Light OJ: 1347 – Aladdin and the Magical Lamp

0

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1347


Solution Idea:
###############
Solution idea for this problem is following-
1. Concatenate 3 input string one after another and make one single string.
2. Build Suffix array and store every step rank.
3. Run sliding window or two pointer on sorted suffix array and find the range in which 3 string presents. and determine the LCP of beginning and ending string of that range segment.
4. Largest LCP value find during step 3 is the answer.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/


#define mx 30005

int SA[mx],tempSA[mx];
int RA[mx],tempRA[mx];
int c[mx];
//int LCP[mx],PLCP[mx],Phi[mx];
int P[18][mx],stp;
string str;
char s1[mx];
int n;

void counting_sort(int k)
{
    int maxi=max(300,n);
    ms(c,0);
    for(int i=0; i<n; i++)
    {
        int a=i+k<n?RA[i+k]:0;
        c[a]++;
    }
    for(int i=0,sum=0; i<maxi; i++)
    {
        int x=c[i];
        c[i]=sum;
        sum+=x;
    }

    for(int i=0; i<n; i++)
    {
        int a=SA[i]+k<n?RA[SA[i]+k]:0;
        int b=c[a];
        c[a]++;
        tempSA[b]=SA[i];
    }

    for(int i=0; i<n; i++)
        SA[i]=tempSA[i];
}

void build_Suffix_Array()
{
    stp=0;
    for(int i=0; i<n; i++)
    {
        RA[i]=str[i];
        SA[i]=i;
        P[stp][i]=RA[i];
    }

    stp++;

    for(int k=1; k<n; k*=2)
    {
        counting_sort(k);
        counting_sort(0);
        int r=0;
        tempRA[SA[0]]=r=0;
        for(int i=1; i<n; i++)
        {
            if(RA[SA[i]]==RA[SA[i-1]] && RA[SA[i]+k]==RA[SA[i-1]+k])
                tempRA[SA[i]]=r;
            else
                tempRA[SA[i]]=++r;
        }
        for(int i=0; i<n; i++)
        {
            RA[i]=tempRA[i];
            P[stp][i]=RA[i];
        }
        stp++;
        if(RA[SA[n-1]]==n-1) break;
    }
    stp--;
}


int find_lcp(int x, int y)
{
    int ret=0;
    if(x==y) return n-x;
    for(int k=stp; k>=0 && x<n && y<n; k--)
    {
        if(P[k][x]==P[k][y])
        {
            x+=(1<<k);
            y+=(1<<k);
            ret+=(1<<k);
        }
    }
    return ret;
}


int vis[5];

int getRange(int idx, int pos1, int pos2)
{
    if(idx<pos1) return 1;
    if(idx<pos2) return 2;
    return 3;
}



int main()
{

//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        str.clear();
        scanf("%s",s1);
        str+=string(s1);
        str+="@";
        int pos1=SZ(str)-1;
        scanf("%s",s1);
        str+=string(s1);
        str+="$";
        int pos2=SZ(str)-1;
        scanf("%s",s1);
        str+=string(s1);
        str+="#";
        n=SZ(str);
//        cout<<str<<endl;
        build_Suffix_Array();

//        for(int i=0; i<n; i++)
//            cout<<str.substr(SA[i])<<endl;

        int ans=0;

        int i=3,j=3;
        ms(vis,0);
        int cnt=0;
        while(j<n)
        {
            int a=getRange(SA[j],pos1,pos2);
            if(vis[a]==0)
            {
                cnt++;
            }
            vis[a]++;
            if(cnt==3)
            {
                int temp=find_lcp(SA[i],SA[j]);
                ans=max(ans,temp);
            }
            while(cnt>=3)
            {
                a=getRange(SA[i],pos1,pos2);
                vis[a]--;
                i++;
                if(vis[a]==0)
                    cnt--;
                if(cnt==3)
                {
                    int temp=find_lcp(SA[i],SA[j]);
                    ans=max(ans,temp);
                }
            }
            j++;
        }
        PRINT_CASE;
        pf("%d\n",ans);
    }


    return 0;
}


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Light OJ: 1314 – Names for Babies

