【HDOJ3341】Lost's revenge（AC自动机，DP）

题意：给出一个n个模式串，一个目标串，问把目标串重新排位最多能产生多少个模式串，可以重叠且所有串只包含A C G T。

n<=10,len[i]<=10

len(s)<=40

Cas<=30

思路：TLE，估计被卡常了

可以将题意理解为重新构造一个ACGT个数都与原目标串相同的新串，则目标串中有用的信息只有ACGT个数

建出Trie图，跑一遍AC自动机，再用一个二维dp[i,j]表示trie上i号节点，字母使用情况为j的模式串最多出现次数

其中j为状态压缩量，是一个四维的量压成一维，因为不压的话会MLE

dp[v,h(a,b,c,d)]=max(dp[v,h(a,b,c,d)],dp[u,h(a-1,b,c,d)]+size[v])等四种转移

其中v=map[u,i]，size[v]表示trie上到v节点路径出现次数之和

边界条件dp[1,h(0,0,0,0)]=1

 var map:array[..,..]of longint;
     q,a,size,fa:array[..]of longint;
     hash:array[..,..,..,..]of longint;
     dp:array[..,..]of longint;
     ch:string;
     n,cnt,i,j,k,x,t,y,ans,len,s,cas,a1,c1,g1,t1,u,s1,v,s2,num:longint;
     flag:boolean;
 
 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;
 
 function max(x,y:longint):longint;
 begin
  if x>y then exit(x);
  exit(y);
 end;
 
 procedure build;
 var i,u:longint;
 begin
  u:=;
  for i:= to len do
  begin
   if map[u,a[i]]= then
   begin
    inc(cnt); map[u,a[i]]:=cnt;
   end;
   u:=map[u,a[i]];
  end;
  inc(size[u]);
 end;
 
 procedure acauto;
 var t,w,i,p,son,u:longint;
 begin
  t:=; w:=; q[]:=;
  while t<w do
  begin
   inc(t); u:=q[t];
   size[u]:=size[u]+size[fa[u]];
   for i:= to  do
    if map[u,i]> then
    begin
     son:=map[u,i];
     p:=fa[u];
     if u= then fa[son]:=
      else fa[son]:=map[p,i];
     inc(w); q[w]:=son;
    end
     else
     begin
      p:=fa[u];
      if u= then map[u,i]:=
       else map[u,i]:=map[p,i];
     end;
  end;
 end;
 
 begin
  assign(input,'hdoj3341.in'); reset(input);
  assign(output,'hdoj3341.out'); rewrite(output);
  while not eof do
  begin
   readln(n);
   if n= then break;
   inc(cas);
   for i:= to cnt do
   begin
    size[i]:=; fa[i]:=;
   end;
   for i:= to cnt do
    for j:= to  do map[i,j]:=;
   for i:= to a1 do
    for j:= to c1 do
     for k:= to g1 do
      for x:= to t1 do hash[i,j,k,x]:=;
 
   cnt:=;
   for i:= to n do
   begin
    readln(ch);
    len:=length(ch);
    for j:= to len do
    begin
     case ch[j] of
      'A':a[j]:=;
      'C':a[j]:=;
      'G':a[j]:=;
      'T':a[j]:=;
     end;
    end;
    build;
   end;
   acauto;
   readln(ch);
   len:=length(ch); a1:=; c1:=; g1:=; t1:=;
   for i:= to len do
   begin
    case ch[i] of
     'A':inc(a1);
     'C':inc(c1);
     'G':inc(g1);
     'T':inc(t1);
    end;
   end;
   num:=;
   for i:= to a1 do
    for j:= to c1 do
     for k:= to g1 do
      for x:= to t1 do
      begin
       inc(num); hash[i,j,k,x]:=num;
      end;
 
  for i:= to cnt do
   for j:= to a1 do
    for k:= to c1 do
     for x:= to g1 do
      for y:= to t1 do dp[i,hash[j,k,x,y]]:=-;
   dp[,hash[,,,]]:=;
 
   ans:=;
   for i:= to a1 do
    for j:= to c1 do
     for k:= to g1 do
      for x:= to c1 do
      begin
       if i+j+k+x= then continue;
       s1:=hash[i,j,k,x];
       for u:= to cnt do
        for t:= to  do
        begin
         v:=map[u,t];
         s2:=;
         if (t=)and(i>=) then s2:=hash[i-,j,k,x]
         else if (t=)and(j>=) then s2:=hash[i,j-,k,x]
          else if (t=)and(k>=) then s2:=hash[i,j,k-,x]
           else  if (t=)and(x>=) then s2:=hash[i,j,k,x-];
         if s2= then continue;
         if dp[u,s2]=- then continue;
         dp[v,s1]:=max(dp[v,s1],dp[u,s2]+size[v]);
         ans:=max(ans,dp[v,s1]);
        end;
      end;
   writeln('Case ',cas,': ',ans);
  end;
  close(input);
  close(output);
 end.

