\u5c31\u662f\u628ap\u4e2a\u4e1c\u897f\u5206\u6210k\u4e2a\u975e\u7a7a\u7684\u90e8\u5206\uff0c\u987a\u5e8f\u4e0d\u540c\u7684\u6bd4\u59821234\u548c4321\u89c6\u4e3a\u4e00\u79cd\u3002\u8ba9\u4f60\u6c42\u51fa\u7b54\u6848mod 2007
\u603b\u6240\u5468\u77e5\u8fd9\u662f\u4f20\u8bf4\u4e2d\u7684\u7b2c\u4e8c\u7c7bStirling\u6570\uff0c\u5b83\u7684\u516c\u5f0f\u662fS(p,k)=S(p-1,k-1)+k*S(p-1,k)
\u90a3\u4e48\u4f3c\u4e4e\u597d\u50cf\u5c31\u53ef\u4ee5\u76f4\u63a5\u4e0a\u4e86\uff0c\u4f46\u662fp\u7684\u8303\u56f4\u662f1\u523010\u4ebf\uff0ck\u7684\u8303\u56f4\u662f10\u4ee5\u4e0b\u3002\u3002
\u600e\u4e48\u529e\u634f\uff0c\u6211\u4e00\u5f00\u59cb\u60f3\u8d77\u6765\u8fd9\u4e2a\u51fd\u6570\u6709\u4e00\u4e2a\u516c\u5f0f\uff0cWiki\u4e0a\u6709\uff0c\u4f46\u662f\u6211\u53d1\u73b0\u8fd9\u4e2a\u516c\u5f0f\u8981\u9664\u4e00\u4e2a\u6570\u7684\u56e7\uff0c\u5c31\u6ca1\u529e\u6cd5mod\u4e86\u3002\u3002
\u6211\u60f3\u554a\u60f3\u554a\u3002\u3002\u6700\u540e\u53d1\u73b0\u7531\u4e8ek\u6bd4\u8f83\u5c0f\uff0c\u76f4\u63a5\u77e9\u9635\u4e58\u6cd5\u6765\u8ba1\u7b97\u5c31\u53ef\u4ee5\u4e86\u989d\u3002\u3002
\u662fO(logp*k^3)\u3002\u3002
\u77e9\u9635\u4e58\u6cd5\u662f\u89e3\u51b3\u8fd9\u7c7b\u9012\u63a8\u95ee\u9898\u7684\u826f\u65b9\u554a\uff01
Code\uff1a<\/p>\n
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cstring>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
typedef long long ll;
const int mod=2007;
const int maxn=11;
typedef int data[maxn][maxn];
int p,c;
struct mat
{
data o;
mat(){memset(o,0,sizeof(o));}
int& operator() (int i,int j)
{return o[i][j];}
int operator() (int i,int j) const
{return o[i][j];}
void operator=(const mat&x)
{memmove(o,x.o,sizeof(o));}
void print()
{
rep(i,c)
{
rep(j,c)
cout<<o[i][j]<<" ";
cout<<endl;
}
}
}o;
mat operator*(const mat&a,const mat&b)
{
mat r;
rep(i,c) rep(j,c) rep(k,c)
r(i,j)+=a(i,k)*b(k,j),r(i,j)%=mod;
return r;
}
mat power(int p)
{
if(p==1) return o;
mat tmp=power(p\/2);
tmp=tmp*tmp;
if(p&1) tmp=tmp*o;
return tmp;
}
int main()
{
\/\/freopen("in","r",stdin);
cin>>p>>c;c++;
rep(i,c) o(i,i)=i;
for(int i=1;i<c;i++) o(i,i-1)=1;
mat now=power(p);
\/\/now.print();
int ans=0;
cout<<now(c-1,0)<<endl;
}
\u672c\u9ad8\u4eae\u4ee3\u7801\u4f7f\u7528codeHl\u751f\u6210\uff0c <\/p>\n","protected":false},"excerpt":{"rendered":"
\u5c31\u662f\u628ap\u4e2a\u4e1c\u897f\u5206\u6210k\u4e2a\u975e\u7a7a\u7684\u90e8\u5206\uff0c\u987a\u5e8f\u4e0d\u540c\u7684\u6bd4\u59821234\u548c4321\u89c6\u4e3a\u4e00\u79cd\u3002\u8ba9\u4f60\u6c42\u51fa\u7b54\u6848mod 2007\u603b\u6240\u5468\u77e5\u8fd9\u662f\u4f20\u8bf4\u4e2d\u7684\u7b2c\u4e8c\u7c7bStirling\u6570\uff0c\u5b83\u7684\u516c\u5f0f\u662fS(p,k)=S(p-1,k-1)+k*S(p-1,k)\u90a3\u4e48\u4f3c\u4e4e\u597d\u50cf\u5c31\u53ef\u4ee5\u76f4\u63a5\u4e0a\u4e86\uff0c\u4f46\u662fp\u7684\u8303\u56f4\u662f1\u523010\u4ebf\uff0ck\u7684\u8303\u56f4\u662f10\u4ee5\u4e0b\u3002\u3002\u600e\u4e48\u529e\u634f\uff0c\u6211\u4e00\u5f00\u59cb\u60f3\u8d77\u6765\u8fd9\u4e2a\u51fd\u6570\u6709\u4e00\u4e2a\u516c\u5f0f\uff0cWiki\u4e0a\u6709\uff0c\u4f46\u662f\u6211\u53d1\u73b0\u8fd9\u4e2a\u516c\u5f0f\u8981\u9664\u4e00\u4e2a\u6570\u7684\u56e7\uff0c\u5c31\u6ca1\u529e\u6cd5mod\u4e86\u3002\u3002\u6211\u60f3\u554a\u60f3\u554a\u3002\u3002\u6700\u540e\u53d1\u73b0\u7531\u4e8ek\u6bd4\u8f83\u5c0f\uff0c\u76f4\u63a5\u77e9\u9635\u4e58\u6cd5\u6765\u8ba1\u7b97\u5c31\u53ef\u4ee5\u4e86\u989d\u3002\u3002\u662fO(logp*k^3)\u3002\u3002\u77e9\u9635\u4e58\u6cd5\u662f\u89e3\u51b3\u8fd9\u7c7b\u9012\u63a8\u95ee\u9898\u7684\u826f\u65b9\u554a\uff01Code\uff1a #include<cstdio>#include<iostream>#include<algorithm>#include<string>#include<vector>#include<cstring>#define rep(i,n) for(int i=0;i<n;i++)using namespace std;typedef long long ll;const int mod=2007;const int maxn=11;typedef int data[maxn][maxn];int p,c;struct mat{ data o; mat(){memset(o,0,sizeof(o));} int& operator() (int i,int j) {return o[i][j];} int operator() (int i,int j) const {return o[i][j];} void operator=(const mat&x) {memmove(o,x.o,sizeof(o));} void print() { rep(i,c) { rep(j,c) cout<<o[i][j]<<" "; cout<<endl; } }}o;mat operator*(const mat&a,const mat&b){ […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/126"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=126"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/126\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}