In this post, we will solve HackerRank Circular Palindromes Problem Solution.
A palindrome is a string that reads the same from left to right as it does from right to left.
Given a string, S, of N lowercase English letters, we define a k-length rotation as cutting the first k characters from the beginning of S and appending them to the end of S. For each S. there are N possible k-length rotations (where 0 < k < N). See the Explanation section for examples.
Given N and S, find all N k-length rotations of S; for each rotated string, S. print the maximum possible length of any palindromic substring of S on a new line.
Input Format
The first line contains an integer, N (the length of S). The second line contains a single string, S.
Output Format
There should be N lines of output, where each line k contains an integer denoting the
maximum length of any palindromic substring of rotation S.
Sample Input 0
13
aaaaabbbbaaaa
Sample Output 0
12
12
10
8
8
9
11
13
11
9
8
8
10
Sample Input 1
7
cacbbba
Sample Output 1
3
3
3
3
3
3
3
Sample Input 2
12
eededdeedede
Sample Output 2
5
7
7
7
7
9
9
9
9
7
5
4Explanation
Consider Sample Case 1, where S = “cacbbba”.
The possible rotations, Sk, for string S are:
So = “cacbbba”.
S₁ = “acbbbac”
S2=”cbbbaca”
S3 = “bbbacac”
S4= “bbacacb”
S5 = “bacacbb”
Se=”acacbbb”
The longest palindromic substrings for each S are:
So: “cac” and “bbb”, so we print their length (3) on a new line.
S₁: “bbb”, so we print its length (3) on a new line.
S2: “bbb” and “aca”, so we print their length (3) on a new line.
S3: “bbb”, “aca”, and “cac”, so we print their length (3) on a new line.
S4: “aca” and “cac”, so we print their length (3) on a new line. S5: “aca” and “cac”, so we print their length (3) on a new line.
S6: “aca”, “cac”, and “bbb”, so we print their length (3) on a new line.
Circular Palindromes C Solution
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
void solve(char *str,int *a);
void init( int n );
void range_increment( int i, int j, int val );
int query( int i );
int max(int x,int y);
void update(int x,int y,int z);
void sort_a2(int*a,int*b,int size);
void merge2(int*a,int*left_a,int*right_a,int*b,int*left_b,int*right_b,int left_size, int right_size);
char str[1000001]={0};
int N,NN,a[2000004],tree[2000000],ans[500000],b[500000],c[500000];
int main(){
int i,j;
scanf("%d%s",&NN,str);
strncpy(str+NN,str,NN);
solve(str,a);
init(NN);
for(i=0;i<4*NN;i++)
if(a[i])
if(i%2)
update(i/2-a[i]/2,i/2+a[i]/2,a[i]);
else
update(i/2-a[i]/2,i/2+a[i]/2-1,a[i]);
for(i=0;i<NN;i++){
ans[i]=query(i);
b[i]=ans[i];
c[i]=i;
}
sort_a2(b,c,NN);
for(i=NN;i>=0;i--){
for(j=c[i];1;j=(j-1+NN)%NN)
if(ans[j]-ans[(j-1+NN)%NN]>2)
ans[(j-1+NN)%NN]=ans[j]-2;
else
break;
for(j=c[i];1;j=(j+1)%NN)
if(ans[j]-ans[(j+1)%NN]>2)
ans[(j+1)%NN]=ans[j]-2;
else
break;
}
for(i=0;i<NN;i++)
printf("%d\n",ans[i]);
return 0;
}
void solve(char *str,int *a){
char *p;
int len,R,Ri,i,j,mi;
len=strlen(str);
p=(char*)malloc(2*(len+1)*sizeof(char));
for(i=0;i<len;i++){
p[2*i]='#';
p[2*i+1]=str[i];
}
p[2*i]='#';
p[2*i+1]=0;
a[0]=R=Ri=0;
for(i=1;i<=len*2;i++)
if(i>=R){
if(p[i]!='#')
a[i]=1;
else
a[i]=0;
for(j=i+1;1;j++)
if(j<=2*len && 2*i-j>=0 && p[j]==p[2*i-j]){
if(p[j]!='#')
a[i]+=2;
}
else{
Ri=i;
R=j-1;
break;
}
}
else{
mi=2*Ri-i;
if(i+a[mi]>=R || mi==a[mi]){
a[i]=R-i;
for(j=R+1;1;j++)
if(j<=2*len && 2*i-j>=0 && p[j]==p[2*i-j]){
if(p[j]!='#')
a[i]+=2;
}
else{
Ri=i;
R=j-1;
break;
}
}
else
a[i]=a[mi];
}
free(p);
return;
}
void init( int n ){
N = 1;
while( N < n ) N *= 2;
