design aalgorithm to make the assignment of reviewers to papers

Given a text txt[0..n-1] and a pattern pat[0..m-1], write a function search(char pat[], char txt[]) that prints all occurrences of pat[] in txt[]. You may assume that n > m.

Examples:

Try Amazon Test Series that Includes topic-wise practice questions on all important DSA topics along with 10 practice contests of 2 hours each. Designed with years of experience.

Input:  txt[] = "THIS IS A TEST TEXT"         pat[] = "TEST" Output: Pattern found at index 10  Input:  txt[] =  "AABAACAADAABAABA"         pat[] =  "AABA" Output: Pattern found at index 0         Pattern found at index 9         Pattern found at index 12                  

Recommended: Please solve it on " PRACTICE " first, before moving on to the solution.

Pattern searching is an important problem in computer science. When we do search for a string in notepad/word file or browser or database, pattern searching algorithms are used to show the search results.

We have discussed Naive pattern searching algorithm in the previous post. The worst case complexity of the Naive algorithm is O(m(n-m+1)). The time complexity of KMP algorithm is O(n) in the worst case.

KMP (Knuth Morris Pratt) Pattern Searching
The Naive pattern searching algorithm doesn't work well in cases where we see many matching characters followed by a mismatching character. Following are some examples.

          txt[] = "AAAAAAAAAAAAAAAAAB"    pat[] = "AAAAB"     txt[] = "ABABABCABABABCABABABC"    pat[] =  "ABABAC" (not a worst case, but a bad case for Naive)        

The KMP matching algorithm uses degenerating property (pattern having same sub-patterns appearing more than once in the pattern) of the pattern and improves the worst case complexity to O(n). The basic idea behind KMP's algorithm is: whenever we detect a mismatch (after some matches), we already know some of the characters in the text of the next window. We take advantage of this information to avoid matching the characters that we know will anyway match. Let us consider below example to understand this.

          Matching Overview          txt = "AAAAABAAABA"  pat = "AAAA"  We compare first window of          txt          with          pat          txt = "AAAAABAAABA"  pat = "AAAA"  [Initial position] We find a match. This is same as Naive String Matching.  In the next step, we compare next window of          txt          with          pat. txt = "AAAAA          BAAABA"  pat =  "AAAA          " [Pattern shifted one position] This is where KMP does optimization over Naive. In this  second window, we only compare fourth          A          of pattern with fourth character of current window of text to decide  whether current window matches or not. Since we know  first three characters will anyway match, we skipped  matching first three characters.          Need of Preprocessing?          An important question arises from the above explanation,  how to know how many characters to be skipped. To know this,  we pre-process pattern and prepare an integer array  lps[] that tells us the count of characters to be skipped.        

Preprocessing Overview:

• KMP algorithm preprocesses pat[] and constructs an auxiliary lps[] of size m (same as size of pattern) which is used to skip characters while matching.
• name lps indicates longest proper prefix which is also suffix.. A proper prefix is prefix with whole string not allowed. For example, prefixes of "ABC" are "", "A", "AB" and "ABC". Proper prefixes are "", "A" and "AB". Suffixes of the string are "", "C", "BC" and "ABC".
• We search for lps in sub-patterns. More clearly we focus on sub-strings of patterns that are either prefix and suffix.
• For each sub-pattern pat[0..i] where i = 0 to m-1, lps[i] stores length of the maximum matching proper prefix which is also a suffix of the sub-pattern pat[0..i].

                lps[i] = the longest proper prefix of pat[0..i]                which is also a suffix of pat[0..i].            

  Note : lps[i] could also be defined as longest prefix which is also proper suffix. We need to use properly at one place to make sure that the whole substring is not considered.

