BZOJ4556 [Tjoi2016&Heoi2016]字符串【后缀数组 + 主席树 + 二分 + ST表】

题目

佳媛姐姐过生日的时候，她的小伙伴从某东上买了一个生日礼物。生日礼物放在一个神奇的箱子中。箱子外边写了

一个长为n的字符串s，和m个问题。佳媛姐姐必须正确回答这m个问题，才能打开箱子拿到礼物，升职加薪，出任CE

O，嫁给高富帅，走上人生巅峰。每个问题均有a,b,c,d四个参数，问你子串s[a..b]的所有子串和s[c..d]的最长公

共前缀的长度的最大值是多少？佳媛姐姐并不擅长做这样的问题，所以她向你求助，你该如何帮助她呢？

输入格式

输入的第一行有两个正整数n,m，分别表示字符串的长度和询问的个数。接下来一行是一个长为n的字符串。接下来

m行，每行有4个数a,b,c,d，表示询问s[a..b]的所有子串和s[c..d]的最长公共前缀的最大值。1<=n,m<=100,000,

字符串中仅有小写英文字母，a<=b,c<=d,1<=a,b,c,d<=n

输出格式

对于每一次询问，输出答案。

输入样例

5 5

aaaaa

1 1 1 5

1 5 1 1

2 3 2 3

2 4 2 3

2 3 2 4

输出样例

题解

一开始看错题，，原来是要求s[a...b]所有子串和子串s[c...d]的最大LCP【注意s[c...d]只是一个字符串】

那么我们二分一下答案

就需要快速判断子串c的height分组中是否存在子串s[a...b]

这个拿主席树记录位置存在信息就可以做到

height分组的边界可以倍增用ST表判断

还要注意不要越过子串的边界

#include<iostream>

#include<cstdio>

#include<cmath>

#include<cstring>

#include<algorithm>

#define LL long long int

#define Redge(u) for (int k = h[u],to; k; k = ed[k].nxt)

#define REP(i,n) for (int i = 1; i <= (n); i++)

#define BUG(s,n) for (int i = 1; i <= (n); i++) cout<<s[i]<<' '; puts("");

using namespace std;

const int maxn = 200005,maxm = 6000005,INF = 1000000000;

inline int read(){

	int out = 0,flag = 1; char c = getchar();

	while (c < 48 || c > 57){if (c == '-') flag = -1; c = getchar();}

	while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();}

	return out * flag;

}

int n,q;

char s[maxn];

int sa[maxn],rank[maxn],height[maxn],t1[maxn],t2[maxn],bac[maxn],m;

void getSA(){

	int *x = t1,*y = t2; m = 256;

	for (int i = 0; i <= m; i++) bac[i] = 0;

	for (int i = 1; i <= n; i++) bac[x[i] = s[i]]++;

	for (int i = 1; i <= m; i++) bac[i] += bac[i - 1];

	for (int i = n; i; i--) sa[bac[x[i]]--] = i;

	for (int k = 1; k <= n; k <<= 1){

		int p = 0;

		for (int i = n - k + 1; i <= n; i++) y[++p] = i;

		for (int i = 1; i <= n; i++) if (sa[i] - k > 0) y[++p] = sa[i] - k;

		for (int i = 0; i <= m; i++) bac[i] = 0;

		for (int i = 1; i <= n; i++) bac[x[y[i]]]++;

		for (int i = 1; i <= m; i++) bac[i] += bac[i - 1];

		for (int i = n; i; i--) sa[bac[x[y[i]]]--] = y[i];

		swap(x,y);

		p = x[sa[1]] = 1;

		for (int i = 2; i <= n; i++)

			x[sa[i]] = (y[sa[i]] == y[sa[i - 1]] && y[sa[i] + k] == y[sa[i - 1] + k] ? p : ++p);

		if (p >= n) break;

		m = p;

	}

	for (int i = 1; i <= n; i++) rank[sa[i]] = i;

	for (int i = 1,k = 0; i <= n; i++){

		if (k) k--;

		int j = sa[rank[i] - 1];

		while (s[i + k] == s[j + k]) k++;

		height[rank[i]] = k;

	}

}

int sum[maxm],ls[maxm],rs[maxm],rt[maxn],cnt;

void add(int& u,int pre,int l,int r,int pos){

	sum[u = ++cnt] = sum[pre] + 1;

	ls[u] = ls[pre]; rs[u] = rs[pre];

	if (l == r) return;

	int mid = l + r >> 1;

	if (mid >= pos) add(ls[u],ls[pre],l,mid,pos);

	else add(rs[u],rs[pre],mid + 1,r,pos);

}

int query(int u,int v,int l,int r,int L,int R){

	if (l >= L && r <= R) return sum[u] - sum[v];

	int mid = l + r >> 1;

	if (mid >= R) return query(ls[u],ls[v],l,mid,L,R);

	if (mid < L) return query(rs[u],rs[v],mid + 1,r,L,R);

	return query(ls[u],ls[v],l,mid,L,R) + query(rs[u],rs[v],mid + 1,r,L,R);

}

int a,b,c,d;

int bin[maxn],Log[maxn],mn[maxn][20];

void build(){

	for (int i = 1; i <= n; i++) add(rt[i],rt[i - 1],1,n,sa[i]);

	bin[0] = 1;

	for (int i = 1; i <= 20; i++) bin[i] = bin[i - 1] << 1;

	Log[0] = -1;

	for (int i = 1; i < maxn; i++) Log[i] = Log[i >> 1] + 1;

	for (int i = 1; i <= n; i++) mn[i][0] = height[i];

	for (int i = 1; i <= 17; i++)

		for (int j = 1; j <= n; j++){

			if (j + bin[i] - 1 > n) break;

			mn[j][i] = min(mn[j][i - 1],mn[j + bin[i - 1]][i - 1]);

		}

}

int getm(int l,int r){

	if (l > r) return INF;

	int t = Log[r - l + 1];

	return min(mn[l][t],mn[r - bin[t] + 1][t]);

}

bool check(int len){

	if (len == 0) return true;

	int u = rank[c],tmp,l = u,r = u;

	for (int i = 17; i >= 0; i--){

		tmp = l - bin[i];

		if (tmp > 0 && getm(tmp + 1,u) >= len) l = tmp;

		tmp = r + bin[i];

		if (tmp <= n && getm(u + 1,tmp) >= len) r = tmp;

	}

	return query(rt[r],rt[l - 1],1,n,a,b - len + 1);

}

void solve(){

	while (q--){

		a = read(); b = read();

		c = read(); d = read();

		int l = 0,r = min(d - c + 1,b - a + 1),mid;

		while (l < r){

			mid = l + r + 1 >> 1;

			if (check(mid)) l = mid;

			else r = mid - 1;

		}

		printf("%d\n",l);

	}

}

int main(){

	//freopen("in.in","r",stdin);

	n = read(); q = read();

	scanf("%s",s + 1);

	getSA();

	build();

	solve();

	return 0;

}