0

Problem Link : http://www.lightoj.com/volume_showproblem.php?problem=1314


Solution Idea:

Build Suffix array and LCP array. Then find the distinct substring using LCP arrray by the formula (Length of the suffix – LCP of this and the previous suffix). But in this problem we need to calculate the length which lie in the given range. Think about it.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/


#define mx 100005

int SA[mx],tempSA[mx];
int RA[mx],tempRA[mx];
int c[mx];
int LCP[mx],PLCP[mx],Phi[mx];
//int P[18][mx];
char str[mx];
int n;

void counting_sort(int k)
{
    int maxi=max(300,n);
    ms(c,0);
    for(int i=0; i<n; i++)
    {
        int a=i+k<n?RA[i+k]:0;
        c[a]++;
    }
    for(int i=0,sum=0; i<maxi; i++)
    {
        int x=c[i];
        c[i]=sum;
        sum+=x;
    }

    for(int i=0; i<n; i++)
    {
        int a=SA[i]+k<n?RA[SA[i]+k]:0;
        int b=c[a];
        c[a]++;
        tempSA[b]=SA[i];
    }

    for(int i=0; i<n; i++)
        SA[i]=tempSA[i];
}

void build_Suffix_Array()
{
    for(int i=0; i<n; i++)
    {
        RA[i]=str[i];
        SA[i]=i;
    }

    for(int k=1; k<n; k*=2)
    {
        counting_sort(k);
        counting_sort(0);
        int r=0;
        tempRA[SA[0]]=r=0;
        for(int i=1; i<n; i++)
        {
            if(RA[SA[i]]==RA[SA[i-1]] && RA[SA[i]+k]==RA[SA[i-1]+k])
                tempRA[SA[i]]=r;
            else
                tempRA[SA[i]]=++r;
        }
        for(int i=0; i<n; i++)
        {
            RA[i]=tempRA[i];
        }
        if(RA[SA[n-1]]==n-1) break;
    }
}

void build_LCP()
{
    Phi[SA[0]]=-1;
    for(int i=1; i<n; i++)
        Phi[SA[i]]=SA[i-1];
    for(int i=0,L=0; i<n; i++)
    {
        if(Phi[i]==-1)
        {
            PLCP[i]=0;
            continue;
        }
        while(str[i+L]==str[Phi[i]+L]) L++;
        PLCP[i]=L;
        L=max(L-1,0);
    }

    for(int i=0; i<n; i++)
        LCP[i]=PLCP[SA[i]];
}



int main()
{

//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        scanf("%s",str);
        strcat(str,"$");
        n=strlen(str);
        build_Suffix_Array();
        build_LCP();


//        string ss=str;
//        for(int i=0;i<n;i++)
//            cout<<SA[i]<<" ";
//        cout<<endl;
//        for(int i=0;i<n;i++)
//            cout<<LCP[i]<<" ";
//        cout<<endl;
//        for(int i=0;i<n;i++)
//            cout<<ss.substr(SA[i])<<endl;

        int a,b;
        sff(a,b);

        int ans=0;
        for(int i=1;i<n;i++)
        {
            int len=n-SA[i]-1;
            int temp=len-LCP[i];
            if(len>b)
                temp-=(len-b);
            if(LCP[i]<a)
                temp-=(a-LCP[i]-1);
            temp=max(temp,0);
            ans+=temp;
        }

        PRINT_CASE;
        pf("%d\n",ans);

    }

    return 0;
}


SPOJ: LPS – Longest Palindromic Substring

0

Problem Link : http://www.spoj.com/problems/LPS/


Solution Idea:
——————
This one is the straight forward implementation of manachar’s algorithm. You can learn about manachar algorithm form the following links-
1. Hackerearth’s Note
2. Hackerank Topic
3. Youtube