  Examples of lps[] construction: For the pattern "AAAA",  lps[] is [0, 1, 2, 3]  For the pattern "ABCDE",  lps[] is [0, 0, 0, 0, 0]  For the pattern "AABAACAABAA",  lps[] is [0, 1, 0, 1, 2, 0, 1, 2, 3, 4, 5]  For the pattern "AAACAAAAAC",  lps[] is [0, 1, 2, 0, 1, 2, 3, 3, 3, 4]   For the pattern "AAABAAA",  lps[] is [0, 1, 2, 0, 1, 2, 3]            

  Searching Algorithm:
  Unlike Naive algorithm, where we slide the pattern by one and compare all characters at each shift, we use a value from lps[] to decide the next characters to be matched. The idea is to not match a character that we know will anyway match.

  How to use lps[] to decide next positions (or to know a number of characters to be skipped)?

  • We start comparison of pat[j] with j = 0 with characters of current window of text.
  • We keep matching characters txt[i] and pat[j] and keep incrementing i and j while pat[j] and txt[i] keep matching.
  • When we see a mismatch
    • We know that characters pat[0..j-1] match with txt[i-j…i-1] (Note that j starts with 0 and increment it only when there is a match).
    • We also know (from above definition) that lps[j-1] is count of characters of pat[0…j-1] that are both proper prefix and suffix.
    • From above two points, we can conclude that we do not need to match these lps[j-1] characters with txt[i-j…i-1] because we know that these characters will anyway match. Let us consider above example to understand this.

  txt[] = "AAAAABAAABA"  pat[] = "AAAA" lps[] = {0, 1, 2, 3}   i = 0, j = 0 txt[] = "                AAAAABAAABA"  pat[] = "                AAAA" txt[i] and pat[j] match, do i++, j++  i = 1, j = 1 txt[] = "AAAAABAAABA"  pat[] = "AAAA" txt[i] and pat[j] match, do i++, j++  i = 2, j = 2 txt[] = "AAAAABAAABA"  pat[] = "AAAA" pat[i] and pat[j] match, do i++, j++  i = 3, j = 3 txt[] = "AAAA              ABAAABA"  pat[] = "AAAA              " txt[i] and pat[j] match, do i++, j++  i = 4, j = 4 Since j == M, print              pattern found              and reset j, j = lps[j-1] = lps[3] = 3  Here unlike Naive algorithm, we do not match first three  characters of this window. Value of lps[j-1] (in above  step) gave us index of next character to match. i = 4, j = 3 txt[] = "AAAAA              BAAABA"  pat[] =  "AAAA              " txt[i] and pat[j] match, do i++, j++  i = 5, j = 4 Since j == M, print              pattern found              and reset j, j = lps[j-1] = lps[3] = 3  Again unlike Naive algorithm, we do not match first three  characters of this window. Value of lps[j-1] (in above  step) gave us index of next character to match. i = 5, j = 3 txt[] = "AAAAAB              AAABA"  pat[] =   "AAAA              " txt[i] and pat[j] do NOT match and j > 0, change only j j = lps[j-1] = lps[2] = 2  i = 5, j = 2 txt[] = "AAAAABAAABA"  pat[] =    "AAAA" txt[i] and pat[j] do NOT match and j > 0, change only j j = lps[j-1] = lps[1] = 1   i = 5, j = 1 txt[] = "AAAAABAAABA"  pat[] =     "AAAA" txt[i] and pat[j] do NOT match and j > 0, change only j j = lps[j-1] = lps[0] = 0  i = 5, j = 0 txt[] = "AAAAA                BAAABA"  pat[] =      "                AAAA" txt[i] and pat[j] do NOT match and j is 0, we do i++.  i = 6, j = 0 txt[] = "AAAAAB                AAABA"  pat[] =       "                AAAA" txt[i] and pat[j] match, do i++ and j++  i = 7, j = 1 txt[] = "AAAAABAAABA"  pat[] =       "AAAA" txt[i] and pat[j] match, do i++ and j++  We continue this way...            

