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HDU4622:Reincarnation(后缀数组,求区间内不同子串的个数)

Problem Description
Now you are back,and have a task to do:
Given you a string s consist of lower-case English letters only,denote f(s) as the number of distinct sub-string of s.
And you have some query,each time you should calculate f(s[l...r]), s[l...r] means the sub-string of s start from l end at r.
 

Input
The first line contains integer T(1<=T<=5), denote the number of the test cases.
For each test cases,the first line contains a string s(1 <= length of s <= 2000).
Denote the length of s by n.
The second line contains an integer Q(1 <= Q <= 10000),denote the number of queries.
Then Q lines follows,each lines contains two integer l, r(1 <= l <= r <= n), denote a query.
 

Output
For each test cases,for each query,print the answer in one line.
 

Sample Input
2 bbaba 5 3 4 2 2 2 5 2 4 1 4 baaba 5 3 3 3 4 1 4 3 5 5 5
 

Sample Output
3 1 7 5 8 1 3 8 5 1
Hint
I won‘t do anything against hash because I am nice.Of course this problem has a solution that don‘t rely on hash.
 

Author
WJMZBMR
 

Source
2013 Multi-University Training Contest 3
 

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题意:
求区间内不同子串的个数

思路:
论文里面有求整个串的不同子串的个数。我们能够引申到这道题
对于整个串,我们的求法是全部子串数减去全部height的值,而height就是lcp
那么对于某个区间,我们仅仅要求出全部包括在这个区间的后缀。然后减去互相之间的lcp就可以
关键是我们要保持这个区间的后缀的字典序

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <vector>
#include <math.h>
#include <bitset>
#include <algorithm>
#include <climits>
using namespace std;

#define LS 2*i
#define RS 2*i+1
#define UP(i,x,y) for(i=x;i<=y;i++)
#define DOWN(i,x,y) for(i=x;i>=y;i--)
#define MEM(a,x) memset(a,x,sizeof(a))
#define W(a) while(a)
#define gcd(a,b) __gcd(a,b)
#define LL long long
#define N 2005
#define MOD 1000000007
#define INF 0x3f3f3f3f
#define EXP 1e-8
#define rank rank1
int wa[N],wb[N],wsf[N],wv[N],sa[N];
int rank[N],height[N],s[N],a[N];
char str[N],str1[N],str2[N];
#define F(x) ((x)/3+((x)%3==1?

0:tb)) #define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2) //sa:字典序中排第i位的起始位置在str中第sa[i] //rank:就是str第i个位置的后缀是在字典序排第几 //height:字典序排i和i-1的后缀的最长公共前缀 int cmp(int *r,int a,int b,int k) { return r[a]==r[b]&&r[a+k]==r[b+k]; } void getsa(int *r,int *sa,int n,int m)//n要包括末尾加入的0 { int i,j,p,*x=wa,*y=wb,*t; for(i=0; i<m; i++) wsf[i]=0; for(i=0; i<n; i++) wsf[x[i]=r[i]]++; for(i=1; i<m; i++) wsf[i]+=wsf[i-1]; for(i=n-1; i>=0; i--) sa[--wsf[x[i]]]=i; p=1; j=1; for(; p<n; j*=2,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++) wsf[i]=0; for(i=0; i<n; i++) wsf[wv[i]]++; for(i=1; i<m; i++) wsf[i]+=wsf[i-1]; for(i=n-1; i>=0; i--) sa[--wsf[wv[i]]]=y[i]; t=x; x=y; y=t; x[sa[0]]=0; for(p=1,i=1; i<n; i++) x[sa[i]]=cmp(y,sa[i-1],sa[i],j)? p-1:p++; } } void getheight(int *r,int n)//n不保存最后的0 { int i,j,k=0; for(i=1; i<=n; i++) rank[sa[i]]=i; for(i=0; i<n; i++) { if(k) k--; else k=0; j=sa[rank[i]-1]; while(r[i+k]==r[j+k]) k++; height[rank[i]]=k; } } int Log[N]; int best[30][N]; void setLog() { Log[0] = -1; for(int i=1; i<N; i++) { Log[i]=(i&(i-1))?Log[i-1]:Log[i-1] + 1 ; } } void RMQ(int n) //初始化RMQ { for(int i = 1; i <= n ; i ++) best[0][i] = height[i]; for(int i = 1; i <= Log[n] ; i ++) { int limit = n - (1<<i) + 1; for(int j = 1; j <= limit ; j ++) { best[i][j] = min(best[i-1][j] , best[i-1][j+(1<<i>>1)]); } } } int LCP(int a,int b) //询问a,b后缀的最长公共前缀 { a ++; int t = Log[b - a + 1]; return min(best[t][a] , best[t][b - (1<<t) + 1]); } int t,n,m; int solve(int l,int r,int n) { int ans = (r-l+1)*(r-l+2)/2; int last = -1; int cnt = r-l+1; for(int i = 1; i<=n; i++) { if(!cnt) break; if(sa[i]<l || sa[i]>r) continue; cnt--; if(last == -1) { last = i; continue; } int a = last; int b = i; if(a>b) swap(a,b); int lcp = LCP(a,b); int la = r-sa[last]+1;//区间内该串的尾部 int lb = r-sa[i]+1; if(la>=lb && lcp>=lb);//la包括lb了,那么就用la继续往后比較,借此保持字典序,来模拟得到该区间的全部height else last = i; ans-=min(lcp,min(la,lb)); } return ans; } int main() { int i,j,k,len,l,r; scanf("%d",&t); setLog(); W(t--) { scanf("%s",str); scanf("%d",&m); len = strlen(str); for(i = 0; i<len; i++) s[i] = str[i]-'a'+1; s[len] = 0; getsa(s,sa,len+1,30); getheight(s,len); RMQ(len); while(m--) { scanf("%d%d",&l,&r); printf("%d\n",solve(l-1,r-1,len)); } } return 0; }



HDU4622:Reincarnation(后缀数组,求区间内不同子串的个数)