int i;
for( i = 1; i < N + n; i++ ) tree[i] = 0;
}
void range_increment( int i, int j, int val ){
for( i += N, j += N; i <= j; i = ( i + 1 ) / 2, j = ( j - 1 ) / 2 )
{
if( i % 2 == 1 ) tree[i] = max(tree[i],val);
if( j % 2 == 0 ) tree[j] = max(tree[j],val);
}
}
int query( int i ){
int ans = 0,j;
for( j = i + N; j; j /= 2 ) ans = max(ans,tree[j]);
return ans;
}
int max(int x,int y){
return (x>y)?x:y;
}
void update(int x,int y,int z){
if(z>NN){
int m=x+z/2;
if(z%2)
if(NN%2)
update(m-NN/2,m+NN/2,NN);
else
update(m-NN/2+1,m+NN/2-1,NN-1);
else
if(NN%2)
update(m-NN/2,m+NN/2-1,NN-1);
else
update(m-NN/2,m+NN/2-1,NN);
}
if(y<NN){
range_increment(0,x,z);
range_increment(y+1,NN-1,z);
}
else
range_increment(y-NN+1,x,z);
return;
}
void sort_a2(int*a,int*b,int size){
if (size < 2)
return;
int m = (size+1)/2,i;
int*left_a,*left_b,*right_a,*right_b;
left_a=(int*)malloc(m*sizeof(int));
right_a=(int*)malloc((size-m)*sizeof(int));
left_b=(int*)malloc(m*sizeof(int));
right_b=(int*)malloc((size-m)*sizeof(int));
for(i=0;i<m;i++){
left_a[i]=a[i];
left_b[i]=b[i];
}
for(i=0;i<size-m;i++){
right_a[i]=a[i+m];
right_b[i]=b[i+m];
}
sort_a2(left_a,left_b,m);
sort_a2(right_a,right_b,size-m);
merge2(a,left_a,right_a,b,left_b,right_b,m,size-m);
free(left_a);
free(right_a);
free(left_b);
free(right_b);
return;
}
void merge2(int*a,int*left_a,int*right_a,int*b,int*left_b,int*right_b,int left_size, int right_size){
int i = 0, j = 0;
while (i < left_size|| j < right_size) {
if (i == left_size) {
a[i+j] = right_a[j];
b[i+j] = right_b[j];
j++;
} else if (j == right_size) {
a[i+j] = left_a[i];
b[i+j] = left_b[i];
i++;
} else if (left_a[i] <= right_a[j]) {
a[i+j] = left_a[i];
b[i+j] = left_b[i];
i++;
} else {
a[i+j] = right_a[j];
b[i+j] = right_b[j];
j++;
}
}
return;
}Circular Palindromes C++ Solution
#include<bits/stdc++.h>
using namespace std;
#define REP(i,a,b) for(i=a;i<b;i++)
#define rep(i,n) REP(i,0,n)
#define mygc(c) (c)=getchar_unlocked()
#define mypc(c) putchar_unlocked(c)
#define ll long long
#define ull unsigned ll
void reader(int *x){int k,m=0;*x=0;for(;;){mygc(k);if(k=='-'){m=1;break;}if('0'<=k&&k<='9'){*x=k-'0';break;}}for(;;){mygc(k);if(k<'0'||k>'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);}
void reader(ll *x){int k,m=0;*x=0;for(;;){mygc(k);if(k=='-'){m=1;break;}if('0'<=k&&k<='9'){*x=k-'0';break;}}for(;;){mygc(k);if(k<'0'||k>'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);}
void reader(double *x){scanf("%lf",x);}
int reader(char c[]){int i,s=0;for(;;){mygc(i);if(i!=' '&&i!='\n'&&i!='\r'&&i!='\t'&&i!=EOF) break;}c[s++]=i;for(;;){mygc(i);if(i==' '||i=='\n'||i=='\r'||i=='\t'||i==EOF) break;c[s++]=i;}c[s]='\0';return s;}
template <class T, class S> void reader(T *x, S *y){reader(x);reader(y);}
template <class T, class S, class U> void reader(T *x, S *y, U *z){reader(x);reader(y);reader(z);}
template <class T, class S, class U, class V> void reader(T *x, S *y, U *z, V *w){reader(x);reader(y);reader(z);reader(w);}
void writer(int x, char c){int s=0,m=0;char f[10];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);}
void writer(ll x, char c){int s=0,m=0;char f[20];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);}
void writer(double x, char c){printf("%.15f",x);mypc(c);}
void writer(const char c[]){int i;for(i=0;c[i]!='\0';i++)mypc(c[i]);}
void writer(const char x[], char c){int i;for(i=0;x[i]!='\0';i++)mypc(x[i]);mypc(c);}
template<class T> void writerLn(T x){writer(x,'\n');}
template<class T, class S> void writerLn(T x, S y){writer(x,' ');writer(y,'\n');}
