import java.util.*;
import java.io.*;
  
class GFG { 

    static void fillLPS(String str, int lps[])
    {
        int n=str.length(),len=0;
        lps[0]=0;
        int i=1;
        while(i<n){
            if(str.charAt(i)==str.charAt(len))
            {len++;lps[i]=len;i++;}
            else
            {if(len==0){lps[i]=0;i++;}
                else{len=lps[len-1];}
            }
        }
    }

    static void KMP(String pat,String txt)
    {
        int N=txt.length();
        int M=pat.length();
        int[] lps=new int[M];
        fillLPS(pat,lps);
        int i=0,j=0;
        while(i<N){
            if(pat.charAt(j)==txt.charAt(i)){i++;j++;}
    
            if (j == M) { 
                System.out.println("Found pattern at index " + (i - j));
                j = lps[j - 1]; 
            } 
            else if (i < N && pat.charAt(j) != txt.charAt(i)) { 
                if (j == 0) 
                    i++;
                else
                    j = lps[j - 1];  
            }
        }
    }

    public static void main(String args[]) 
    {   String txt = "ababcababaad",pat="ababa";
        KMP(pat,txt);
    }  
     
} 

// Efficient Code O(n)

import java.util.*;
import java.io.*;
  
class GFG { 
  
    static void fillLPS(String str, int lps[])
    {
        int n=str.length(),len=0;
        lps[0]=0;
        int i=1;
        while(i<n){
            if(str.charAt(i)==str.charAt(len))
            {len++;lps[i]=len;i++;}
            else
            {if(len==0){lps[i]=0;i++;}
                else{len=lps[len-1];}
            }
        }
    }
  
    public static void main(String args[]) 
    {   String txt = "abacabad";int[] lps=new int[txt.length()];
        fillLPS(txt,lps);
        for(int i=0;i<txt.length();i++){
            System.out.print(lps[i]+" ");
        } 
    } 
} 




// Naive Code O(n^3)

import java.util.*;
import java.io.*;
  
class GFG { 

    static int longPropPreSuff(String str, int n)
    {
        for(int len=n-1;len>0;len--){
            boolean flag=true;
            for(int i=0;i<len;i++)
                if(str.charAt(i)!=str.charAt(n-len+i))
                    flag=false;
                    
            if(flag==true)
                return len;
        }
        return 0;
    }

    static void fillLPS(String str, int lps[]){
        for(int i=0;i<str.length();i++){
        lps[i]=longPropPreSuff(str,i+1);
        }
    }
  
    public static void main(String args[]) 
    {   String txt = "abacabad";int[] lps=new int[txt.length()];
        fillLPS(txt,lps);
        for(int i=0;i<txt.length();i++){
            System.out.print(lps[i]+" ");
    }  
    } 
} 

import java.util.*;
import java.io.*;
  
class GFG { 
    static final int d=256;
    static final int q=101;   
    static void RBSearch(String pat,String txt,int M, int N)
    {
        //Compute (d^(M-1))%q
        int h=1;
        for(int i=1;i<=M-1;i++)
            h=(h*d)%q;
        
        //Compute p and to
        int p=0,t=0;
        for(int i=0;i<M;i++){
            p=(p*d+pat.charAt(i))%q;
            t=(t*d+txt.charAt(i))%q;
        }
        
        for(int i=0;i<=(N-M);i++){
           //Check for hit
           if(p==t){
               boolean flag=true;
               for(int j=0;j<M;j++)
                    if(txt.charAt(i+j)!=pat.charAt(j)){flag=false;break;}
                if(flag==true)System.out.print(i+" ");
           }
           //Compute ti+1 using ti
           if(i<N-M){
               t=((d*(t-txt.charAt(i)*h))+txt.charAt(i+M))%q;
            if(t<0)t=t+q;
           }
        }
        
    }
  
    public static void main(String args[]) 
    {   String txt = "GEEKS FOR GEEKS";String pat="GEEK";
        System.out.print("All index numbers where pattern found: ");
        RBSearch(pat,txt,4,15);  
    } 
} 

import java.util.*;
import java.io.*;
  
class GFG { 
       
    static void patSearchinng(String txt,String pat)
    {
        int m=pat.length();
        int n=txt.length();
        for(int i=0;i<=(n-m); )
        {
            int j;
            for(j=0;j<m;j++)
                if(pat.charAt(j)!=txt.charAt(i+j))
                    break;
            
            if(j==m)
                System.out.print(i+" ");
            if(j==0)
                i++;
            else
                i=(i+j);
        }
    }
  
    public static void main(String args[]) 
    {   String txt = "ABCABCD";String pat="ABCD";
        System.out.print("All index numbers where pattern found: ");
        patSearchinng(txt,pat);  
    } 
} 

import java.util.*;
import java.io.*;
  
class GFG { 
       
    static void patSearchinng(String txt,String pat)
    {
        int m=pat.length();
        int n=txt.length();
        for(int i=0;i<=(n-m);i++){
      	    int j;
            for(j=0;j<m;j++)
                if(pat.charAt(j)!=txt.charAt(i+j))
              	    break;
            
        if(j==m)
            System.out.print(i+" ");
        }
    }
  
    public static void main(String args[]) 
    {   String txt = "ABCABCD";String pat="ABCD";
        System.out.print("All index numbers where pattern found: ");
        patSearchinng(txt,pat);  
    } 
} 

m -> Pattern length
n -> Text length
1 <= m <=n
---------------------------------------------------------------------------------------------------

// NO PREPROCESSING

Naive : O((n-m+1)*m)

Naive (When all characters of Pattern are distinct) : O(n)
---------------------------------------------------------------------------------------------------

// PREPROCESS PATTERN
  
Rabin Karp : O((n-m+1)*m)  // But, better then naive on average

KMP Algorithm : O(n)
---------------------------------------------------------------------------------------------------

// PREPROCESS TEXT
  
Suffix Tree : O(m)