题目链接 http://acm.hdu.edu.cn/showproblem.php?pid=3613
Best Reward
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 940 Accepted Submission(s): 390
Problem Description
After an uphill battle, General Li won a great victory. Now the head of state decide to reward him with honor and treasures for his great exploit.
One of these treasures is a necklace made up of 26 different kinds of gemstones, and the length of the necklace is n. (That is to say: n gemstones are stringed together to constitute this necklace, and each of these gemstones belongs to only one of the 26 kinds.)
In accordance with the classical view, a necklace is valuable if and only if it is a palindrome - the necklace looks the same in either direction. However, the necklace we mentioned above may not a palindrome at the beginning. So the head of state decide to cut the necklace into two part, and then give both of them to General Li.
All gemstones of the same kind has the same value (may be positive or negative because of their quality - some kinds are beautiful while some others may looks just like normal stones). A necklace that is palindrom has value equal to the sum of its gemstones' value. while a necklace that is not palindrom has value zero.
Now the problem is: how to cut the given necklace so that the sum of the two necklaces's value is greatest. Output this value.
One of these treasures is a necklace made up of 26 different kinds of gemstones, and the length of the necklace is n. (That is to say: n gemstones are stringed together to constitute this necklace, and each of these gemstones belongs to only one of the 26 kinds.)
In accordance with the classical view, a necklace is valuable if and only if it is a palindrome - the necklace looks the same in either direction. However, the necklace we mentioned above may not a palindrome at the beginning. So the head of state decide to cut the necklace into two part, and then give both of them to General Li.
All gemstones of the same kind has the same value (may be positive or negative because of their quality - some kinds are beautiful while some others may looks just like normal stones). A necklace that is palindrom has value equal to the sum of its gemstones' value. while a necklace that is not palindrom has value zero.
Now the problem is: how to cut the given necklace so that the sum of the two necklaces's value is greatest. Output this value.
Input
The first line of input is a single integer T (1 ≤ T ≤ 10) - the number of test cases. The description of these test cases follows.
For each test case, the first line is 26 integers: v1, v2, ..., v26 (-100 ≤ vi ≤ 100, 1 ≤ i ≤ 26), represent the value of gemstones of each kind.
The second line of each test case is a string made up of charactor 'a' to 'z'. representing the necklace. Different charactor representing different kinds of gemstones, and the value of 'a' is v1, the value of 'b' is v2, ..., and so on. The length of the string is no more than 500000.
For each test case, the first line is 26 integers: v1, v2, ..., v26 (-100 ≤ vi ≤ 100, 1 ≤ i ≤ 26), represent the value of gemstones of each kind.
The second line of each test case is a string made up of charactor 'a' to 'z'. representing the necklace. Different charactor representing different kinds of gemstones, and the value of 'a' is v1, the value of 'b' is v2, ..., and so on. The length of the string is no more than 500000.
Output
Output a single Integer: the maximum value General Li can get from the necklace.
Sample Input
2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
aba
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
acacac
Sample Output
1 6
原串的前缀与（原串前后颠倒得到的反串）的前缀长度相同，那么原串对应的这段字符则为回文串。模拟算出ex[i],可以得出ex[i]+i=len，且如果前半段（到i)不是回文，则直接判断（i+1)以后的是否为回文即可。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <stack>
using namespace std;
const int inf=0x3fffffff;
const int maxn=500000+10;
char str1[maxn],str2[maxn];
int nt[maxn],ex1[maxn],ex2[maxn],dp[maxn];
int kind[26];
int slen,tlen;
void get_next(char *s)
{
nt[0]=slen;
int l,r;
for(l=0;l<slen-1&&s[l]==s[l+1];l++);
nt[1]=l;
l=1;
for(int i=2;i<slen;i++)
{
r=l+nt[l]-1;
if(nt[i-l]+i-1>=r)
{
int p=r-i+1>0?r-i+1:0;
while(p+i<slen&&s[p]==s[p+i])
p++;
nt[i]=p;
l=i;
}
else
nt[i]=nt[i-l];
}
}
void get_extand(char *s,char *t,int *ex)
{
memset(nt,0,sizeof(nt));
get_next(s);
int l=0,r;
while(l<slen&&s[l]==t[l])
l++;
ex[0]=l;
l=0;
for(int i=1;i<tlen;i++)
{
r=ex[l]+l-1;
if(nt[i-l]+i-1>=r)
{
int p=r-i+1>0?r-i+1:0;
while(p+i<tlen&&s[p]==t[i+p])
p++;
ex[i]=p;
l=i;
}
else
ex[i]=nt[i-l];
}
}
int main()
{
//freopen("in.txt","r",stdin);
int T;
scanf("%d",&T);
while(T--)
{
for(int i=0;i<26;i++)
scanf("%d",&kind[i]);
scanf("%s",str1);
memset(dp,0,sizeof(dp));
dp[0]=0;
tlen=slen=strlen(str1);
for(int i=1;i<=slen;i++)
dp[i]=dp[i-1]+kind[str1[i-1]-'a'];
for(int i=slen-1,j=0;i>=0;i--,j++)
str2[j]=str1[i];
str2[slen]=' ';
get_extand(str1,str2,ex1);
get_extand(str2,str1,ex2);
int ans=0;
for(int i=0;i<slen;i++)
{
int temp=0;
if(i&&ex1[i]+i==slen)
{
int p=ex1[i];
temp+=dp[p];
if(ex2[p]+p==slen)
{
temp+=dp[slen]-dp[p];
}
}
else
{
int p=i+1;
if(ex2[p]+p==slen)
temp+=dp[slen]-dp[p];
}
ans=ans>temp?ans:temp;
//printf("i->%d ans->%d
",i,ans);
}
printf("%d
",ans);
}
return 0;
}