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

#define mx 600005

char s1[mx];
int p[mx];
int n;

string process(string &str)
{
    string ret;
    ret+='$';
    ret+='#';
    for(int i=0;i<SZ(str);i++)
    {
       ret+=str[i];
       ret+='#';
    }
    ret+='@';
    return ret;
//    cout<<str<<endl;
}

int manacher(string &str)
{
    int c=0,r=0;
    for(int i=1;i<SZ(str)-1;i++)
    {
        int miror=c+c-i;
        if(i<r)
            p[i]=min(p[miror],r-i);
        while(str[i+1+p[i]]==str[i-1-p[i]])
            p[i]++;
        if(i+p[i]>r)
        {
            c=i;
            r=i+p[i];
        }
    }
    int ret=0;
    for(int i=0;i<SZ(str);i++)
        ret=max(ret,p[i]);
    return ret;
}

int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

      string str;

      scanf("%d",&n);
      scanf("%s",s1);

      str=s1;
      str=process(str);
      int ans=manacher(str);
      printf("%d\n",ans);

    return 0;
}



SPOJ: LCS – Longest Common Substring

0

Problem Link : http://www.spoj.com/problems/LCS/


Solution Idea:

This is the problem no 6 on Suffix array paper .
The question need to find the maximum value of LCP[] array between two consecutive suffixes where this two consecutive suffixes are from different input string.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

#define mx 500005

int SA[mx],tempSA[mx];
int RA[mx],tempRA[mx];
int c[mx];
int Phi[mx],PLCP[mx],LCP[mx];
char str[mx],str1[mx];
int n;

void counting_sort(int k)
{
    int maxi=max(n,300);
    ms(c,0);
    for(int i=0; i<n; i++)
    {
        int a=i+k<n?RA[i+k]:0;
        c[a]++;
    }
    for(int i=0,sum=0; i<maxi; i++)
    {
        int x=c[i];
        c[i]=sum;
        sum+=x;
    }

    for(int i=0; i<n; i++)
    {
        int a=SA[i]+k<n?RA[SA[i]+k]:0;
        int b=c[a];
        c[a]++;
        tempSA[b]=SA[i];
    }

    for(int i=0; i<n; i++)
        SA[i]=tempSA[i];
}

void build_SA()
{
    for(int i=0; i<n; i++)
    {
        RA[i]=str[i];
        SA[i]=i;
    }

    for(int k=1; k<n; k*=2)
    {
        counting_sort(k);
        counting_sort(0);

        int r=0;
        tempRA[SA[0]]=r=0;

        for(int i=1; i<n; i++)
        {
            if(RA[SA[i]]==RA[SA[i-1]] && RA[SA[i]+k]==RA[SA[i-1]+k])
                tempRA[SA[i]]=r;
            else
                tempRA[SA[i]]=++r;
        }

        for(int i=0; i<n; i++)
            RA[i]=tempRA[i];

        if(RA[SA[n-1]]==n-1) break;
    }
}

void build_LCP()
{
    Phi[SA[0]]=-1;
    for(int i=1; i<n; i++)
        Phi[SA[i]]=SA[i-1];
    for(int i=0,L=0; i<n; i++)
    {
        if(Phi[i]==-1)
        {
            PLCP[i]=0;
            continue;
        }
        while(str[i+L]==str[Phi[i]+L]) L++;
        PLCP[i]=L;
        L=max(L-1,0);
    }

    for(int i=0; i<n; i++)
        LCP[i]=PLCP[SA[i]];

