URAL 1297. Palindrome(字尾陣列求最大回文串)

題目大意：給你一串字串，讓你求出來它存在的最長連續的迴文串。

解題思路：先把字串逆序加到陣列中，然後用字尾陣列求解。兩種方法：1，列舉排名，直接比較rank相同的字串的位置差是不是len。如果是的話，就記錄求解；2，列舉地址，求第i地址與第2*len-i+1的lcp的最大值。

PS：需要注意如果多解輸出靠前的字串。

兩種寫法寫在了一起，分別是Del，和Del1函式。

ThesampletextthatcouldbereadedthesameinbothordersArozaupalanalapuazorA

ArozaupalanalapuazorA

#include <algorithm>
#include <iostream>
#include <stdlib.h>
#include <string.h>
#include <iomanip>
#include <stdio.h>
#include <string>
#include <queue>
#include <cmath>
#include <stack>
#include <ctime>
#include <map>
#include <set>
#define eps 1e-9
///#define M 1000100
///#define LL __int64
#define LL long long
///#define INF 0x7ffffff
#define INF 0x3f3f3f3f
#define PI 3.1415926535898
#define zero(x) ((fabs(x)<eps)?0:x)
#define mod 1000000007

#define Read() freopen("autocomplete.in","r",stdin)
#define Write() freopen("autocomplete.out","w",stdout)
#define Cin() ios::sync_with_stdio(false)

using namespace std;


inline int read()
{
    char ch;
    bool flag = false;
    int a = 0;
    while(!((((ch = getchar()) >= '0') && (ch <= '9')) || (ch == '-')));
    if(ch != '-')
    {
        a *= 10;
        a += ch - '0';
    }
    else
    {
        flag = true;
    }
    while(((ch = getchar()) >= '0') && (ch <= '9'))
    {
        a *= 10;
        a += ch - '0';
    }
    if(flag)
    {
        a = -a;
    }
    return a;
}
void write(int a)
{
    if(a < 0)
    {
        putchar('-');
        a = -a;
    }
    if(a >= 10)
    {
        write(a / 10);
    }
    putchar(a % 10 + '0');
}

const int maxn = 20050;

int wa[maxn], wb[maxn], wv[maxn], ws1[maxn];
int sa[maxn];

int cmp(int *r, int a, int b, int l)
{
    return r[a] == r[b] && r[a+l] == r[b+l];
}

void da(int *r, int *sa, int n, int m)
{
    int i, j, p, *x = wa, *y = wb;
    for(i = 0; i < m; i++) ws1[i] = 0;
    for(i = 0; i < n; i++) ws1[x[i] = r[i]]++;
    for(i = 1; i < m; i++) ws1[i] += ws1[i-1];
    for(i = n-1; i >= 0; i--) sa[--ws1[x[i]]] = i;

    for(j = 1, p = 1; p < n; j <<= 1, m = p)
    {
        for(p = 0, i = n-j; i < n; i++) y[p++] = i;
        for(i = 0; i < n; i++)
            if(sa[i] >= j) y[p++] = sa[i]-j;
        for(i = 0; i < n; i++) wv[i] = x[y[i]];
        for(i = 0; i < m; i++) ws1[i] = 0;
        for(i = 0; i < n; i++) ws1[wv[i]]++;
        for(i = 1; i < m; i++) ws1[i] += ws1[i-1];
        for(i = n-1; i >= 0; i--) sa[--ws1[wv[i]]] = y[i];
        for(swap(x, y), p = 1, x[sa[0]] = 0, i = 1; i < n; i++)
            x[sa[i]] = cmp(y, sa[i-1], sa[i], j)?p-1:p++;
    }
}


int rank[maxn], height[maxn];
void calheight(int *r, int *sa, int n)
{
    int i, j, k = 0;
    for(i = 1; i <= n; i++) rank[sa[i]] = i;
    for(int i = 0; i < n; height[rank[i++]] = k)
        for(k?k--:0, j = sa[rank[i]-1]; r[i+k] == r[j+k]; k++);
    return ;
}

int dp[maxn][30];


void RMQ(int len)
{
    for(int i = 1; i <= len; i++)
        dp[i][0] = height[i];
    for(int j = 1; 1<<j <= maxn; j++)
    {
        for(int i = 1; i+(1<<j)-1 <= len; i++)
            dp[i][j] = min(dp[i][j-1], dp[i+(1<<(j-1))][j-1]);
    }
}
int lg[maxn];

int querry(int l, int r)
{
    int k = lg[r-l+1];
    return min(dp[l][k], dp[r-(1<<k)+1][k]);
}


void init()
{
    lg[0] = -1;
    for (int i = 1; i < maxn; ++i)
        lg[i] = lg[i>>1] + 1;
}
char str[maxn];
int seq[maxn];

void Del1(int n)
{
    int Max = 0;
    int pos = 0;
    for(int i = 0; i < n; i++)
    {
        int l = rank[i];
        int r = rank[2*n-i+1];
        if(l > r) swap(l, r);
        int tmp = querry(l+1, r);
        if(tmp*2 > Max)
        {
            Max = tmp*2;
            pos = i;
        }
        l = rank[i];
        r = rank[2*n-i];
        if(l > r) swap(l, r);
        tmp = querry(l+1, r);
        if(tmp*2-1 > Max)
        {
            Max = tmp*2-1;
            pos = i;
        }
    }
    for (int i = pos-Max/2; Max--; ++i)
        putchar(seq[i]);
    puts("");
    return ;
}

void Del(int n, int len)
{
    int Max = 1;
    int pos = 0;
    for(int i = 1; i <= n; i++)
    {
        int tmp = height[i];
        int l = sa[i-1];
        int r = sa[i];
        if(l > r) swap(l, r);
        if(l >= len || r <= len) continue;
        if(l+tmp != n-r) continue;
        if(tmp > Max)
        {
            Max = tmp;
            pos = l;
        }
        else if(tmp == Max && l < pos)
            pos = l;
    }
    for(int i = pos, ans = 0; ans < Max; i++, ans++)
        printf("%c",seq[i]);
    puts("");
    return ;
}

int main()
{
    ///init();
    while(~scanf("%s", str))
    {
        int len = strlen(str);
        int ans = 0;
        for(int i = 0; i < len; i++) seq[ans++] = str[i];
        seq[ans++] = 1;
        for(int i = len-1; i >= 0; i--) seq[ans++] = str[i];
        seq[ans] = 0;
        int Len = ans;
        da(seq, sa, Len+1, 128);
        calheight(seq, sa, Len);
        Del(ans, len);///列舉位置，判斷lcp是否為位置差;
        ///Del1(len);///列舉位置，判斷區間的lcp;
    }
    return 0;
}