{"id":68,"date":"2025-01-11T23:09:28","date_gmt":"2025-01-11T15:09:28","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=68"},"modified":"2025-01-11T23:09:28","modified_gmt":"2025-01-11T15:09:28","slug":"d-tavas-and-malekas-%e8%a7%a3%e6%9e%90%e5%ad%97%e4%b8%b2%e5%8c%b9%e9%85%8d","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=68","title":{"rendered":"D. Tavas and Malekas \u89e3\u6790(\u5b57\u4e32\u5339\u914d)"},"content":{"rendered":"\n

Codeforce 535 D. Tavas and Malekas \u89e3\u6790(\u5b57\u4e32\u5339\u914d)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF535D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u500b\u5b57\u4e32$p$\u548c\u4e00\u4e9b$index$\u4ee3\u8868\u5b57\u4e32$p$\u5728\u54ea\u4e9b\u4f4d\u7f6e\u6703\u548c\u9577\u5ea6\u70ba$n$\u7684\u5b57\u4e32$s$\u5339\u914d\uff0c\u6c42\u6709\u591a\u5c11\u7a2e$s$\u7684\u53ef\u80fd\u6027\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u6211\u9084\u662f\u53ea\u6703$hash$<\/p>\n

<div class=\u201cVVVcopyrightAAA\u201d;>@copyright petjelinux \u7248\u6b0a\u6240\u6709<br>
\n<a href=\u201chttps:\/\/www.cnblogs.com\/petjelinux\/\u201d>\u89c0\u770b\u66f4\u591a\u6b63\u7248\u539f\u59cb\u6587\u7ae0\u8acb\u81f3petjelinux\u7684blog<\/a><\/div><\/p>\n

\u60f3\u6cd5<\/h3>\n

$p$\u6c92\u6709\u8986\u84cb\u5230\u7684$index$\u6578\u91cf\u8a18\u505a$cnt$\uff0c\u5982\u679c\u90a3\u4e9b\u6703\u91cd\u758a\u7684$p$\u6c92\u6709\u77db\u76fe\u7684\u8a71\uff0c\u90a3\u7b54\u6848\u5c31\u662f$26^{cnt}$\uff0c\u56e0\u70ba\u6709$cnt$\u7684\u683c\u5b50\u90fd\u662f\u5b8c\u5168\u81ea\u7531\u7684\u3002
\n\u9019\u984c\u6709\u4e09\u7a2e\u4f5c\u6cd5\uff0c\u90fd\u662f\u8981\u5224\u65b7\u91cd\u758a\u7684$p$\u6709\u6c92\u6709\u77db\u76fe\u3002\u6ce8\u610f\uff0c\u6211\u5011\u6bcf\u6b21\u5224\u65b7\u4e00\u500b\u5f9e$y[i]$\u958b\u59cb\u7684$p$\u5b57\u4e32\u6709\u6c92\u6709\u548c\u524d\u9762\u91cd\u758a\u6642\uff0c\u53ea\u9700\u8981\u548c\u5f9e$y[i-1]$\u958b\u59cb\u7684$p$\u5b57\u4e32\u6bd4\u8f03\u5c31\u597d\uff0c\u7562\u7adf\u5982\u679c$y[i-2]$\u958b\u59cb\u7684$p$\u5b57\u4e32\u548c$y[i-1]$\u958b\u59cb\u7684$p$\u5b57\u4e32\u6c92\u6709\u77db\u76fe\u7684\u8a71\uff0c\u90a3\u9ebc$y[i-2]$\u958b\u59cb\u7684$p$\u5b57\u4e32\u548c$y[i]$\u958b\u59cb\u7684$p$\u5b57\u4e32\u5c31\u4e0d\u6703\u6709\u77db\u76fe(\u5982\u679c$y[i-1]$\u958b\u59cb\u7684\u5b57\u4e32\u548c$y[i]$\u958b\u59cb\u7684\u5b57\u4e32\u6c92\u6709\u77db\u76fe)\u3002
\n\u4e09\u7a2e\u5339\u914d\u5b57\u4e32\u7684\u65b9\u5f0f\u662f:<\/p>\n

