{"id":160,"date":"2010-03-19T19:34:00","date_gmt":"2010-03-19T11:34:00","guid":{"rendered":"http:\/\/localhost\/?p=160"},"modified":"2010-03-19T19:34:00","modified_gmt":"2010-03-19T11:34:00","slug":"scoi2009_get_lost","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=160","title":{"rendered":"[SCOI2009]\u8ff7\u8def"},"content":{"rendered":"\n

[SCOI2009]\u8ff7\u8def <\/p>\n

Time Limit:10000MS  Memory Limit:165536K
Total Submit:40 Accepted:24
Case Time Limit:1000MS<\/p>\n

Description <\/strong><\/p>\n

windy\u5728\u6709\u5411\u56fe\u4e2d\u8ff7\u8def\u4e86\u3002
\u8be5\u6709\u5411\u56fe\u6709 N \u4e2a\u8282\u70b9\uff0cwindy\u4ece\u8282\u70b9 0 \u51fa\u53d1\uff0c\u4ed6\u5fc5\u987b\u6070\u597d\u5728 T \u65f6\u523b\u5230\u8fbe\u8282\u70b9 N-1\u3002
\u73b0\u5728\u7ed9\u51fa\u8be5\u6709\u5411\u56fe\uff0c\u4f60\u80fd\u544a\u8bc9windy\u603b\u5171\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u8def\u5f84\u5417\uff1f
\u6ce8\u610f\uff1awindy\u4e0d\u80fd\u5728\u67d0\u4e2a\u8282\u70b9\u9017\u7559\uff0c\u4e14\u901a\u8fc7\u67d0\u6709\u5411\u8fb9\u7684\u65f6\u95f4\u4e25\u683c\u4e3a\u7ed9\u5b9a\u7684\u65f6\u95f4\u3002 <\/p>\n

Input <\/strong><\/p>\n

\u7b2c\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570\uff0cN T\u3002
\u63a5\u4e0b\u6765\u6709 N \u884c\uff0c\u6bcf\u884c\u4e00\u4e2a\u957f\u5ea6\u4e3a N \u7684\u5b57\u7b26\u4e32\u3002
\u7b2ci\u884c\u7b2cj\u5217\u4e3a’0’\u8868\u793a\u4ece\u8282\u70b9i\u5230\u8282\u70b9j\u6ca1\u6709\u8fb9\u3002
\u4e3a’1’\u5230’9’\u8868\u793a\u4ece\u8282\u70b9i\u5230\u8282\u70b9j\u9700\u8981\u8017\u8d39\u7684\u65f6\u95f4\u3002 <\/p>\n

Output <\/strong><\/p>\n

\u5305\u542b\u4e00\u4e2a\u6574\u6570\uff0c\u53ef\u80fd\u7684\u8def\u5f84\u6570\uff0c\u8fd9\u4e2a\u6570\u53ef\u80fd\u5f88\u5927\uff0c\u53ea\u9700\u8f93\u51fa\u8fd9\u4e2a\u6570\u9664\u4ee52009\u7684\u4f59\u6570\u3002 <\/p>\n

Sample Input <\/strong><\/p>\n

\u3010\u8f93\u5165\u6837\u4f8b\u4e00\u3011
2 2
11
00<\/p>\n

\u3010\u8f93\u5165\u6837\u4f8b\u4e8c\u3011
5 30
12045
07105
47805
12024
12345<\/p>\n

Sample Output <\/strong><\/p>\n

\u3010\u8f93\u51fa\u6837\u4f8b\u4e00\u3011
1<\/p>\n

\u3010\u6837\u4f8b\u89e3\u91ca\u4e00\u3011
0->0->1<\/p>\n

\u3010\u8f93\u51fa\u6837\u4f8b\u4e8c\u3011
852<\/p>\n

Hint <\/strong><\/p>\n

30%\u7684\u6570\u636e\uff0c\u6ee1\u8db3 2 <= N <= 5 \uff1b 1 <= T <= 30 \u3002
100%\u7684\u6570\u636e\uff0c\u6ee1\u8db3 2 <= N <= 10 \uff1b 1 <= T <= 1000000000 \u3002<\/p>\n