template<class T, class S, class U> void writerLn(T x, S y, U z){writer(x,' ');writer(y,' ');writer(z,'\n');}
template<class T> void writerArr(T x[], int n){int i;if(!n){mypc('\n');return;}rep(i,n-1)writer(x[i],' ');writer(x[n-1],'\n');}
template<class T> void sort(int N, T a[], void *mem = NULL){sort(a,a+N);}
template<class T1, class T2> void sort(int N, T1 a[], T2 b[], void *mem){int i;pair<T1,T2> *r=(pair<T1, T2>*)mem;rep(i,N)r[i].first=a[i],r[i].second=b[i];sort(r,r+N);rep(i,N)a[i]=r[i].first,b[i]=r[i].second;}
template<class T1, class T2, class T3> void sort(int N, T1 a[], T2 b[], T3 c[], void *mem){int i;pair<T1,pair<T2,T3> > *r=(pair<T1,pair<T2,T3> >*)mem;rep(i,N)r[i].first=a[i],r[i].second.first=b[i],r[i].second.second=c[i];sort(r,r+N);rep(i,N)a[i]=r[i].first,b[i]=r[i].second.first,c[i]=r[i].second.second;}
template<class T1, class T2, class T3, class T4> void sort(int N, T1 a[], T2 b[], T3 c[], T4 d[], void *mem){int i;pair<pair<T1,T2>,pair<T3,T4> > *r=(pair<pair<T1,T2>,pair<T3,T4> >*)mem;rep(i,N)r[i].first.first=a[i],r[i].first.second=b[i],r[i].second.first=c[i],r[i].second.second=d[i];sort(r,r+N);rep(i,N)a[i]=r[i].first.first,b[i]=r[i].first.second,c[i]=r[i].second.first,d[i]=r[i].second.second;}
char memarr[77000000]; void *mem = memarr;
#define MD 1000000007
template<class T>
struct rollingHash64{
int len;
T *data;
ull *sum, *rev, *pw;
ull mul;
ull getinv(ull a){
ull t,s=a,u=0,v=1,e;
e = numeric_limits<ull>::max() / s;
t -= e * s;
u -= e * v;
swap(t,s);
swap(u,v);
while(s){
e=t/s;
t-=e*s;
u-=e*v;
swap(t,s);
swap(u,v);
}
return u;
}
void* init(int n, T *arr, ull m = 0, void *mem = NULL){
int i; ull v;
mul = m;
if(mul==0) mul = 2*(rand()%1000000000) + 1000000001ULL;
len = n;
data = arr;
if(mem == NULL){
pw = (ull*)malloc(sizeof(ull)*(2*len+1));
sum = (ull*)malloc(sizeof(ull)*(len+1));
rev = (ull*)malloc(sizeof(ull)*(len+1));
} else {
pw = (ull*)mem;
sum = pw + 2*len + 1;
rev = sum + len + 1;
mem = rev + len + 1;
}
v = getinv(mul);
pw = pw + len;
pw[0] = 1;
rep(i,len) pw[ i+1] = pw[ i] * mul;
rep(i,len) pw[-i-1] = pw[-i] * v;
sum[0] = 0;
rep(i,len) sum[i+1] = sum[i] + (ull)data[i] * pw[i];
rev[len] = 0;
for(i=len-1;i>=0;i--) rev[i] = rev[i+1] + (ull)data[i] * pw[len-i-1];
return mem;
}
ull get(int a, int b, int off=0){
ull res;
if(a <= b){
res = (sum[b+1] - sum[a]) * pw[-a+off] + (b-a+1);
} else {
res = (rev[b] - rev[a+1]) * pw[-(len-1-a)+off] + (a-b+1);
}
return res;
}
};
template<class T>
void manacher(int n, T arr[], int res[]) {
int i, j, k;
for(i=0,j=0; i<2*n; i+=k, j=max(j-k,0)) {
while(i-j >= 0 && i+j+1 < 2*n && arr[(i-j)/2] == arr[(i+j+1)/2]) ++j;
res[i] = j;
for(k=1; i-k >= 0 && res[i]-k >= 0 && res[i-k] != res[i]-k; ++k)
res[i+k] = min(res[i-k], res[i]-k);
}
}
template<class T>
struct lazySegtreeMinVal{
int N, logN;
T *data;
T *fixval; char *fixed;
T *addval;
void malloc(int maxN){
int i;
for(i=1;i<maxN;i*=2);
data = (T*)std::malloc(sizeof(T)*2*i);
fixval = (T*)std::malloc(sizeof(T)*i);
addval = (T*)std::malloc(sizeof(T)*i);
fixed = (char*)std::malloc(sizeof(char)*i);
}
T& operator[](int i){
return data[N+i];
}
void setN(int n, int zerofill = 1){
int i;
for(i=1,logN=0;i<n;i*=2,logN++);
N = i;
if(zerofill) rep(i,N) data[N+i] = 0;
}
void build(void){
int i;
for(i=N-1;i;i--) data[i] = min(data[2*i],data[2*i+1]);
REP(i,1,N) fixed[i] = 0;
REP(i,1,N) addval[i] = 0;
}
inline void push_one(int a, int sz){
if(fixed[a]){
if(sz > 1){
fixed[a*2] = fixed[a*2+1] = 1;
fixval[a*2] = fixval[a*2+1] = fixval[a];