    \n
  1. Rolling hash\uff0c\u76f4\u63a5\u6bd4\u5c0d\u5b50\u5b57\u4e32\u7684hash\u503c\u770b\u770b\u4e00\u4e0d\u4e00\u6a23\u3002<\/li>\n
  2. KMP\uff0c\u53ea\u9700\u8981\u7dad\u8b77\u5931\u6557\u51fd\u6578\uff0c\u7531\u65bc\u5931\u6557\u51fd\u6578\u4ee3\u8868\u4e00\u500b\u6700\u9577\u7684\u524d\u7db4\u7684\u9577\u5ea6\u4f7f\u5f97\u5728$j-1$\u7d50\u675f\u7684\u5b57\u4e32\u7684\u5f8c\u7db4\u548c\u524d\u7db4\u4e00\u6a23\uff0c\u90a3\u9ebc\u6211\u5011\u53ea\u8981\u770b\u770b$p$\u5b57\u4e32\u7684\u91cd\u758a\u90e8\u5206\u662f\u5426\u6c92\u6709\u77db\u76fe\u5c31\u597d\u3002<\/li>\n
  3. Z-Algorithm\uff0c\u548cKMP\u5982\u51fa\u4e00\u8f4d\uff0c\u53ea\u4e0d\u904e\u9019\u6b21$Z$\u51fd\u6578\u4ee3\u8868\u5f9e$j$\u958b\u59cb\u5f80\u5f8c\u7684\u5b57\u4e32\u548c\u6574\u500b\u5b57\u4e32\u7684\u6700\u9577\u524d\u7db4\u9577\u5ea6\u3002\u4e00\u6a23\u53ea\u8981\u770b\u770b$p$\u5b57\u4e32\u7684\u91cd\u758a\u90e8\u5206\u662f\u5426\u6c92\u6709\u77db\u76fe\u5c31\u597d\u3002<\/li>\n<\/ol>\n