}

int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

    int pos;

    scanf("%s %s",str,str1);
    strcat(str,"$");
    pos=strlen(str)-1;
    strcat(str,str1);
    strcat(str,"#");
    n=strlen(str);
    build_SA();
    build_LCP();
//    string ss=str;
//    for(int i=0;i<n;i++)
//        cout<<SA[i]<<" ";
//    cout<<endl;
//    for(int i=0;i<n;i++)
//        cout<<LCP[i]<<" ";
//    cout<<endl;
//    for(int i=0;i<n;i++)
//        cout<<ss.substr(SA[i])<<endl;

    int ans=0;

    for(int i=1; i<n; i++)
    {
        if((SA[i]<pos && (SA[i-1]>pos)) || ((SA[i]>pos && SA[i-1]<pos)))
        {
            ans=max(ans,LCP[i]);
        }
    }

    pf("%d\n",ans);

    return 0;
}


UVa 760 – DNA Sequencing

0

Problem Link : http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=701


Solution Idea:
1. Concatenate two string then build suffix array and LCP array.
1. Now find those position in LCP array where two consecutive suffix is from two
different input string.
3. Now take the maximum of LCP[these indexes]
4. After that generate string from this position with the determined maximum
length value.
5. Print the distinct strings from these strings.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/


#define mx 1005

int SA[mx],tempSA[mx];
int RA[mx],tempRA[mx];
int c[mx];
int LCP[mx],PLCP[mx],Phi[mx];
char str[mx],str1[mx];
int n;

void counting_sort(int k)
{
    int maxi=max(300,n);
    ms(c,0);
    for(int i=0; i<n; i++)
    {
        int a=i+k<n?RA[i+k]:0;
        c[a]++;
    }
    for(int i=0,sum=0; i<maxi; i++)
    {
        int x=c[i];
        c[i]=sum;
        sum+=x;
    }

    for(int i=0; i<n; i++)
    {
        int a=SA[i]+k<n?RA[SA[i]+k]:0;
        int b=c[a];
        c[a]++;
        tempSA[b]=SA[i];
    }

    for(int i=0; i<n; i++)
        SA[i]=tempSA[i];
}

void build_Suffix_Array()
{
    for(int i=0; i<n; i++)
    {
        RA[i]=str[i];
        SA[i]=i;
    }

    for(int k=1; k<n; k*=2)
    {
        counting_sort(k);
        counting_sort(0);
        int r=0;
        tempRA[SA[0]]=r=0;
        for(int i=1; i<n; i++)
        {
            if(RA[SA[i]]==RA[SA[i-1]] && RA[SA[i]+k]==RA[SA[i-1]+k])
                tempRA[SA[i]]=r;
            else
                tempRA[SA[i]]=++r;
        }
        for(int i=0; i<n; i++)
        {
            RA[i]=tempRA[i];
        }
        if(RA[SA[n-1]]==n-1) break;
    }
}

void build_LCP()
{
    Phi[SA[0]]=-1;
    for(int i=1; i<n; i++)
        Phi[SA[i]]=SA[i-1];
    for(int i=0,L=0; i<n; i++)
    {
        if(Phi[i]==-1)
        {
            PLCP[i]=0;
            continue;
        }
        while(str[i+L]==str[Phi[i]+L]) L++;
        PLCP[i]=L;
        L=max(L-1,0);
    }

    for(int i=0; i<n; i++)
        LCP[i]=PLCP[SA[i]];
}

map<string,bool>mp;

int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

    bool check=0;
    while(scanf("%s",str)!=EOF)
    {
        scanf("%s",str1);
        strcat(str,"$");
        int l1=strlen(str)-1;
        strcat(str,str1);
        strcat(str,"#");
        n=strlen(str);
        build_Suffix_Array();
        build_LCP();
        string str2=str;
        int ans=0,maxi=0;

        if(check)
            pf("\n");
        check=1;