data[a*2] = data[a*2+1] = fixval[a];
} else {
data[a*2] = data[a*2+1] = fixval[a];
}
fixed[a] = 0;
addval[a] = 0;
return;
}
if(addval[a] != 0){
if(sz > 1){
if(fixed[a*2]) fixval[a*2] += addval[a];
else addval[a*2] += addval[a];
if(fixed[a*2+1]) fixval[a*2+1] += addval[a];
else addval[a*2+1] += addval[a];
data[a*2] += addval[a];
data[a*2+1] += addval[a];
} else {
data[a*2] += addval[a];
data[a*2+1] += addval[a];
}
addval[a] = 0;
return;
}
}
inline void push(int a){
int i, aa;
for(i=logN;i;i--){
aa = a>>i;
push_one(aa, 1<<(i-1));
}
}
inline void build(int a){
while(a > 1){
a /= 2;
if(fixed[a]){
data[a] = fixval[a];
} else {
data[a] = min(data[a*2], data[a*2+1]);
if(addval[a] != 0) data[a] += addval[a];
}
}
}
inline void change(int a, int b, T val){
int aa, bb;
if(a >= b) return;
aa = (a += N);
bb = (b += N);
push(a); push(b-1);
if(a%2) data[a++] = val;
if(b%2) data[--b] = val;
a /= 2;
b /= 2;
while(a < b){
if(a%2) fixed[a]=1, fixval[a]=val, data[a++] = val;
if(b%2) fixed[--b]=1, fixval[b]=val, data[b] = val;
a /= 2;
b /= 2;
}
build(aa);
build(bb-1);
}
inline void add(int a, int b, T val){
int sz = 1, aa, bb;
if(a >= b) return;
aa = (a += N);
bb = (b += N);
push(a); push(b-1);
if(a%2) data[a++] += val;
if(b%2) data[--b] += val;
a /= 2;
b /= 2;
while(a < b){
sz *= 2;
if(a%2){
if(fixed[a]) fixval[a] += val; else addval[a] += val;
data[a++] += val;
}
if(b%2){
b--;
if(fixed[b]) fixval[b] += val; else addval[b] += val;
data[b] += val;
}
a /= 2;
b /= 2;
}
build(aa);
build(bb-1);
}
inline T getMinVal(int a, int b){
T res;
int sz = 1;
a += N;
b += N;
push(a); push(b-1);
res = std::numeric_limits<T>::max();
while(a < b){
if(a%2) res = min(res, data[a++]);
if(b%2) res = min(res, data[--b]);
a /= 2;
b /= 2;
}
return res;
}
};
int N;
char S[2000000];
int rad[3000000];
int res[1000000];
int ss[3000000], ee[3000000], vv[3000000], nx[1000000];
int get_nx(int i){
if(nx[i]==-1) return i;
if(i==N-1) return nx[i] = N;
return nx[i] = get_nx(nx[i]);
}
int main(){
int i, j, k, st, ed, m, d;
// rollingHash64<char> h;
// lazySegtreeMinVal<int> t;
reader(&N,S);
// h.init(N,S);
// t.malloc(N);
// t.setN(N);
// t.build();
rep(i,N) S[N+i] = S[i];
manacher(2*N, S, rad);
rep(i,4*N){
k = min(N,rad[i]);
if(i%2==0 && k%2==0) k--;
if(i%2==1 && k%2==1) k--;
if(rad[i]==0) continue;
st = i/2 - (k-1)/2;
ed = i/2 + k/2;
m = ed-st+1;
ss[i] = (st-(N-m)+N+N)%N;
ee[i] = (st+N+N)%N;
vv[i] = m;
// rep(j,N-m+1) res[(st+N-j)%N] = max(res[(st+N-j)%N], m);
}
sort(4*N, vv, ss, ee, mem);
rep(i,N+1) nx[i] = -1;
for(i=4*N-1;i>=0;i--){
if(ss[i] <= ee[i]){
k = ss[i];
while(k <= ee[i]){
// writerLn(ss[i],k,ee[i]);
res[k] = max(res[k], vv[i]);
if(nx[k]==-1) nx[k] = k+1;
k = get_nx(k);
}
} else {
k = ss[i];
while(k < N){
// writerLn(ss[i],k,N);
res[k] = max(res[k], vv[i]);
if(nx[k]==-1) nx[k] = k+1;
k = get_nx(k);
}
k = 0;
while(k <= ee[i]){
// writerLn(0,k,ee[i]);
res[k] = max(res[k], vv[i]);
if(nx[k]==-1) nx[k] = k+1;
k = get_nx(k);
}
}
}
REP(i,1,2*N) res[i%N] = max(res[i%N], res[(i-1)%N]-2);
for(i=2*N-2;i>=0;i--) res[i%N] = max(res[i%N], res[(i+1)%N]-2);
rep(i,N) writerLn(res[i]);
return 0;
}Circular Palindromes C Sharp Solution
using System.CodeDom.Compiler;
using System.Collections.Generic;
using System.Collections;
using System.ComponentModel;
using System.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Reflection;
using System.Runtime.Serialization;
using System.Text.RegularExpressions;
using System.Text;
using System;
class Result
{
/*
* Complete the 'circularPalindromes' function below.
