Ordered Fractions usaco

题目翻译来自http://www.nocow.cn/index.php/Translate:USACO/frac1

Translate:USACO/frac1

 

Ordered Fractions顺序的分数

输入一个自然数N,对于一个最简分数a/b（分子和分母互质的分数）,满足1<=b<=N,0<=a/b<=1,请找出所有满足条件的分数。

描述

这有一个例子，当N=5时，所有解为：

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

给定一个自然数N，1<=n<=160，请编程按分数值递增的顺序输出所有解。

注：①0和任意自然数的最大公约数就是那个自然数②互质指最大公约数等于1的两个自然数。

格式

PROGRAM NAME: frac1

INPUT FORMAT:

(file frac1.in)

单独的一行　一个自然数N(1..160)

OUTPUT FORMAT:

(file frac1.out)

每个分数单独占一行，按照大小次序排列

SAMPLE INPUT

5

SAMPLE OUTPUT

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

【题解】

列举--》快排--》输出（注意重复的）

{
ID:fuzhong2
PROG:frac1
LANG:PASCAL
}
var
 s,f:array[1..25600] of longint;
 z:array[1..25600] of real;
 w:real;
  n,i,j,p:longint;
procedure com(var x,y:longint);
   var
   i:longint;
   begin
   for i:= y div 2 +1 downto 2 do
     begin
       if (y mod i=0) and (x mod i=0) then begin y:=y div i; x:=x div i; exit; end;
     end;
     end;
procedure qsort(l,h:longint);
var
 i,j,tt:integer;
 t,m:real;
begin
 i:=l; j:=h;
 m:=z[(i+j) div 2];
 repeat
 while z[i]<m do inc(i);
 while m<z[j] do dec(j);
   if i<=j then
  begin
   t:=z[i]; z[i]:=z[j]; z[j]:=t;
   tt:=f[i];f[i]:=f[j];f[j]:=tt;
tt:=s[i];s[i]:=s[j];s[j]:=tt;
  inc(i); dec(j);
  end;
  until i>j;
 if i<h then qsort(i,h);
 if j>l then qsort(l,j);
end;
begin
  assign(input,'frac1.in'); reset(input);
  assign(output,'frac1.out');rewrite(output);
  read(n);
  p:=0;
  for i:= 1 to n do
  for j:=1 to i-1 do
    begin
    inc(p);
    f[p]:=i;
    s[p]:=j;
    z[p]:=(j/i*10000)div 1;
    end;
qsort(1,p);
w:=-1;
writeln('0/1');
for i:= 1 to p do
  begin
  if z[i]=w then continue else w:=z[i];
  com(s[i],f[i]);
  writeln(s[i],'/',f[i]);
  end;
writeln('1/1');
close(input);
close(output);
end.

真心写的有点乱

USER: fu zhongqing [fuzhong2]
TASK: frac1
LANG: PASCAL

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.000 secs, 676 KB]
   Test 2: TEST OK [0.000 secs, 676 KB]
   Test 3: TEST OK [0.000 secs, 676 KB]
   Test 4: TEST OK [0.000 secs, 676 KB]
   Test 5: TEST OK [0.000 secs, 676 KB]
   Test 6: TEST OK [0.000 secs, 676 KB]
   Test 7: TEST OK [0.000 secs, 676 KB]
   Test 8: TEST OK [0.000 secs, 676 KB]
   Test 9: TEST OK [0.000 secs, 676 KB]
   Test 10: TEST OK [0.000 secs, 676 KB]
   Test 11: TEST OK [0.011 secs, 676 KB]

All tests OK.

Your program ('frac1') produced all correct answers! This is your submission #2 for this problem. Congratulations!

Here are the test data inputs:

------- test 1 ----
1
------- test 2 ----
2
------- test 3 ----
4
------- test 4 ----
7
------- test 5 ----
10
------- test 6 ----
15
------- test 7 ----
24
------- test 8 ----
50
------- test 9 ----
75
------- test 10 ----
100
------- test 11 ----
160

Keep up the good work!

Thanks for your submission!