s\n", $i, join' ', map{ sprintf "%2u", $j = ( $j + $
+i + 11 ) % 17 } 0 .. 16; 
};; ##                                                                
+  ##^^##
 0: 11  5 16 10  4 15  9  3 14  8  2 13  7  1 12  6  0
 1: 13  8  3 15 10  5  0 12  7  2 14  9  4 16 11  6  1
 2: 15 11  7  3 16 12  8  4  0 13  9  5  1 14 10  6  2
 3:  0 14 11  8  5  2 16 13 10  7  4  1 15 12  9  6  3
 4:  2  0 15 13 11  9  7  5  3  1 16 14 12 10  8  6  4
 5:  4  3  2  1  0 16 15 14 13 12 11 10  9  8  7  6  5
 6:  6  6  6  6  6  6  6  6  6  6  6  6  6  6  6  6  6 <<<<<<<<<<<<< h
+ere
 7:  8  9 10 11 12 13 14 15 16  0  1  2  3  4  5  6  7
 8: 10 12 14 16  1  3  5  7  9 11 13 15  0  2  4  6  8
 9: 12 15  1  4  7 10 13 16  2  5  8 11 14  0  3  6  9
10: 14  1  5  9 13  0  4  8 12 16  3  7 11 15  2  6 10
11: 16  4  9 14  2  7 12  0  5 10 15  3  8 13  1  6 11
12:  1  7 13  2  8 14  3  9 15  4 10 16  5 11  0  6 12
13:  3 10  0  7 14  4 11  1  8 15  5 12  2  9 16  6 13
14:  5 13  4 12  3 11  2 10  1  9  0  8 16  7 15  6 14
15:  7 16  8  0  9  1 10  2 11  3 12  4 13  5 14  6 15
16:  9  2 12  5 15  8  1 11  4 14  7  0 10  3 13  6 16

for( my $i=0; $i<17; ++$i ) { 
    my $j = $i; 
    printf "%2u: %s\n", $i, join' ', map{ sprintf "%2u", $j = ( $j + $
+i + 7 ) % 17 } 0 .. 16; 
};; ##                                                                
+  ##^##
 0:  7 14  4 11  1  8 15  5 12  2  9 16  6 13  3 10  0
 1:  9  0  8 16  7 15  6 14  5 13  4 12  3 11  2 10  1
 2: 11  3 12  4 13  5 14  6 15  7 16  8  0  9  1 10  2
 3: 13  6 16  9  2 12  5 15  8  1 11  4 14  7  0 10  3
 4: 15  9  3 14  8  2 13  7  1 12  6  0 11  5 16 10  4
 5:  0 12  7  2 14  9  4 16 11  6  1 13  8  3 15 10  5
 6:  2 15 11  7  3 16 12  8  4  0 13  9  5  1 14 10  6
 7:  4  1 15 12  9  6  3  0 14 11  8  5  2 16 13 10  7
 8:  6  4  2  0 15 13 11  9  7  5  3  1 16 14 12 10  8
 9:  8  7  6  5  4  3  2  1  0 16 15 14 13 12 11 10  9
10: 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10   <<<<<<<<<<<<<
+< Here
11: 12 13 14 15 16  0  1  2  3  4  5  6  7  8  9 10 11
12: 14 16  1  3  5  7  9 11 13 15  0  2  4  6  8 10 12
13: 16  2  5  8 11 14  0  3  6  9 12 15  1  4  7 10 13
14:  1  5  9 13  0  4  8 12 16  3  7 11 15  2  6 10 14
15:  3  8 13  1  6 11 16  4  9 14  2  7 12  0  5 10 15
16:  5 11  0  6 12  1  7 13  2  8 14  3  9 15  4 10 16

for( my $i = 0; $i < 17; ++$i ) { 
    my $j = $i; 
    printf "%2u: %s\n", $i, join' ', map{ sprintf "%2u", $j = ( $j + $
+i + 3 ) % 17 } 0 .. 16; 
};; ##                                                                
+  ##^##
 0:  3  6  9 12 15  1  4  7 10 13 16  2  5  8 11 14  0
 1:  5  9 13  0  4  8 12 16  3  7 11 15  2  6 10 14  1
 2:  7 12  0  5 10 15  3  8 13  1  6 11 16  4  9 14  2
 3:  9 15  4 10 16  5 11  0  6 12  1  7 13  2  8 14  3
 4: 11  1  8 15  5 12  2  9 16  6 13  3 10  0  7 14  4
 5: 13  4 12  3 11  2 10  1  9  0  8 16  7 15  6 14  5
 6: 15  7 16  8  0  9  1 10  2 11  3 12  4 13  5 14  6
 7:  0 10  3 13  6 16  9  2 12  5 15  8  1 11  4 14  7
 8:  2 13  7  1 12  6  0 11  5 16 10  4 15  9  3 14  8
 9:  4 16 11  6  1 13  8  3 15 10  5  0 12  7  2 14  9
10:  6  2 15 11  7  3 16 12  8  4  0 13  9  5  1 14 10
11:  8  5  2 16 13 10  7  4  1 15 12  9  6  3  0 14 11
12: 10  8  6  4  2  0 15 13 11  9  7  5  3  1 16 14 12
13: 12 11 10  9  8  7  6  5  4  3  2  1  0 16 15 14 13
14: 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14   <<<<<<<<<<<<<
+<< Here
15: 16  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
16:  1  3  5  7  9 11 13 15  0  2  4  6  8 10 12 14 16
[download]

---

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