URAL 1297 最长回文子串(后缀数组)

 

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

input

ThesampletextthatcouldbereadedthesameinbothordersArozaupalanalapuazorA

output

ArozaupalanalapuazorA

 

/*
URAL 1297 最长回文子串(后缀数组)

算法合集之《后缀数组——处理字符串的有力工具》：
穷举每一位，然后计算以这个字符为中心的最长回文子串。注意这里要分两
种情况，一是回文子串的长度为奇数，二是长度为偶数。两种情况都可以转化为
求一个后缀和一个反过来写的后缀的最长公共前缀。具体的做法是：将整个字符
串反过来写在原字符串后面，中间用一个特殊的字符隔开。这样就把问题变为了
求这个新的字符串的某两个后缀的最长公共前缀。

所以我们只需先对初始的字符串进行一下处理，然后分别进行奇偶判断得到
最长回文子串的位置和长度

hhh-2016-03-13 15:41:30
*/
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <stack>
#include <map>
using namespace std;
typedef long long ll;
typedef long double ld;
#define lson (i<<1)
#define rson ((i<<1)|1)
const int maxn = 5005;

int t1[maxn],t2[maxn],c[maxn];
bool cmp(int *r,int a,int b,int l)
{
    return r[a]==r[b] &&r[l+a] == r[l+b];
}

void get_sa(int str[],int sa[],int Rank[],int height[],int n,int m)
{
    n++;
    int p,*x=t1,*y=t2;
    for(int i = 0; i < m; i++) c[i] = 0;
    for(int i = 0; i < n; i++) c[x[i] = str[i]]++;
    for(int i = 1; i < m; i++) c[i] += c[i-1];
    for(int i = n-1; i>=0; i--) sa[--c[x[i]]] = i;
    for(int j = 1; j <= n; j <<= 1)
    {
        p = 0;
        for(int i = n-j; i < n; i++) y[p++] = i;
        for(int i = 0; i < n; i++) if(sa[i] >= j) y[p++] = sa[i]-j;
        for(int i = 0; i < m; i++) c[i] = 0;
        for(int i = 0; i < n; i++) c[x[y[i]]]++ ;
        for(int i = 1; i < m; i++) c[i] += c[i-1];
        for(int i = n-1; i >= 0; i--)  sa[--c[x[y[i]]]] = y[i];

        swap(x,y);
        p = 1;
        x[sa[0]] = 0;
        for(int i = 1; i < n; i++)
            x[sa[i]] = cmp(y,sa[i-1],sa[i],j)? p-1:p++;
        if(p >= n) break;
        m = p;
    }
    int k = 0;
    n--;
    for(int i = 0; i <= n; i++)
        Rank[sa[i]] = i;
    for(int i = 0; i < n; i++)
    {
        if(k) k--;
        int j = sa[Rank[i]-1];
        while(str[i+k] == str[j+k]) k++;
        height[Rank[i]] = k;
    }
}


int mm[maxn];
int dp[20][maxn];
int Rank[maxn],height[maxn];
int sa[maxn],str[maxn];
char ts[maxn];

void ini_RMQ(int n)
{
    mm[0] = -1;
    for(int i = 1;i <= n;i++)
        mm[i] = (((i & (i-1)) == 0) ? mm[i-1]+1:mm[i-1]);

    for(int i =1;i <= n;i++)
        dp[0][i] = height[i];
    for(int i = 1;i <= mm[n];i++)
    {
        for(int j = 1;j+(1<<i)-1 <= n;j++)
        {
            int a = dp[i-1][j];
            int b = dp[i-1][j+(1<<(i-1))];
            dp[i][j] = min(a,b);
        }
    }
}

int askRMQ(int a,int b)
{
    int t = mm[b-a+1];
    b -= (1<<t)-1;
    return min(dp[t][a],dp[t][b]);
}


int fin(int a,int b)
{
    a = Rank[a],b = Rank[b];
    if(a > b) swap(a,b);
    return askRMQ(a+1,b);
}

int main()
{
    while(scanf("%s",ts) != EOF)
    {
        int len = strlen(ts);
        for(int i = 0;i < len;i++)
            str[i] = ts[i];
        str[len] = 1;
        for(int i = 0;i < len;i++)
            str[i+len+1] = ts[len-i-1];
        str[len*2+1] = 0;

        get_sa(str,sa,Rank,height,2*len+1,128);
        ini_RMQ(2*len+1);

        int ans = 0,pos;
        int tp;
        for(int i = 0;i < len;i++)
        {
            tp = fin(i,len*2+1-i);
            if(tp*2 > ans)
            {
                ans = tp*2;
                pos = i-tp;
            }
            tp = fin(i,len*2-i);
            if(tp*2-1 > ans)
            {
                ans = tp*2-1;
                pos = i-tp+1;
            }
        }
        ts[pos+ans] = 0;
        printf("%s\n",ts+pos);
    }
    return 0;
}