*
* The function is expected to return an INTEGER_ARRAY.
* The function accepts STRING s as parameter.
*/
private static char[] S; private static int[][] R;
private static ValueTuple<int, int>[] tp;
private static int fsize, ileft;
public static List<int> circularPalindromes(string s)
{
int N = s.Length, m = 2 * N - 1;
tp = new ValueTuple<int, int>[N];
S = new char[m]; R = new int[2][];
for (int i = 0; i < 2; i++)
R[i] = new int[m];
s.ToCharArray().CopyTo(S, 0);
s.Substring(0, N - 1).ToCharArray().CopyTo(S, N);
fsize = N; N = (N << 1) - 1;
manacher(N, 0);
manacher(N, 1);
process_manacher_table(N);
List<int> res = new List<int>();
if (tp[0].Item2 == 0) res.Add(1);
else res.Add(tp[0].Item2);
int cur = res[0], cur2 = tp[0].Item1;
for (int i = 1; i < fsize; i++)
{
cur2--;
cur = cur2 > 0 ? cur : cur - 2 > 0 ? cur - 2 : 1;
if (cur > tp[i].Item2)
{
res.Add(cur);
int a2 = tp[i].Item2;
int a1 = tp[i].Item1;
if (cur - ((a1 - cur2) * 2) < a2)
{
int z = (cur - a2) / 2, v1 = z + i + 1;
if (v1 < fsize) upDate(a1 - cur2 - z, a2, v1);
}
}
else
{
int a2 = tp[i].Item2;
int a1 = tp[i].Item1;
if (a2 - ((cur2 - a1) * 2) < cur)
{
int z = (a2 - cur) / 2, v1 = z + i + a1;
if (v1 < fsize) upDate(cur2 - a1 - z, cur, v1);
}
cur = tp[i].Item2;
res.Add(cur);
cur2 = tp[i].Item1;
int ii = 1;
while (i - ii >= 0 && cur - 2 * ii > res[i - ii])
{
res[i - ii] = cur - 2 * ii;
ii++;
}
}
}
return res;
}
private static void process_manacher_table(int n)
{
for (int i = 0; i < n; ++i)
{
adjust_and_gather(i, 0);
adjust_and_gather(i, 1);
}
}
private static void adjust_and_gather(int pos, int parity)
{
int ptr = R[parity][pos];
if ((parity == 0 && ptr == 1) || (parity == 1 && ptr == 0)) return;
int flen = (ptr << 1) - (parity ^ 1), lx;
if (flen > fsize) flen = (fsize - parity) %2== 1 ? fsize : fsize - 1;
ptr = (flen+1) / 2;
lx = pos - ptr + 1;
ileft = Math.Max(0, lx - (fsize - flen));
int same = lx - ileft + 1;
upDate(same, flen, ileft);
}
private static void upDate(int v, int flen, int ileft)
{
int a1 = tp[ileft].Item1;
int a2 = tp[ileft].Item2;
if (a2 >= flen && a2 - ((v - a1) * 2) > flen)
return;
else if (a2 < flen && flen - ((a1 - v) * 2) > a2)
tp[ileft] = (v, flen);
else if (a2 < flen && flen - ((a1 - v) * 2) < a2)
{
tp[ileft] = (v, flen);
int z = (flen - a2) / 2, v1 = z + ileft + v;
if (v1 < fsize)upDate(a1 - v - z, a2, v1);
}
else if (a2 > flen && a2 - ((v - a1) * 2) < flen)
{
int z = (a2 - flen) / 2, v1 = z + ileft + a1;
if (v1 < fsize) upDate(v - a1 - z, flen, v1);
}
else if (a2 == flen && v > a1) tp[ileft] = (v, flen);
}
private static void manacher(int length, int rx)
{
int i, j, k; var table = R[rx];
for (i = j = 0; i < length; i += k, j = Math.Max(j - k, 0))
{
while (i - j >= 0 && i + j + rx < length && S[i - j] == S[i + j + rx])
++j;
table[i] = j;
for (k = 1; k < j && table[i - k] != table[i] - k; ++k)
{
table[i + k] = Math.Min(table[i - k], table[i] - k);
}
}
}
}
class Solution
{
public static void Main(string[] args)
{
TextWriter textWriter = new StreamWriter(@System.Environment.GetEnvironmentVariable("OUTPUT_PATH"), true);
int n = Convert.ToInt32(Console.ReadLine().Trim());
string s = Console.ReadLine();
List<int> result = Result.circularPalindromes(s);
textWriter.WriteLine(String.Join("\n", result));
textWriter.Flush();
textWriter.Close();
}
}Circular Palindromes Java Solution
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class E2 {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
int n = ni();
char[] s = ns(n);
char[] s2 = new char[2*n];
for(int i = 0;i < n;i++){
s2[i] = s2[i+n] = s[i];
}
int[] pal = palindrome(s2);
// tr(pal, pal.length, n);
long[] es = new long[16*n];
int p = 0;
for(int i = 0;i < 4*n;i+=2){
pal[i] = Math.min(pal[i], n-((n&1)^1));
es[p++] = (long)(i/2)<<32|i;
es[p++] = (long)(i/2+pal[i]/2)<<32|i;
es[p++] = (long)(i/2+n-pal[i]/2-1)<<32|i;
es[p++] = (long)(i/2+n)<<32|i;
}
for(int i = 1;i < 4*n;i+=2){
pal[i] = Math.min(pal[i], n-((n&1)));
es[p++] = (long)(i/2)<<32|i;
es[p++] = (long)(i/2+pal[i]/2)<<32|i;
es[p++] = (long)(i/2+n-pal[i]/2)<<32|i;