Source <\/strong><\/p>\n

Day2<\/p>\n

\u6211\u64e6\u554a\uff0161.187.179.132:8080\/JudgeOnline\/showproblem<\/a>
\u6211\u4e00\u5f00\u59cb\u6ca1\u60f3\u51fa\u6765\u600e\u4e48\u505a\uff0c\u5f88\u660e\u663e\u8981\u7528\u77e9\u9635\u4e58\u6cd5\uff0c\u6240\u4ee5\u6211\u5c31\u60f3\u600e\u4e48\u641e\u3002\u3002
\u6211\u60f3\u4e86\u534a\u5929\u6ca1\u6709\u4ec0\u4e48\u5934\u7eea\uff0c\u611f\u89c9\u8fd9\u4e2a\u957f\u5ea6\u5f88\u9ebb\u70e6\uff0c\u611f\u89c9\u77e9\u9635\u4e58\u6cd5\u5c31\u662f\u4ece\u4e00\u4e2a\u63a8\u51fa\u4e0b\u4e00\u4e2a\uff0c\u63a8\u4e0d\u51fa\u4e0b\u9762\u5f88\u591a\u4e2a\u989d\u3002\u3002\u5f88\u5934\u75bc\u3002
\u8fc7\u4e86\u4e00\u5929\u53d1\u73b0\u7531\u4e8e\u957f\u5ea6\u6700\u957f\u662f9\u3002\u3002\u3002\u6240\u4ee5\u628a\u6bcf9\u4e2a\u6253\u5305\u8d77\u6765\u5c31\u518d\u9012\u63a8\u5c31OK\u4e86\u3002\u3002
\u53ef\u662f\u6211\uff1a

\u6655\u6b7b\u4e86\u3002\u3002\u90a3\u51e0\u4e2aWA\u662f\u6211\u6545\u610f\u5199return 0\u67e5\u51fa\u9519\u70b9\u7684\u3002\u3002
\u6700\u540e\u53d1\u73b0\u539f\u6765\u56e0\u4e3a\u77e9\u9635\u6709\u70b9\u5927\uff0c\u5bfc\u81f4\u5982\u679c\u6211\u76f4\u63a5\u5728\u4e58\u6cd5\u91cc\u5199\u4e34\u65f6\u53d8\u91cf\u7684\u8bdd\u4f1aMLE\u3002\u3002
\u9760\u9760\u9760\u3002\u3002\u6211\u672c\u6765\u5c31\u6ca1\u4ec0\u4e48AC\u7387\u7684\u3002\u3002\u73b0\u5728\u60b2\u5267\u5927\u53d1\u4e86\u3002\u3002
Code\uff1a
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cstring>
#define rep(i,n) for(int i=0;i<n;i++)
#define pb push_back
using namespace std;
const int maxt=9,maxv=90,maxn=10,mod=2009;
int n,v;
inline int node(int time,int pos)
{
return time*n+pos;
}
int tmp[maxv][maxv];
struct Mat
{
int M[maxv][maxv];
int&operator()(int i,int j){return M[i][j];}
Mat(){memset(M,0,sizeof(M));}
void operator*=(Mat&o)
{
memset(tmp,0,sizeof(tmp));
rep(i,v)rep(j,v)rep(k,v)
tmp[i][j]+=M[i][k]*o(k,j),tmp[i][j]%=mod;
memcpy(M,tmp,sizeof(M));
}
void operator=(const Mat&o)
{
memcpy(M,o.M,sizeof(M));
}
}orig;
int Map[maxn][maxn];
void Power(int n,Mat&ret)
{
if(n==1){ret=orig;return;}
Power(n\/2,ret);
ret*=ret;
if(n&1)ret*=orig;
}
int main()
{
\/\/freopen("in","r",stdin);
\/\/freopen("road.in","r",stdin);
\/\/freopen("road.out","w",stdout);
int T;
scanf("%d %d",&n,&T);char x;v=n*9;
rep(i,n)
{
scanf("n");
rep(j,n)scanf("%c",&x),Map[i][j]=x-‘0’;
}
rep(i,n)for(int t=0;t<8;t++)
orig(node(t,i),node(t+1,i))++;
rep(i,n)rep(j,n)if(Map[j][i])
orig(node(8,i),node(9-Map[j][i],j))++;
Mat Ans;Power(T,Ans);
int dp[maxn][maxt]={0};
dp[0][0]=1;
for(int t=1;t<maxt;t++)
{
rep(i,n)rep(j,n)
if(Map[j][i])
if(t-Map[j][i]>=0)
{
dp[i][t]+=dp[j][t-Map[j][i]];
dp[i][t]%=mod;
}
}
int ans=0;
rep(i,n)rep(t,maxt)
{
ans+=Ans(node(0,n-1),node(t,i))*dp[i][t];
ans%=mod;
}
cout<<ans<<endl;
} <\/p>\n","protected":false},"excerpt":{"rendered":"

