Bzoj3676 [Apio2014] palindrome string

Time limit:20 Sec Memory limit:128 MB
submit:2079 solved:899 Description

Consider a string s that contains only the lowercase Latin alphabet. We define the "out" of a substring t of s
The present value is the number of occurrences of T in s multiplied by the length of T. Please find out the most in all palindrome strings of S
Large occurrence value.

Input

Enter only one row for a non-empty string s that contains only a lowercase letter (A-Z).

Output

Outputs an integer that is the largest occurrence of a palindrome substring.

Sample Input"Sample Input L"
Abacaba

"Sample input 2]
Www

Sample Output"Sample Output L"
7

Sample Output 2]
4
HINT

A string is a palindrome when and only if it reads from left to right and reads from right to left exactly the same.

In the first example, there are 7 palindrome substrings: A,b,c,aba,aca,bacab,abacaba, wherein:

A appears 4 times with a value of 4:1:1=4

B appears 2 times with a value of 2:1:1=2

C appears 1 times with a value of l:1:l=l

ABA appears 2 times with a value of 2:1:3=6

ACA appears 1 times with a value of 1=1:3=3

Bacab appears 1 times with a value of 1:1:5=5

Abacaba appears 1 times with a value of 1:1:7=7

Therefore, the maximum palindrome string occurrence value is 7.

"Data size and scoring"

The data satisfies the 1≤ string length ≤300000.

Source

String Palindrome automatic Machine

In the Huang long blog, turned to this magical thing--palindrome automaton

Studied for half a day, this thing and ac automata, suffix automata somewhat similar (all automata), through the fail pointer in the tree jump to complete the matching string.

Palindrome automatic machine, each node represents a palindrome string, each to add a character to the automaton, the current total string update the longest palindrome suffix:

For example: Aoaueoqwelje Abababa, the longest palindrome suffix is abababa, if added a b,abababab is not a palindrome string, so along the fail pointer back to the longest palindrome suffix string ababa, (there is a b) +ababa+ (the newly added B) Can form a palindrome string, create a new node to represent it, and record the length and number of occurrences of the message.

Here is a detailed explanation http://blog.csdn.net/u013368721/article/details/42100363

So this is a template problem. Note that statistics are counted when the number of occurrences is counted, in order to accumulate the number of occurrences of fail pointing position

1 /*by Silvern*/2#include <algorithm>3#include <iostream>4#include <cstring>5#include <cstdio>6#include <cmath>7#include <vector>8 using namespacestd;9 Const intmxn=350100;Ten intRead () { One     intx=0, f=1;CharCh=GetChar (); A      while(ch<'0'|| Ch>'9'){if(ch=='-') f=-1; ch=GetChar ();} -      while(ch>='0'&& ch<='9') {x=x*Ten+ch-'0'; ch=GetChar ();} -     returnx*F; the } - CharS[MXN]; - Long Longans=0; - structhwm{ +     intt[mxn][ -]; -     intFA[MXN]; +     intL[MXN],SZ[MXN]; A     intS,cnt,last; at     voidinit () { -s=cnt=last=fa[0]=fa[1]=1; l[1]=-1; -         return; -     } -     voidAddintCintN) { -         intp=Last ; in          for(; s[n-l[p]-1]!=s[n];p =fa[p]); -         if(!T[p][c]) { to             intnp=++cnt;l[np]=l[p]+2; +             intk=Fa[p]; -              while(s[n-l[k]-1]!=s[n]) k=Fa[k]; theFA[NP]=T[K][C];// *t[p][c]=NP; $         }Panax Notoginsenglast=T[p][c]; -++Sz[last]; the         return; +     }     A     voidsolve () { the          for(inti=cnt;i;i--){ +sz[fa[i]]+=Sz[i]; -             Long LongTmp= (Long Long) sz[i]*L[i]; $             if(Tmp>ans) ans=tmp; $         } -         return; -     } the }HW; - intMain () {Wuyi     inti,j; thescanf"%s", s+1); - hw.init (); Wu     intLen=strlen (s+1); -      for(i=1; i<=len;i++) Hw.add (s[i]-'a', i); About hw.solve (); $printf"%lld\n", ans); -     return 0; -}

Bzoj3676 [Apio2014] palindrome string