es[p++] = (long)(i/2+n)<<32|i;
}
Arrays.sort(es, 0, p);
MaxHeap inc = new MaxHeap(4*n+1);
MaxHeap dec = new MaxHeap(4*n+1);
MaxHeap flat = new MaxHeap(4*n+1);
int[] st = new int[4*n];
int q = 0;
for(int i = 0;i < 2*n-1;i++){
while(q < p && es[q]>>>32 <= i){
int ind = (int)es[q];
if(st[ind] == 0){
inc.add(ind, (pal[ind]&1)-2*i);
}else if(st[ind] == 1){
inc.remove(ind);
flat.add(ind, pal[ind]);
}else if(st[ind] == 2){
flat.remove(ind);
dec.add(ind, pal[ind]+2*i);
}else if(st[ind] == 3){
dec.remove(ind);
}
st[ind]++;
q++;
}
if(i >= n-1){
// tr("i", i);
int max = 0;
if(inc.size() > 0)max = Math.max(inc.max()+2*i, max);
// tr(max);
if(dec.size() > 0)max = Math.max(dec.max()-2*i, max);
// tr(max);
max = Math.max(flat.max(), max);
// tr(max);
out.println(max);
}
}
}
public static class MaxHeap {
public int[] a;
public int[] map;
public int[] imap;
public int n;
public int pos;
public static int INF = Integer.MIN_VALUE;
public MaxHeap(int m)
{
n = m+2;
a = new int[n];
map = new int[n];
imap = new int[n];
Arrays.fill(a, INF);
Arrays.fill(map, -1);
Arrays.fill(imap, -1);
pos = 1;
}
public int add(int ind, int x)
{
int ret = imap[ind];
if(imap[ind] < 0){
a[pos] = x; map[pos] = ind; imap[ind] = pos;
pos++;
up(pos-1);
}
return ret != -1 ? a[ret] : x;
}
public int update(int ind, int x)
{
int ret = imap[ind];
if(imap[ind] < 0){
a[pos] = x; map[pos] = ind; imap[ind] = pos;
pos++;
up(pos-1);
}else{
int o = a[ret];
a[ret] = x;
up(ret);
down(ret);
// if(a[ret] < o){
// up(ret);
// }else{
// down(ret);
// }
}
return x;
}
public int remove(int ind)
{
if(pos == 1)return INF;
if(imap[ind] == -1)return INF;
pos--;
int rem = imap[ind];
int ret = a[rem];
map[rem] = map[pos];
imap[map[pos]] = rem;
imap[ind] = -1;
a[rem] = a[pos];
a[pos] = INF;
map[pos] = -1;
up(rem);
down(rem);
return ret;
}
public int max() { return a[1]; }
public int argmax() { return map[1]; }
public int size() { return pos-1; }
private void up(int cur)
{
for(int c = cur, p = c>>>1;p >= 1 && a[p] < a[c];c>>>=1, p>>>=1){
int d = a[p]; a[p] = a[c]; a[c] = d;
int e = imap[map[p]]; imap[map[p]] = imap[map[c]]; imap[map[c]] = e;
e = map[p]; map[p] = map[c]; map[c] = e;
}
}
private void down(int cur)
{
for(int c = cur;2*c < pos;){
int b = a[2*c] > a[2*c+1] ? 2*c : 2*c+1;
if(a[b] > a[c]){
int d = a[c]; a[c] = a[b]; a[b] = d;
int e = imap[map[c]]; imap[map[c]] = imap[map[b]]; imap[map[b]] = e;
e = map[c]; map[c] = map[b]; map[b] = e;
c = b;
}else{
break;
}
}
}
}
public static int[] palindrome(char[] str)
{
int n = str.length;
int[] r = new int[2*n];
int k = 0;
for(int i = 0, j = 0;i < 2*n;i += k, j = Math.max(j-k, 0)){
// normally
while(i-j >= 0 && i+j+1 < 2*n && str[(i-j)/2] == str[(i+j+1)/2])j++;
r[i] = j;
// skip based on the theorem
for(k = 1;i-k >= 0 && r[i]-k >= 0 && r[i-k] != r[i]-k;k++){
r[i+k] = Math.min(r[i-k], r[i]-k);
}
}
return r;
}
void run() throws Exception
{
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
}
public static void main(String[] args) throws Exception { new E2().run(); }
private byte[] inbuf = new byte[1024];
private int lenbuf = 0, ptrbuf = 0;
private int readByte()
{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
private double nd() { return Double.parseDouble(ns()); }
private char nc() { return (char)skip(); }
private String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private char[][] nm(int n, int m)
{
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}
private int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
private int ni()
{
int num = 0, b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}Circular Palindromes JavaScript Solution
'use strict';
const fs = require('fs');
process.stdin.resume();
process.stdin.setEncoding('utf-8');
let inputString = '';
let currentLine = 0;
process.stdin.on('data', function(inputStdin) {
inputString += inputStdin;
});
process.stdin.on('end', function() {
inputString = inputString.split('\n');
main();
});
function readLine() {
return inputString[currentLine++];
}
/*
* Complete the 'circularPalindromes' function below.
