Ordered Fractions 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

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）

 1 {
 2 ID:fuzhong2
 3 PROG:frac1
 4 LANG:PASCAL
 5 }
 6 var
 7  s,f:array[1..25600] of longint;
 8  z:array[1..25600] of real;
 9  w:real;
10   n,i,j,p:longint;
11 procedure com(var x,y:longint);
12    var
13    i:longint;
14    begin
15    for i:= y div 2 +1 downto 2 do
16      begin
17        if (y mod i=0) and (x mod i=0) then begin y:=y div i; x:=x div i; exit; end;
18      end;
19      end;
20 procedure qsort(l,h:longint);
21 var
22  i,j,tt:integer;
23  t,m:real;
24 begin
25  i:=l; j:=h;
26  m:=z[(i+j) div 2];
27  repeat
28  while z[i]<m do inc(i);
29  while m<z[j] do dec(j);
30    if i<=j then
31   begin
32    t:=z[i]; z[i]:=z[j]; z[j]:=t;
33    tt:=f[i];f[i]:=f[j];f[j]:=tt;
34 tt:=s[i];s[i]:=s[j];s[j]:=tt;
35   inc(i); dec(j);
36   end;
37   until i>j;
38  if i<h then qsort(i,h);
39  if j>l then qsort(l,j);
40 end;
41 begin
42   assign(input,'frac1.in'); reset(input);
43   assign(output,'frac1.out');rewrite(output);
44   read(n);
45   p:=0;
46   for i:= 1 to n do
47   for j:=1 to i-1 do
48     begin
49     inc(p);
50     f[p]:=i;
51     s[p]:=j;
52     z[p]:=(j/i*10000)div 1;
53     end;
54 qsort(1,p);
55 w:=-1;
56 writeln('0/1');
57 for i:= 1 to p do
58   begin
59   if z[i]=w then continue else w:=z[i];
60   com(s[i],f[i]);
61   writeln(s[i],'/',f[i]);
62   end;
63 writeln('1/1');
64 close(input);
65 close(output);
66 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!