2.1.2 Ordered Fractions

Ordered Fractions

Consider the set of all reduced fractions between 0 and 1 inclusive with denominators less than or equal to N.

Here is the set when N = 5:

0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1

Write a program that, given an integer N between 1 and 160 inclusive, prints the fractions in order of increasing magnitude.

PROGRAM NAME: frac1

INPUT FORMAT

One line with a single integer N.

SAMPLE INPUT (file frac1.in)

5

OUTPUT FORMAT

One fraction per line, sorted in order of magnitude.

SAMPLE OUTPUT (file frac1.out)

0/1
1/5
1/4
1/3
2/5
1/2
3/5
2/3
3/4
4/5
1/1

{
ID: makeeca1
PROG: frac1
LANG: PASCAL
}

var n:longint;
procedure mid(a,b,c,d:longint);
begin
  if b+d>n then exit;
  mid(a,b,a+c,b+d);
  writeln(a+c,'/',b+d);
  mid(a+c,b+d,c,d);
end;
begin
  assign(input,'frac1.in');reset(input);
  assign(output,'frac1.out');rewrite(output);
  readln(n);
  writeln('0/1');
  mid(0,1,1,1);
  writeln('1/1');
  close(input);close(output);
end.