POJ3693Maximum repetition substring【后缀数组】

Language: Default Maximum repetition substring Time Limit: 1000MS   Memory Limit: 65536K Total Submissions: 8053   Accepted: 2457 Description The repetition number of a string is defined as the maximum number R such that the string can be partitioned into R same consecutive substrings. For example, the repetition number of "ababab" is 3 and "ababa" is 1. Given a string containing lowercase letters, you are to find a substring of it with maximum repetition number. Input The input consists of multiple test cases. Each test case contains exactly one line, which gives a non-empty string consisting of lowercase letters. The length of the string will not be greater than 100,000. The last test case is followed by a line containing a '#'. Output For each test case, print a line containing the test case number( beginning with 1) followed by the substring of maximum repetition number. If there are multiple substrings of maximum repetition number, print the lexicographically smallest one. Sample Input ccabababc daabbccaa # Sample Output Case 1: ababab Case 2: aa Source 2008 Asia Hefei Regional Contest Online by USTC

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#define F(x) ((x)/3+((x)%3==1?0:tb))
#define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2)
using namespace std;
const int MAX=300010;
int dp[MAX][33];
int wa[MAX],wb[MAX],ws[MAX],wv[MAX],sa[MAX];
int rank[MAX],height[MAX],s[MAX];
char str[MAX];
int MIN(int a,int b){
return a<b?a:b;
}
int c0(int *r,int a,int b){
return r[a]==r[b]&&r[a+1]==r[b+1]&&r[a+2]==r[b+2];
}
int c12(int k,int *r,int a,int b){
if(k==2)return r[a]<r[b]||r[a]==r[b]&&c12(1,r,a+1,b+1);
else return r[a]<r[b]||r[a]==r[b]&&wv[a+1]<wv[b+1];
}
void sort(int *r,int *a,int *b,int n,int m){
int i;
for(i=0;i<n;++i)
wv[i]=r[a[i]];
for(i=0;i<m;++i)
ws[i]=0;
for(i=0;i<n;++i)
ws[wv[i]]++;
for(i=1;i<m;++i)
ws[i]+=ws[i-1];
for(i=n-1;i>=0;--i)
b[--ws[wv[i]]]=a[i];
return ;
}
void dc3(int *r,int *sa,int n,int m){
int i,j,*rn=r+n,*san=sa+n,ta=0,tb=(n+1)/3,tbc=0,p;
r
=r[n+1]=0;
for(i=0;i<n;++i){
if(i%3!=0)
wa[tbc++]=i;
}
sort(r+2,wa,wb,tbc,m);
sort(r+1,wb,wa,tbc,m);
sort(r,wa,wb,tbc,m);
for(p=1,rn[F(wb[0])]=0,i=1;i<tbc;i++)
rn[F(wb[i])]=c0(r,wb[i-1],wb[i])?p-1:p++;
if(p<tbc)
dc3(rn,san,tbc,p);
else {
for(i=0;i<tbc;++i)
san[rn[i]]=i;
}
for(i=0;i<tbc;++i){
if(san[i]<tb)
wb[ta++]=san[i]*3;
}
if(n%3==1)
wb[ta++]=n-1;
sort(r,wb,wa,ta,m);
for(i=0;i<tbc;++i)
wv[wb[i]=G(san[i])]=i;
for(i=0,j=0,p=0;i<ta && j<tbc;++p)
sa[p]=c12(wb[j]%3,r,wa[i],wb[j])?wa[i++]:wb[j++];
for(;i<ta;++p)
sa[p]=wa[i++];
for(;j<tbc;++p)
sa[p]=wb[j++];
return;
}
void getHeight(int *r,int n){
int i, j, k = 0;
for(i=1;i<=n;++i) rank[sa[i]] = i;
for(i=0;i<n;height[rank[i++]]=k){
for(k?k--:0,j=sa[rank[i]-1];r[i+k]==r[j+k];k++);
}
}
void RMQ(int n)
{
for(int i=1;i<=n;++i)
dp[i][0]=height[i];
for(int j=1;j<=log2(n+1);j++){
for(int i=1;i+(1<<j)-1<=n;++i){
dp[i][j]=MIN(dp[i][j-1],dp[i+(1<<(j-1))][j-1]);
}
}
}
int query(int l,int r)
{
l=rank[l];
r=rank[r];
if(l>r)
{
int tmp=l;
l=r;
r=tmp;
}
l++;
int k=log2(r-l+1);
return MIN(dp[l][k],dp[r-(1<<k)+1][k]);
}
int main()
{
int t=0;
while(scanf("%s",str)>0){
if(str[0]=='#')
break;
printf("Case %d: ",++t);
int len=strlen(str);
for(int i=0;i<len;++i)
s[i]=str[i]-'a'+1;
s[len]=0;
dc3(s,sa,len+1,35);
getHeight(s,len);
RMQ(len);
int num=0,pos=0,l;
for(int i=1;i<=len/2;++i){
for(int j=0;j<len-i;j+=i){
if(str[j]!=str[j+i])
continue;
int k=query(j,j+i);
int count=k/i+1;
int r=i-k%i,p=j,cnt=0;
for(int m=j-1;m>j-i&&str[m]==str[m+i]&&m>=0;m--){
cnt++;
if(cnt==r){
count++;
p=m;
}
else
if(rank[p]>rank[m]){
p=m;
}
}
if(num<count){
num=count;
pos=p;
l=count*i;
}
else if(num==count&&rank[pos]>rank[p]){
pos=p;
l=count*i;
}
}
}
if(num<2){
char ch='z';
for(int i=0;i<len;++i)
if(str[i]<ch)
ch=str[i];
printf("%c\n",ch);
continue;
}
for(int i=pos;i<pos+l;++i)
printf("%c",str[i]);
printf("\n");
}
return 0;
}