    \u7a0b\u5f0f\u78bc(Rolling hash):<\/h3>\n
    const int _n=1e6+10;  \nint t,n,m;  \nconst int _N = _n;  \/\/ str len  \nconst int _p1 = 31, _M = 1000000009;  \nint pnM[_N] = {0};  \/\/ p^n mod M  \nint hp[_N] = {0};   \/\/ hash prefix  \nchar p[_N];  \nint lenp,y[_n];  \n  \ninline void genpnM() {  \n  int res = 1;  \/\/p^0%M  \n  pnM[0] = 1;  \n  for (int i = 1; i < _N; i++) pnM[i] = res = (res * 1ll * _p1) % _M;  \n}  \ninline void genhp() {  \/\/hp[n]=hash prefix[0,n)  \n  int res = 0;  \n  hp[0] = 0;  \/\/[0,0) is empty string  \n  for (int i = 1; i <= lenp; i++) hp[i] = res = (res * 1ll * _p1 + p[i - 1] * 1ll) % _M;  \n}  \ninline int dhash(char s[]) {  \/\/direct hash  \n  int len = strlen(s);  \n  int res = 0;  \n  for (int i = 1; i <= len; i++) res = (res * 1ll * _p1 + s[i - 1] * 1ll) % _M;  \n  return res;  \n}  \ninline int hashlr(int l, int r) {  \/\/[l,r)  \n  int tmp = hp[r] * 1ll - pnM[r - l] * 1ll * hp[l] % _M;  \n  if (tmp < 0) tmp += _M;  \n  return tmp;  \n}  \n\/\/\u4ee5\u4e0a\u662frolling hash\u6a21\u677f  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n>>m>>p;lenp=strlen(p);rep(i,0,m){cin>>y[i];y[i]--;}  \n  genpnM();genhp();  \n  int cnt=y[0];rep(i,1,m){  \n    if(y[i-1]+lenp-1>=y[i]){  \n      if(hashlr(y[i]-y[i-1],lenp)!=hashlr(0,lenp-(y[i]-y[i-1]))){  \n        cout<<0<<'\\n';return 0;  \n      }  \n    }  \n    else cnt+=y[i]-(y[i-1]+lenp-1)-1;  \n  }cnt+=n-(y[m-1]+lenp);  \n  if(m==0)cnt=n;  \n  cout<<powmod(26,cnt)<<'\\n';  \n  return 0;  \n}  \n<\/code><\/pre>\n
    \u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b
    \n    Submission<\/a><\/p>\n
    \u7a0b\u5f0f\u78bc(KMP):<\/h3>\n
    const int _n=1e6+10;  \nint t,n,m;  \nchar p[_n];  \nint lenp,y[_n],jj,F[_n];  \nbool vis[_n];  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n>>m>>p;lenp=strlen(p);rep(i,0,m){cin>>y[i];y[i]--;}  \n  \/*F[0]=-1,jj=-1;rep(i,0,lenp){  \n    jj=F[i];  \n    while(jj!=-1 and p[i]!=p[jj])jj=F[jj];  \n    F[i+1]=jj+1; \/\/if jj==-1, F[i]=0  \n  }*\/ \/\/\u4e5f\u884c  \n  F[0]=-1;  \n  for(int i = 0, j = -1; i < lenp; F[++i] = ++j) { \/\/\u8a08\u7b97\u5931\u6557\u51fd\u6578\uff0c\u4e00\u822c\u4f86\u8aaai<lenp-1\uff0c\u4f46\u662f\u9019\u984c\u6211\u5011\u9700\u8981i<lenp  \n    while (j != -1 && p[i] != p[j]) j = F[j];  \n  }  \n  jj=F[lenp];  \n  while(jj!=-1){ \/\/\u770b\u770b\u54ea\u4e9b\u524d\u7db4\u53ef\u4ee5\u548c\u6574\u689d\u5b57\u4e32p\u7684\u5f8c\u7db4\u5339\u914d  \n    vis[jj]=1;  \n    jj=F[jj];  \n  }  \n  int cnt=y[0];rep(i,1,m){  \n    if(y[i-1]+lenp-1>=y[i]){  \n      if(!vis[lenp-(y[i]-y[i-1])]){  \n        cout<<0<<'\\n';return 0;  \n      }  \n    }  \n    else cnt+=y[i]-(y[i-1]+lenp-1)-1;  \n  }cnt+=n-(y[m-1]+lenp);  \n  if(m==0)cnt=n;  \n  cout<<powmod(26,cnt)<<'\\n';  \n  return 0;  \n}  \n<\/code><\/pre>\n
    \u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b
    \n    Submission<\/a><\/p>\n
    \u7a0b\u5f0f\u78bc(Z-Algorithm):<\/h3>\n
    const int _n=1e6+10;  \nint t,n,m,lenp,Z[_n],y[_n];  \nchar p[_n];  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n>>m>>p;lenp=strlen(p);rep(i,0,m){cin>>y[i];y[i]--;}  \n  int L = 0, R = 0;  \n  for (int i = 1; i < lenp; i++) {  \n    if (i > R) {  \n      L = R = i;  \n      while (R < n && p[R-L] == p[R]) R++;  \n      Z[i] = R-L; R--;  \n    } else {  \n      int k = i-L;  \n      if (Z[k] < R-i+1) Z[i] = Z[k];  \n      else {  \n        L = i;  \n        while (R < n && p[R-L] == p[R]) R++;  \n        Z[i] = R-L; R--;  \n      }  \n    }  \n  }  \n  int cnt=y[0];rep(i,1,m){  \n    if(y[i-1]+lenp-1>=y[i]){  \n      if(Z[y[i]-y[i-1]]!=lenp-(y[i]-y[i-1])){  \n        cout<<0<<'\\n';return 0;  \n      }  \n    }  \n    else cnt+=y[i]-(y[i-1]+lenp-1)-1;  \n  }cnt+=n-(y[m-1]+lenp);  \n  if(m==0)cnt=n;  \n  cout<<powmod(26,cnt)<<'\\n';  \n  return 0;  \n}  \n<\/code><\/pre>\n
    \u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b
    \n    Submission<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[10,9,28],"class_list":["post-68","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-28"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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