UPD（2018.10.27）：C++重写 果然C++常数小

 #include<cstdio>
 #include<cstring>
 #include<string>
 #include<cmath>
 #include<iostream>
 #include<algorithm>
 #include<map>
 #include<set>
 #include<queue>
 #include<vector>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef vector<int> VI;
 #define fi first
 #define se second
 #define MP make_pair
 #define N   610
 #define M   7010
 #define eps 1e-8
 #define pi  acos(-1)
 #define oo  1e9
 #define MOD 10007
 
 int nxt[N][],q[N],size[N],fa[N],num[][][][],dp[N][],
     A,C,G,T,len,cnt;
 char b[M],ch[M];
 
 void build()
 {
     int u=;
     for(int i=;i<=len;i++)
     {
         int t;
         if(b[i]=='A') t=;
         if(b[i]=='C') t=;
         if(b[i]=='G') t=;
         if(b[i]=='T') t=;
         if(!nxt[u][t]) nxt[u][t]=++cnt;
         u=nxt[u][t];
     }
     size[u]++;
 }
 
 void acauto()
 {
     int t=; int w=; q[]=;
     while(t<w)
     {
         int u=q[++t];
         size[u]+=size[fa[u]];
         for(int i=;i<=;i++)
         {
              if(nxt[u][i])
               {
                  int son=nxt[u][i];
                  int p=fa[u];
                  if(u==) fa[son]=;
                   else fa[son]=nxt[p][i];
                  q[++w]=son;
              }
               else
               {
                  int p=fa[u];
                  if(u==) nxt[u][i]=;
                   else nxt[u][i]=nxt[p][i];
               }
         }
     }
 }
 
 int main()
 {
     //freopen("hdoj3341.in","r",stdin);
     //freopen("hdoj3341.out","w",stdout);
     int n;
     int cas=;
     A=C=G=T=cnt=;
     while(scanf("%d",&n)!=EOF)
     {
         if(n==) break;
         cas++;
         for(int i=;i<=cnt;i++) size[i]=fa[i]=;
         for(int i=;i<=cnt;i++)
          for(int j=;j<=;j++) nxt[i][j]=;
         for(int i=;i<=A;i++)
          for(int j=;j<=C;j++)
           for(int k=;k<=G;k++)
            for(int x=;x<=T;x++) num[i][j][k][x]=;
         cnt=;
         for(int i=;i<=n;i++){scanf("%s",b+); len=strlen(b+); build();}
         acauto();
         scanf("%s",ch+);
         len=strlen(ch+);
         A=C=G=T=;
         for(int i=;i<=len;i++)
         {
             if(ch[i]=='A') A++;
             if(ch[i]=='C') C++;
             if(ch[i]=='G') G++;
             if(ch[i]=='T') T++;
         }
         int s=;
         for(int i=;i<=A;i++)
          for(int j=;j<=C;j++)
           for(int k=;k<=G;k++)
            for(int x=;x<=T;x++) num[i][j][k][x]=++s;
         for(int i=;i<=cnt;i++)
          for(int j=;j<=A;j++)
           for(int k=;k<=C;k++)
            for(int x=;x<=G;x++)
             for(int y=;y<=T;y++) dp[i][num[j][k][x][y]]=-;
         dp[][num[][][][]]=;
         int ans=;
         for(int i=;i<=A;i++)
          for(int j=;j<=C;j++)
           for(int k=;k<=G;k++)
            for(int x=;x<=T;x++)
            {
                     if(i+j+k+x==) continue;
                     int s1=num[i][j][k][x];
                     for(int u=;u<=cnt;u++)
                  for(int t=;t<=;t++)
                    {
                        int v=nxt[u][t];
                        int s2=;
                        if(t==&&i>=) s2=num[i-][j][k][x];
                        if(t==&&j>=) s2=num[i][j-][k][x];
                     if(t==&&k>=) s2=num[i][j][k-][x];
                     if(t==&&x>=) s2=num[i][j][k][x-];
                     if(s2==||dp[u][s2]==-) continue;
                     dp[v][s1]=max(dp[v][s1],dp[u][s2]+size[v]);
                     ans=max(ans,dp[v][s1]);
                  }
             }
         printf("Case %d: %d\n",cas,ans);
     }
     return ;
 }