倍增
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
using namespace std;
const int MAX=300010;
int dp[MAX][33];
int wa[MAX],wb[MAX],ws[MAX],wv[MAX],sa[MAX];
int rank[MAX],height[MAX],s[MAX];
char str[MAX];
int MIN(int a,int b){
return a<b?a:b;
}
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,*t;
for(i=0;i<m;++i) ws[i]=0;
for(i=0;i<n;++i) ws[x[i]=r[i]]++;
for(i=1;i<m;++i) ws[i]+=ws[i-1];
for(i=n-1;i>=0;--i) sa[--ws[x[i]]]=i;
for(j=1,p=1;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) ws[i]=0;
for(i=0;i<n;++i) ws[wv[i]]++;
for(i=1;i<m;++i) ws[i]+=ws[i-1];
for(i=n-1;i>=0;--i) sa[--ws[wv[i]]]=y[i];
for(t=x,x=y,y=t,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++;
}
return;
}
void getHeight(int *r,int n){
int i, j, k = 0;
for(i=1;i<=n;++i) rank[sa[i]] = i;
for(i=0;i<n;height[rank[i++]]=k){
for(k?k--:0,j=sa[rank[i]-1];r[i+k]==r[j+k];k++);
}
}
void RMQ(int n)
{
for(int i=1;i<=n;++i)
dp[i][0]=height[i];
for(int j=1;j<=log2(n+1);j++){
for(int i=1;i+(1<<j)-1<=n;++i){
dp[i][j]=MIN(dp[i][j-1],dp[i+(1<<(j-1))][j-1]);
}
}
}
int query(int l,int r)
{
l=rank[l];
r=rank[r];
if(l>r)
{
int tmp=l;
l=r;
r=tmp;
}
l++;
int k=log2(r-l+1);
return MIN(dp[l][k],dp[r-(1<<k)+1][k]);
}
int main()
{
int t=0;
while(scanf("%s",str)>0){
if(str[0]=='#')
break;
printf("Case %d: ",++t);
int len=strlen(str);
for(int i=0;i<len;++i)
s[i]=str[i]-'a'+1;
s[len]=0;
da(s,sa,len+1,35);
getHeight(s,len);
RMQ(len);
int num=0,pos=0,l;
for(int i=1;i<=len/2;++i){
for(int j=0;j<len-i;j+=i){
if(str[j]!=str[j+i])
continue;
int k=query(j,j+i);
int count=k/i+1;
int r=i-k%i,p=j,cnt=0;
for(int m=j-1;m>j-i&&str[m]==str[m+i]&&m>=0;m--){
cnt++;
if(cnt==r){
count++;
p=m;
}
else
if(rank[p]>rank[m]){
p=m;
}
}
if(num<count){
num=count;
pos=p;
l=count*i;
}
else if(num==count&&rank[pos]>rank[p]){
pos=p;
l=count*i;
}
}
}
if(num<2){
char ch='z';
for(int i=0;i<len;++i)
if(str[i]<ch)
ch=str[i];
printf("%c\n",ch);
continue;
}
for(int i=pos;i<pos+l;++i)
printf("%c",str[i]);
printf("\n");
}
return 0;
}