bupt204nbsp;北邮多校J题nbsp;nbsp;后最数组+LC…

解题报告

题目 ：http://acm.bupt.edu.cn/onlinejudge/newoj/showProblem/show_problem.php?problem_id=204

算法 ：利用后缀数组求出以每个点为中心的最长回文长度，然后利用二分长度和RMQ搞

思路 ：利用后缀数组求出以每个点为中心的最长回文长度，但是偶数和奇数的情况要注意一下，我没想到好方法，只是偶数的维护了一次RMQ，奇数的又维护了一次RMQ。假设求区间[l,r]内的最长回文子串，我们枚举回文串一半的长度mid（奇数原长2×mid + 1）然后判一下在区间[l + mid, r – mid] 内有没有一个以某个点为中心长度大于等于2×mid+1的点，有的话说明这个mid可以被满足，同时我们还要考虑在区间[l + mid, r – mid + 1]中有没有一个长度大于等于2×mid的偶数回文串，这时我们记录最大的长度。由于北邮内存卡的较紧，奇数和偶数是分开处理的。

要注意的是枚举l和r是，奇数情况l从0开始，偶数情况l从1开始。

后缀数组最威武！

 

提交情况 ：MLE，TLE， wa， 3天， AC 一次

 

AC code：

 

 

#include <cstdio>

#include <cstring>

#include <cctype>

#include <cmath>

#include <cstdlib>

#include <ctime>

#include <map>

#include <set>

#include <vector>

#include <algorithm>

using namespace std;

 

typedef int I64;

typedef unsigned int uI64;

typedef double real;

const double LE =log(2.0);

 

const uI64 B[32] = {1, 2, 4, 8, 16,32, 64, 128, 256, 512, 1024, 2048,4096, 8192, 16384, 32768, 65536, 131072,262144, 524288, 1048576, 2097152, 4194304, 8388608,16777216, 33554432, 67108864, 134217728, 268435456,536870912, 1073741824, 2147483648};

#define MAX(a, b) ((a) > (b) ?(a) : (b))

#define MIN(a, b) ((a) < (b) ?(a) : (b))

#define mem(a, b) memset(a, b, sizeof(a))

#define fup(i, a, b) for(i = a; i < b; ++i)

#define fdn(i, a, b) for(i = a; i > b; --i)

#define INF 210000000

 

I64 Gcd(I64 a, I64 b){return b ? Gcd(b, a% b) : a;}

I64 Lcm(I64 a, I64 b){return a / Gcd(a, b)* b; }

 

#define MAXL 400010

#define MAXCHAR 300

#define MAXJ 20

 

char str[MAXL];

I64 Rank[MAXL], ST_min[MAXJ][MAXL],ST_max[MAXJ][MAXL / 2], ANS[MAXL / 2],ql[MAXL], qr[MAXL / 2];

I64 L;

 

bool cmp(I64 *tp, I64 a, I64 b, I64l){

    return tp[a] == tp[b] && tp[a+ l] == tp[b + l];

}

 

void Get_SA(){

    I64 len = L +1, i, m = MAXCHAR, *t, *rank =Rank, *SA = ql, *buc = ST_min[2],*y = ST_min[4], *nrank = ST_min[6];

    fup(i, 0, m) buc[i]= 0;

    fup(i, 0, len) buc[rank[i]= str[i]] ++;

    fup(i, 0, m) buc[i +1] += buc[i];

    fdn(i, len  - 1, -1) SA[--buc[rank[i]]]= i;

    for(I64 p= 1, k = 1; p < len;k <<= 1, m = p){

       for(p =0, i = len - k; i < len;++ i) y[p ++] = i;

       fup(i, 0, len) if(SA[i] >= k) y[p ++]= SA[i] - k;

       fup(i, 0, m) buc[i]= 0;

       fup(i, 0, len) buc[nrank[i]= rank[y[i]]] ++;

       fup(i, 0, m) buc[i +1] += buc[i];

       fdn(i, len - 1, -1)SA[--buc[nrank[i]]] = y[i];

       for(t =y, y = rank, rank = t, rank[SA[0]]= 0, i = p = 1; i <len; ++i)

           rank[SA[i]] = cmp(y,SA[i - 1], SA[i], k) ? p -1 : p ++;

