[NDK 球迷购票]

[题目来源]：NOIP基础题目集

[关键字]：数学

[题目大意]：m个人拿50的去买票，n个人拿100的去买票，问有多少种能使钱找开的方案。

//============================================================================================================

[分析]：祥见《程序设计中的组合数学》P43页。此时若n = m则为Catalan数。

[代码]：

View Code

  1 type
  2   rec = record
  3     len: longint;
  4     dat: array[0..200] of longint;
  5   end;
  6 var
  7   n, m, tot: longint;
  8   ans: rec;
  9   su, d: array[0..3000] of longint;
 10 
 11 procedure cheng(var ans: rec; x: longint);
 12 var
 13   k, i: longint;
 14 begin
 15   k := 0;
 16   for i := 1 to ans.len do
 17     begin
 18       ans.dat[i] := ans.dat[i]*x+k;
 19       k := ans.dat[i] div 10000;
 20       ans.dat[i] := ans.dat[i] mod 10000;
 21     end;
 22   while k > 0 do
 23     begin
 24       inc(ans.len);
 25       ans.dat[ans.len] := k mod 10000;
 26       k := k div 10000;
 27     end;
 28 end;
 29 
 30 procedure work;
 31 var
 32    i, j, k: longint;
 33 begin
 34   for i := m+2 to m+n do
 35     begin
 36       j := 0;
 37       k := i;
 38       while k > 1 do
 39         begin
 40           inc(j);
 41           while k mod su[j] = 0 do
 42             begin
 43               inc(d[j]);
 44               k := k div su[j];
 45             end;
 46         end;
 47     end;
 48   k := m+1-n;
 49   j := 0;
 50   while k > 1 do
 51     begin
 52       inc(j);
 53       while k mod su[j] = 0 do
 54         begin
 55           inc(d[j]);
 56           k := k div su[j];
 57         end;
 58     end;
 59   //for i := 1 to tot do
 60     //if d[i] <> 0 then writeln(su[i],'',d[i]);
 61   for i := 2 to n do
 62     begin
 63       j := 0;
 64       k := i;
 65       while k > 1 do
 66         begin
 67           inc(j);
 68           while k mod su[j] = 0 do
 69             begin
 70               dec(d[j]);
 71               k := k div su[j];
 72             end;
 73         end;
 74     end;
 75   ans.len := 1;
 76   ans.dat[1] := 1;
 77   for i := 1 to tot do
 78     while d[i] > 0 do
 79       begin
 80         cheng(ans,su[i]);
 81         dec(d[i]);
 82       end;
 83   //cheng(ans,m+1-n);
 84   write(ans.dat[ans.len]);
 85   for i := ans.len-1 downto 1 do
 86     begin
 87       if ans.dat[i] < 10 then begin write('000',ans.dat[i]); continue; end;
 88       if ans.dat[i] < 100 then begin write('00',ans.dat[i]); continue; end;
 89       if ans.dat[i] < 1000 then begin write('0',ans.dat[i]); continue; end;
 90     end;
 91 end;
 92 
 93 procedure make;
 94 var
 95   i, j: longint;
 96   f: boolean;
 97 begin
 98   for i := 2 to m+n do
 99     begin
100       f := true;
101       for j := 2 to i-1 do
102         if i mod j = 0 then
103           begin  f := false; break; end;
104       if f then
105         begin inc(tot); su[tot] := i; end;
106     end;
107 end;
108 
109 begin
110   assign(input,'d:\in.txt');reset(input);
111   assign(output,'d:\out.txt');rewrite(output);
112   readln(m,n);
113   make;
114   work;
115   close(input);
116   close(output);
117 end.