*
* The function is expected to return an INTEGER_ARRAY.
* The function accepts STRING s as parameter.
*/
function circularPalindromes(s) {
s = s.split('');
let currentLength, equalsLength, j1, j2;
const length = s.length;
const length2 = s.length - 1;
const largest = new Array(s.length).fill(0);
for (let i = 0; i < s.length; i++) {
currentLength = 1;
j1 = (i < 1) ? length2 : i - 1;
j2 = (i >= length2) ? 0 : i + 1;
while (s[i] === s[j2] && currentLength < length) {
currentLength++;
if (++j2 >= length) j2 = 0;
}
equalsLength = currentLength;
if (currentLength > 1) {
checkEqual(largest, i, currentLength);
i += currentLength - 1;
}
while (s[j1] === s[j2] && currentLength < length && j1 !== j2) {
currentLength += 2;
if (--j1 < 0) j1 = length2;
if (++j2 >= length) j2 = 0;
}
if (currentLength > equalsLength) {
if(++j1 >= length) j1 = 0;
checkLargest(largest, j1, currentLength, equalsLength);
}
}
return largest;
}
function checkEqual(largest, position, length) {
const limit = position + length;
const middle = position + (length >> 1);
const even = (length & 1) === 0;
for (let i = (position - largest.length + length < 0 ? 0 : position - largest.length + length); i < position; i++) {
if (largest[i] < length) largest[i] = length;
}
for (let i = position + length; i < largest.length; i++) {
if (largest[i] < length) largest[i] = length;
}
for (let i = position, j = position; i < limit; i++, j++) {
if (j >= largest.length) j = i % largest.length;
if (largest[j] < length) largest[j] = length;
if (i < middle){
length--;
} else if (i > middle) {
length++;
} else if (even) {
length++;
}
}
}
function checkLargest(largest, position, length, equalsLength) {
const limit1 = position + (length >> 1) - (equalsLength >> 1);
const limit2 = position + length;
for (let i = (position - largest.length + length < 0 ? 0 : position - largest.length + length); i < position; i++) {
if (largest[i] < length) largest[i] = length;
}
for (let i = position + length; i < largest.length; i++) {
if (largest[i] < length) largest[i] = length;
}
for (let i = position, j = position; i < limit1; i++, j++) {
if (j >= largest.length) j = i % largest.length;
if (largest[j] < length) largest[j] = length;
length -= 2;
}
for (let i = limit1 + equalsLength, j = limit1 + equalsLength; i < limit2; i++, j++) {
if (j >= largest.length) j = i % largest.length;
if (largest[j] < length) largest[j] = length;
length += 2;
}
}
function main() {
const ws = fs.createWriteStream(process.env.OUTPUT_PATH);
const n = parseInt(readLine().trim(), 10);
const s = readLine();
const result = circularPalindromes(s);
ws.write(result.join('\n') + '\n');
ws.end();
}Circular Palindromes Python Solution
#!/bin/python3
import os
import sys
import random
import bisect
#
# Complete the circularPalindromes function below.
#
def get_len(s, ll, flag):
# use flag = 0 for odd number of letters in palindrome, 1 for even
maxlen = 1
l1 = ll - 2
l2 = ll + 1 + flag
while l1>=0 and l2 < len(s) and s[l1] == s[l2]:
maxlen += 1
l1 -= 1
l2 += 1
return 2*maxlen + flag
def max_pal(s):
# find the length of the longest palindrome in s
ls = len(s)
maxlen = 1
for ll in range(1, ls):
if s[ll-1] == s[ll]:
newlen = get_len(s, ll, 0)
if newlen > maxlen:
maxlen = newlen
for ll in range(1, ls-1):
if s[ll-1] == s[ll+1]:
newlen = get_len(s, ll, 1)
if newlen > maxlen:
maxlen = newlen
return maxlen
def get_len_round_fast(slist, ll, lens):
ls = len(slist)
if ls == 1:
return (slist[0][1], slist[0][2])
start = slist[ll][1]
end = slist[ll][2]
l1 = ll - 1
l2 = ll + 1
notdone = True
while notdone and (end - start)<lens and slist[l1 % ls][0] == slist[l2 % ls][0]:
lgth1 = slist[l1][2]-slist[l1][1]
if lgth1 < 0:
lgth1 += lens
ls2 = l2 % ls
lgth2 = slist[ls2][2]-slist[ls2][1]
if lgth2 < 0:
lgth2 += lens
lmax = lens - (end-start)
if lgth1 != lgth2:
notdone = False
# make lgth2 the smaller for subsequent calculations
if lgth1 < lgth2:
lgth2 = lgth1
if lgth2 + lgth2 > lmax:
lgth2 = lmax//2
notdone = False
end+= lgth2
start -= lgth2
l1 -= 1
l2 += 1
# print(l1, l2)
return (start, end)
def compress_string(s):
# replaces strings of contiguous identical characters with (char, #) pairs
# where # is the end of the string sequence
ls = []
cc = '.'