    }

}

 

void Get_height(){

    I64 len = L, i,j, k = 0, *SA = ql, *height= ST_min[0];

    fup(i, 1, len + 1)Rank[SA[i]] = i;

    for(i =0; i < len; height[Rank[i++]] = k)

       for(k ?k -- : 0, j = SA[Rank[i] -1]; str[i + k] == str[j + k];k ++);

}

 

void Built_ST_min(){

    for(I64 j= 1; B[j] <= L; ++ j)

       for(I64 i= 0; i <= L - B[j] +1; i ++)

           ST_min[j][i] = MIN(ST_min[j- 1][i], ST_min[j - 1][i + B[j- 1]]);

}

 

I64 find_ST_min(I64 sux1, I64sux2){

    I64 x = Rank[sux1],y = Rank[sux2];

    if(x >y) swap(x, y);

    I64 len = (I64)(log((double)y - x) / LE);

    return MIN(ST_min[len][x + 1], ST_min[len][y- B[len] + 1]);

}

 

void Built_ST_max(I64 cnel){

    I64 i, j;

    fup(i, 0, cnel){

       j = 2 * cnel- i;

       ST_max[0][i] = find_ST_min(i,j) * 2 - 1;

    }

    for(j =1; B[j] < cnel; ++ j)

       for(i =0; i < cnel - B[j] + 1;++ i){

           ST_max[j][i] = MAX(ST_max[j- 1][i], ST_max[j - 1][i + B[j- 1]]);

       }

}

 

void Built_ST_max1(I64 cnel){

    I64 i, j;

    fup(i, 0, cnel){

       j = 2 * cnel- i + 1;

       ST_max[0][i] = find_ST_min(i,j) * 2;

    }

    for(j =1; B[j] < cnel; ++ j)

       for(i =0; i < cnel - B[j] + 1;++ i){

           ST_max[j][i] = MAX(ST_max[j- 1][i], ST_max[j - 1][i + B[j- 1]]);

       }

}

 

I64 find_ST_max(I64 x, I64y){

    if(x >y) return 0;

    I64 len = (I64)(log((double)y - x + 1) /LE);

    return MAX(ST_max[len][x], ST_max[len][y - B[len]+ 1]);

}

 

 

I64 exist(I64 x, I64y, I64 len){

    if(find_ST_max(x+ len, y - len) >= 2 *len + 1) return 2* len + 1;

    return 0;

}

 

I64 slove(I64 x, I64y, I64 cnel){

    I64 l = 0, r= (y - x + 1) / 2, mid,ans = 0, t;

    while(l <=r){

       mid = l + (r- l) / 2;

       if(t =exist(x, y, mid)){

           ans = t;

           l = mid +1;

       }else r= mid - 1;

    }

    return ans;

}

 

I64 exist2(I64 x, I64y, I64 len){

    if(find_ST_max(x+ len, y - len + 1) >=2 * len) return 2* len;

    return 0;

}

 

I64 slove2(I64 x, I64y, I64 cnel){

    I64 l = 1, r= (y - x + 1) / 2, mid,ans = 0, t;

    while(l <=r){

       mid = l + (r- l) / 2;

       if(t =exist2(x, y, mid)){

           ans = t;

           l = mid +1;

       }else r= mid - 1;

    }

    return ans;

}

 

int main(){

    I64 CASE, i, len, x,y, m;

    scanf("%d",&CASE);

    while(CASE--){

       scanf("%s",str);

       len = strlen(str);

       L = 2 * len +1;

       str[len] = 1;

       fup(i, 1, len + 1)

           str[len + i] =str[len - i];

       str[L] = 0;

       Get_SA();

       Get_height();

       Built_ST_min();

       Built_ST_max(len);

       scanf("%d",&m);

       fup(i, 0, m){

           scanf("%d %d", &ql[i], &qr[i]);

           ANS[i] = slove(ql[i]- 1, qr[i] - 1, len);

       }

       Built_ST_max1(len);

       fup(i, 0, m){

           if(ANS[i] < (x = slove2(ql[i] - 1,qr[i] - 1, len))) ANS[i] = x;

           printf("%d\n",ANS[i]);

       }

    }

    return 0;

}

 

 //在hdu没过