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）

 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!