//        for(int i=0;i<n;i++)
//            cout<<SA[i]<<" ";
//        cout<<endl;
//        for(int i=0;i<n;i++)
//            cout<<LCP[i]<<" ";
//        cout<<endl;
//
//        for(int i=0;i<n;i++)
//        {
//            cout<<str2.substr(SA[i])<<endl;
//        }
//        cout<<endl;

        for(int i=1; i<n; i++)
        {
            if((SA[i]<l1 && SA[i-1]<n && SA[i-1]>l1) || (SA[i]>l1 && SA[i]<n && SA[i-1]<l1))
                maxi=max(maxi,LCP[i]);
        }

        if(maxi==0)
        {
            pf("No common sequence.\n");
            continue;
        }

        mp.clear();

        for(int i=1; i<n; i++)
        {
            if((SA[i]<l1 && SA[i-1]<n && SA[i-1]>l1)|| (SA[i]>l1 && SA[i]<n && SA[i-1]<l1))
            {
                if(LCP[i]==maxi)
                {
                    string temp=str2.substr(SA[i],maxi);
                    if(mp[temp]) continue;
                    else
                        mp[temp]=1;
                    printf("%s\n",temp.c_str());
                }
            }
        }
    }


    return 0;
}


SPOJ: SUBLEX – Lexicographical Substring Search

0

Problem Link : http://www.spoj.com/problems/SUBLEX/


Solution Idea:

My solution for this problem is using suffix array and LCP array.
At first Build Suffix array and LCP array. Then find from which position of the suffix array you can get the K’th substring. Determine the position and determine the length for which it is the K’th smallest substring. Then print it.

We can get number of distinct substring using Suffix Array and LCP array. If you don’t know it how to do this job then solve this problem first.
SPOJ: DISUBSTR – Distinct Substrings


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

#define mx 100005

int SA[mx],tempSA[mx];
int RA[mx],tempRA[mx];
int c[mx];
int LCP[mx],PLCP[mx],Phi[mx];
char str[mx];
int n;

void counting_sort(int k)
{
    int maxi=max(300,n);
    ms(c,0);
    for(int i=0; i<n; i++)
    {
        int a=i+k<n?RA[i+k]:0;
        c[a]++;
    }
    for(int i=0,sum=0; i<maxi; i++)
    {
        int x=c[i];
        c[i]=sum;
        sum+=x;
    }

    for(int i=0; i<n; i++)
    {
        int a=SA[i]+k<n?RA[SA[i]+k]:0;
        int b=c[a];
        c[a]++;
        tempSA[b]=SA[i];
    }

    for(int i=0; i<n; i++)
        SA[i]=tempSA[i];
}

void build_Suffix_Array()
{
    for(int i=0; i<n; i++)
    {
        RA[i]=str[i];
        SA[i]=i;
    }

    for(int k=1; k<n; k*=2)
    {
        counting_sort(k);
        counting_sort(0);
        int r=0;
        tempRA[SA[0]]=r=0;
        for(int i=1; i<n; i++)
        {
            if(RA[SA[i]]==RA[SA[i-1]] && RA[SA[i]+k]==RA[SA[i-1]+k])
                tempRA[SA[i]]=r;
            else
                tempRA[SA[i]]=++r;
        }
        for(int i=0; i<n; i++)
        {
            RA[i]=tempRA[i];
        }
        if(RA[SA[n-1]]==n-1) break;
    }
}

void build_LCP()
{
    Phi[SA[0]]=-1;
    for(int i=1; i<n; i++)
        Phi[SA[i]]=SA[i-1];
    for(int i=0,L=0; i<n; i++)
    {
//        D(i);
        if(Phi[i]==-1)
        {
            PLCP[i]=0;
            continue;
        }
        while(str[i+L]==str[Phi[i]+L]) L++;
        PLCP[i]=L;
        L=max(L-1,0);
    }

    for(int i=0; i<n; i++)
        LCP[i]=PLCP[SA[i]];
}



int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

//    int t;
//    sf(t);
//    TEST_CASE(t)
    {
        scanf("%s",str);
        string str1=str;
        strcat(str,"$");
        n=strlen(str);
        build_Suffix_Array();
        build_LCP();