start = 0
for ss in range(len(s)):
if s[ss] != cc: # new char
ls.append((cc, start, ss))
start = ss
cc = s[ss]
ls.append((cc, start, len(s))) # append the last characters encountered
ls.pop(0) # first value is a throwaway one
if ls[0][0] == ls[-1][0]: # stitch the ends, move the start of sequence before 0
ls[0] = (ls[0][0], ls[-1][1]-len(s), ls[0][2])
ls.pop() # remove last element, now that it is combined with the first
return ls
def make_pal_dict(slist, lens):
ls = len(slist)
dict1 = {}
list1 = []
for ll in range(ls):
(start, stop) = get_len_round_fast(slist, ll, lens)
# print(ll, start, stop)
lgth = stop - start
if lgth > 1:
if start < 0:
start, stop = start+lens, stop+lens
if lgth in dict1:
dict1[lgth].append((start, stop))
else:
dict1[lgth]= [(start, stop)]
bisect.insort(list1, lgth)
for (_, start, stop) in slist:
lgth = stop - start
if lgth > 1:
if start < 0:
start, stop = start+lens, stop+lens
if lgth in dict1:
if (start, stop) in dict1[lgth]:
dict1[lgth].remove((start, stop))
dict1[lgth].append((-start, -stop))
else:
dict1[lgth]= [(-start, -stop)]
bisect.insort(list1, lgth)
return (dict1, list1)
def cp(s):
ls = len(s)
slist = compress_string(s)
# print(slist)
(dict1, list1) = make_pal_dict(slist, ls)
# print(dict1, list1)
maxes = [] # value for k = 0
ll = len(list1)-1 # start here to look for longest palindrome
for k in range(ls):
maxlgth = 1
done = False
ks = k + ls
for ind in range(ll, -1, -1): # go backwards through list of lengths
if done: # max value already reached for a longer word
break
lgth = list1[ind]
if lgth < maxlgth: # only shorter words available past here
break
for (start, stop) in dict1[lgth]:
if start<=0 and stop <= 0: # same chars, no need to cut palindrome at both ends
# print(start, stop, k)
if -start <= k < -stop:
lgth1 = max(-stop - k, k+start)
else:
lgth1 = lgth
if -start < ks <= -stop:
lgth2 = max(ks + start, -stop - ks)
else:
lgth2 = lgth
#print(lgth1, lgth2)
else:
# print(lgth, maxlgth, k, start, stop)
if start <= k <= stop:
lgth1 = abs(start+stop-k-k)
else:
lgth1 = lgth
if start <= ks <= stop:
lgth2 = abs(start+stop-ks-ks)
else:
lgth2 = lgth
if lgth1 > lgth2:
lgth1 = lgth2
if maxlgth < lgth1:
maxlgth = lgth1
# print(maxlgth)
if lgth1 == lgth:
done = True
break
# print("k=", k, "ml=", maxlgth)
maxes.append(maxlgth)
return maxes
def circularPalindromes(s):
#
# Write your code here.
#
debug = 0
if debug == 0:
return cp(s)
elif debug == 1:
for ii in range(1000):
s = ""
for jj in range(10):
s += chr(97 + random.randrange(0, 26))
r1 = cp(s)
r = cp_gold(s)
if r1 != r:
print(r1, "should be", r, "for", s)
return [1, 1, 1]
elif debug == 2:
return cp_gold(s)
else:
(dict1, list1) = make_pal_list(s)
print(dict1, list1)
return cp_gold(s)
def rotate_s(s, val):
val = val % len(s)
return s[val:]+s[:val]
def cp_gold(s):
#
# Write your code here.
#
ls = len(s)
maxes = [max_pal(s)]
for ll in range(1, ls):
s = rotate_s(s, 1)
maxes.append(max_pal(s))
return maxes
if __name__ == '__main__':
fptr = open(os.environ['OUTPUT_PATH'], 'w')
n = int(input())
s = input()
result = circularPalindromes(s)
fptr.write('\n'.join(map(str, result)))
fptr.write('\n')
fptr.close()