[SCOI2009]\u8ff7\u8def Time Limit:10000MS  Memory Limit:165536KTotal Submit:40 Accepted:24 Case Time Limit:1000MS Description windy\u5728\u6709\u5411\u56fe\u4e2d\u8ff7\u8def\u4e86\u3002 \u8be5\u6709\u5411\u56fe\u6709 N \u4e2a\u8282\u70b9\uff0cwindy\u4ece\u8282\u70b9 0 \u51fa\u53d1\uff0c\u4ed6\u5fc5\u987b\u6070\u597d\u5728 T \u65f6\u523b\u5230\u8fbe\u8282\u70b9 N-1\u3002 \u73b0\u5728\u7ed9\u51fa\u8be5\u6709\u5411\u56fe\uff0c\u4f60\u80fd\u544a\u8bc9windy\u603b\u5171\u6709\u591a\u5c11\u79cd\u4e0d\u540c\u7684\u8def\u5f84\u5417\uff1f \u6ce8\u610f\uff1awindy\u4e0d\u80fd\u5728\u67d0\u4e2a\u8282\u70b9\u9017\u7559\uff0c\u4e14\u901a\u8fc7\u67d0\u6709\u5411\u8fb9\u7684\u65f6\u95f4\u4e25\u683c\u4e3a\u7ed9\u5b9a\u7684\u65f6\u95f4\u3002 Input \u7b2c\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570\uff0cN T\u3002 \u63a5\u4e0b\u6765\u6709 N \u884c\uff0c\u6bcf\u884c\u4e00\u4e2a\u957f\u5ea6\u4e3a N \u7684\u5b57\u7b26\u4e32\u3002 \u7b2ci\u884c\u7b2cj\u5217\u4e3a’0’\u8868\u793a\u4ece\u8282\u70b9i\u5230\u8282\u70b9j\u6ca1\u6709\u8fb9\u3002 \u4e3a’1’\u5230’9’\u8868\u793a\u4ece\u8282\u70b9i\u5230\u8282\u70b9j\u9700\u8981\u8017\u8d39\u7684\u65f6\u95f4\u3002 Output \u5305\u542b\u4e00\u4e2a\u6574\u6570\uff0c\u53ef\u80fd\u7684\u8def\u5f84\u6570\uff0c\u8fd9\u4e2a\u6570\u53ef\u80fd\u5f88\u5927\uff0c\u53ea\u9700\u8f93\u51fa\u8fd9\u4e2a\u6570\u9664\u4ee52009\u7684\u4f59\u6570\u3002 Sample Input \u3010\u8f93\u5165\u6837\u4f8b\u4e00\u30112 21100 \u3010\u8f93\u5165\u6837\u4f8b\u4e8c\u30115 301204507105478051202412345 Sample Output \u3010\u8f93\u51fa\u6837\u4f8b\u4e00\u30111 \u3010\u6837\u4f8b\u89e3\u91ca\u4e00\u30110->0->1 \u3010\u8f93\u51fa\u6837\u4f8b\u4e8c\u3011852 Hint 30%\u7684\u6570\u636e\uff0c\u6ee1\u8db3 2 <= N <= 5 \uff1b 1 <= […]<\/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\/160"}],"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=160"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/160\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}