//        for(int i=0; i<n; i++)
//            cout<<SA[i]<<" ";
//        cout<<endl;
//        for(int i=0; i<n; i++)
//            cout<<LCP[i]<<" ";
//        cout<<endl;


        int string_len=SZ(str1);

        int q;
        sf(q);
        while(q--)
        {
            ll k;
            sfl(k);
            ll ans=0;
            int pos=0,len=0;
            for(int i=1;i<n;i++)
            {
                int temp=string_len-SA[i]-LCP[i];
                if(ans+temp<k)
                    ans+=temp;
                else
                {
                    pos=SA[i];
                    len=ans+temp-k;
                    len=LCP[i]+temp-len;
                    break;
                }
            }
            pf("%s\n",str1.substr(pos,len).c_str());
        }

    }

    return 0;
}

SPOJ: DISUBSTR – Distinct Substrings

1

Problem Link : http://www.spoj.com/problems/DISUBSTR/en/


Solution Idea: Build Suffix Array and LCP array. Then the answer will be subtraction of length of the ith suffix and LCP[i].

Answer = Li-LCP[i]

This works because LCP[i] holds the length of the longest common prefix of Suffix SA[i] and SA[i-1] where SA[] is suffix array.

Don’t forget to add an smaller extra or invalid symbol at the end of the string after taking input. Here I add a ‘$’.


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#define sf(a)            scanf("%d",&a)
#define sfl(a)           scanf("%lld",&a)
#define sff(a,b)         scanf("%d %d",&a,&b)
#define sffl(a,b)        scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)      scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

#define mx 1005

int SA[mx],tempSA[mx];
int RA[mx],tempRA[mx];
int c[mx];
int LCP[mx],PLCP[mx],Phi[mx];
char str[mx];
int n;

void counting_sort(int k)
{
    int maxi=max(300,n);
    ms(c,0);
    for(int i=0; i<n; i++)
    {
        int a=i+k<n?RA[i+k]:0;
        c[a]++;
    }
    for(int i=0,sum=0; i<maxi; i++)
    {
        int x=c[i];
        c[i]=sum;
        sum+=x;
    }

    for(int i=0; i<n; i++)
    {
        int a=SA[i]+k<n?RA[SA[i]+k]:0;
        int b=c[a];
        c[a]++;
        tempSA[b]=SA[i];
    }

    for(int i=0; i<n; i++)
        SA[i]=tempSA[i];
}

void build_Suffix_Array()
{
    for(int i=0; i<n; i++)
    {
        RA[i]=str[i];
        SA[i]=i;
    }

    for(int k=1; k<n; k*=2)
    {
        counting_sort(k);
        counting_sort(0);
        int r=0;
        tempRA[SA[0]]=r=0;
        for(int i=1; i<n; i++)
        {
            if(RA[SA[i]]==RA[SA[i-1]] && RA[SA[i]+k]==RA[SA[i-1]+k])
                tempRA[SA[i]]=r;
            else
                tempRA[SA[i]]=++r;
        }
        for(int i=0; i<n; i++)
        {
            RA[i]=tempRA[i];
        }
        if(RA[SA[n-1]]==n-1) break;
    }
}

void build_LCP()
{
    Phi[SA[0]]=-1;
    for(int i=1; i<n; i++)
        Phi[SA[i]]=SA[i-1];
    for(int i=0,L=0; i<n; i++)
    {
//        D(i);
        if(Phi[i]==-1)
        {
            PLCP[i]=0;
            continue;
        }
        while(str[i+L]==str[Phi[i]+L]) L++;
        PLCP[i]=L;
        L=max(L-1,0);
    }

    for(int i=0; i<n; i++)
        LCP[i]=PLCP[SA[i]];
}



int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        scanf("%s",str);
        strcat(str,"$");
        n=strlen(str);
        build_Suffix_Array();
        build_LCP();

//        for(int i=0; i<n; i++)
//            cout<<SA[i]<<" ";
//        cout<<endl;
//        for(int i=0; i<n; i++)
//            cout<<LCP[i]<<" ";
//        cout<<endl;

        int ans=0;

        int string_len=n-1;

        for(int i=1; i<n; i++)
        {
            ans+=(string_len-SA[i]-LCP[i]);
        }

        pf("%d\n",ans);

    }

    return 0;
}