【BZOJ2982】combination（Lucas定理）

题意：求C(n,m)

n,m<=200000000

思路：c(n,m)=c(n mod mo,m mod mo)*c(n div mo,m div mo) mod mo (n>=mo或m>=mo)

c(x,y)=0 (x<y)

c(n,m)=fac[n]*exf[m]*exf[n-m] (n,m<mo)

 1 const mo=10007;
 2 var exf,fac:array[0..1000000]of longint;
 3     n,i,x,y:longint;
 4 
 5 function c(n,m:longint):longint;
 6 begin
 7  if n<m then exit(0);
 8  if (n<mo)and(m<mo) then exit(fac[n]*exf[m] mod mo*exf[n-m] mod mo);
 9  exit(c(n mod mo,m mod mo)*c(n div mo,m div mo) mod mo);
10 end;
11 
12 begin
13  assign(input,'bzoj2982.in'); reset(input);
14  assign(output,'bzoj2982.out'); rewrite(output);
15  readln(n);
16  exf[0]:=1; exf[1]:=1; fac[0]:=1; fac[1]:=1;
17  for i:=2 to 1000000 do
18  begin
19   exf[i]:=exf[mo mod i]*(mo-mo div i) mod mo;
20   fac[i]:=fac[i-1]*i mod mo;
21  end;
22  for i:=1 to 1000000 do exf[i]:=exf[i-1]*exf[i] mod mo;
23 
24  for i:=1 to n do
25  begin
26   readln(x,y);
27   writeln(c(x,y));
28  end;
29  close(input);
30  close(output);
31 end.

 

posted on 2017-02-21 12:13  myx12345  阅读(127)  评论(0)  编辑  收藏  举报

导航