Ural1297 Palindrome（后缀数组）

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　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1297. Palindrome

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　Time limit: 1.0 second
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　Memory limit: 64 MB

The “U.S. Robots” HQ has just received a rather alarming anonymous letter. It states that the agent from the competing «Robots Unlimited» has infiltrated into “U.S. Robotics”. «U.S. Robots» security service would have already started an undercover operation to establish the agent’s identity, but, fortunately, the letter describes communication channel the agent uses. He will publish articles containing stolen data to the “Solaris” almanac. Obviously, he will obfuscate the data, so “Robots Unlimited” will have to use a special descrambler (“Robots Unlimited” part number NPRx8086, specifications are kept secret).

Having read the letter, the “U.S. Robots” president recalled having hired the “Robots Unlimited” ex-employee John Pupkin. President knows he can trust John, because John is still angry at being mistreated by “Robots Unlimited”. Unfortunately, he was fired just before his team has finished work on the NPRx8086 design.

So, the president has assigned the task of agent’s message interception to John. At first, John felt rather embarrassed, because revealing the hidden message isn’t any easier than finding a needle in a haystack. However, after he struggled the problem for a while, he remembered that the design of NPRx8086 was still incomplete. “Robots Unlimited” fired John when he was working on a specific module, the text direction detector. Nobody else could finish that module, so the descrambler will choose the text scanning direction at random. To ensure the correct descrambling of the message by NPRx8086, agent must encode the information in such a way that the resulting secret message reads the same both forwards and backwards.
In addition, it is reasonable to assume that the agent will be sending a very long message, so John has simply to find the longest message satisfying the mentioned property.

Your task is to help John Pupkin by writing a program to find the secret message in the text of a given article. As NPRx8086 ignores white spaces and punctuation marks, John will remove them from the text before feeding it into the program.

Input

The input consists of a single line, which contains a string of Latin alphabet letters (no other characters will appear in the string). String length will not exceed 1000 characters.

Output

The longest substring with mentioned property. If there are several such strings you should output the first of them.

Sample

【思路】

       最长回文子串。

       将字符串反向拼接在后，中间用一个没有出现的字符隔开，则问题转化为求新字符串两个特定后缀的lcp，枚举对称点i，对称数为奇的情况对应求lcp(i,n-i)，对称数为偶的情况对应求lcp(i,n-i-1)。

       如图所示：

       两个后缀的lcp可以用Sparse Table算法（倍增）在O(nlogn)时间内求解。

【代码】

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<iostream>
 4 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
 5 using namespace std;
 6 
 7 const int maxn = 3000+10; 
 8 const int maxd = 22;
 9 
10 int s[maxn];
11 int sa[maxn],c[maxn],t[maxn],t2[maxn];
12 
13 void build_sa(int m,int n) {
14     int i,*x=t,*y=t2;
15     for(i=0;i<m;i++) c[i]=0;
16     for(i=0;i<n;i++) c[x[i]=s[i]]++;
17     for(i=1;i<m;i++) c[i]+=c[i-1];
18     for(i=n-1;i>=0;i--) sa[--c[x[i]]]=i;
19     
20     for(int k=1;k<=n;k<<=1) {
21         int p=0;
22         for(i=n-k;i<n;i++) y[p++]=i;
23         for(i=0;i<n;i++) if(sa[i]>=k) y[p++]=sa[i]-k;
24         
25         for(i=0;i<m;i++) c[i]=0;
26         for(i=0;i<n;i++) c[x[y[i]]]++;
27         for(i=0;i<m;i++) c[i]+=c[i-1];
28         for(i=n-1;i>=0;i--) sa[--c[x[y[i]]]]=y[i];
29         
30         swap(x,y);
31         p=1; x[sa[0]]=0;
32         for(i=1;i<n;i++) 
33             x[sa[i]]=y[sa[i]]==y[sa[i-1]] && y[sa[i]+k]==y[sa[i-1]+k]?p-1:p++;
34         if(p>=n) break;
35         m=p;
36     }
37 }
38 int rank[maxn],height[maxn];
39 void getHeight(int n) {
40     int i,j,k=0;
41     for(i=0;i<=n;i++) rank[sa[i]]=i;
42     for(i=0;i<n;i++) {
43         if(k) k--;
44         j=sa[rank[i]-1];
45         while(s[j+k]==s[i+k]) k++;
46         height[rank[i]]=k;
47     }
48 }
49 int A[maxn][maxd];
50 void RMQ_init(int n) {
51     for(int i=1;i<=n;i++) A[i-1][0]=height[i];
52     for(int k=1;(1<<k)<=n;k++)
53         for(int i=0;(i+(1<<k))<=n;i++)
54             A[i][k]=min(A[i][k-1],A[i+(1<<(k-1))][k-1]);
55 }
56 int query(int l,int r) {
57     int k=0;
58     while(1<<(k+1)<=(r-l+1)) k++;
59     return min(A[l][k],A[r-(1<<k)+1][k]);
60 }
61 int lcp(int a,int b) {
62     int l=rank[a],r=rank[b];
63     if(r<l) swap(l,r); l--,r--;
64     if(r<0) return 0;
65     return query(l+1,r);    //l+1
66 }
67 
68 int n;
69 char expr[maxn];
70 
71 int main() {
72     while(scanf("%s",expr)==1) {
73         int len=strlen(expr),n=2*len+1;
74         for(int i=0;i<len;i++)s[i]=expr[i];
75         s[len]=1;
76         for(int i=0;i<len;i++)s[i+len+1]=expr[len-1-i];
77         s[n]=0;
78 
79         build_sa(‘z‘+1,n+1);
80         getHeight(n);
81         RMQ_init(n); 
82         int ans=0,front,tmp;
83         for(int i=0;i<n;i++) {
84             tmp=lcp(i,n-i-1);
85             if(2*tmp-1>ans) {  //对称个数为奇数 
86                 ans=2*tmp-1;
87                 front=i-tmp+1;
88             }
89             tmp=lcp(i,n-i);
90             if(2*tmp>ans) {  //对称个数为偶数 
91                 ans=2*tmp;
92                 front=i-tmp;
93             }
94         }
95         expr[front+ans]=‘\0‘;
96         printf("%s\n",expr+front);
97     }
98     return 0;
99 }

Ural1297 Palindrome（后缀数组）

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原文地址：http://www.cnblogs.com/lidaxin/p/5002878.html