  
  
  

  C++

  #include <bits/stdc++.h>

  void computeLPSArray( char * pat, int M, int * lps);

  void KMPSearch( char * pat, char * txt)

  {

  int M = strlen (pat);

  int N = strlen (txt);

  int lps[M];

  computeLPSArray(pat, M, lps);

  int i = 0;

  int j = 0;

  while (i < N) {

  if (pat[j] == txt[i]) {

  j++;

  i++;

  }

  if (j == M) {

  printf ( "Found pattern at index %d " , i - j);

  j = lps[j - 1];

  }

  else if (i < N && pat[j] != txt[i]) {

  if (j != 0)

  j = lps[j - 1];

  else

  i = i + 1;

  }

  }

  }

  void computeLPSArray( char * pat, int M, int * lps)

  {

  int len = 0;

  lps[0] = 0;

  int i = 1;

  while (i < M) {

  if (pat[i] == pat[len]) {

  len++;

  lps[i] = len;

  i++;

  }

  else

  {

  if (len != 0) {

  len = lps[len - 1];

  }

  else

  {

  lps[i] = 0;

  i++;

  }

  }

  }

  }

  int main()

  {

  char txt[] = "ABABDABACDABABCABAB" ;

  char pat[] = "ABABCABAB" ;

  KMPSearch(pat, txt);

  return 0;

  }

  Java

  class KMP_String_Matching {

  void KMPSearch(String pat, String txt)

  {

  int M = pat.length();

  int N = txt.length();

  int lps[] = new int [M];

  int j = 0 ;

  computeLPSArray(pat, M, lps);

  int i = 0 ;

  while (i < N) {

  if (pat.charAt(j) == txt.charAt(i)) {

  j++;

  i++;

  }

  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 )

  j = lps[j - 1 ];

  else

  i = i + 1 ;

  }

  }

  }

  void computeLPSArray(String pat, int M, int lps[])

  {

  int len = 0 ;

  int i = 1 ;

  lps[ 0 ] = 0 ;

  while (i < M) {

  if (pat.charAt(i) == pat.charAt(len)) {

  len++;

  lps[i] = len;

  i++;

  }

  else

  {

  if (len != 0 ) {

  len = lps[len - 1 ];

  }

  else

  {

  lps[i] = len;

  i++;

  }

  }

  }

  }

  public static void main(String args[])

  {

  String txt = "ABABDABACDABABCABAB" ;

  String pat = "ABABCABAB" ;

  new KMP_String_Matching().KMPSearch(pat, txt);

  }

  }

  Python

  def KMPSearch(pat, txt):

  M = len (pat)

  N = len (txt)

  lps = [ 0 ] * M

  j = 0

  computeLPSArray(pat, M, lps)

  i = 0

  while i < N:

  if pat[j] = = txt[i]:

  i + = 1

  j + = 1

  if j = = M:

  print ( "Found pattern at index " + str (i - j))

  j = lps[j - 1 ]

  elif i < N and pat[j] ! = txt[i]:

  if j ! = 0 :

  j = lps[j - 1 ]

  else :

  i + = 1

  def computeLPSArray(pat, M, lps):

  len = 0

  lps[ 0 ]

  i = 1

  while i < M:

  if pat[i] = = pat[ len ]:

  len + = 1

  lps[i] = len

  i + = 1

  else :

  if len ! = 0 :

  len = lps[ len - 1 ]

  else :

  lps[i] = 0

  i + = 1

  txt = "ABABDABACDABABCABAB"

  pat = "ABABCABAB"

  KMPSearch(pat, txt)

  C#

  using System;

  class GFG {

  void KMPSearch( string pat, string txt)

  {

  int M = pat.Length;

  int N = txt.Length;

  int [] lps = new int [M];

  int j = 0;

  computeLPSArray(pat, M, lps);

  int i = 0;

  while (i < N) {

  if (pat[j] == txt[i]) {

  j++;

  i++;

  }

  if (j == M) {

  Console.Write( "Found pattern "

  + "at index " + (i - j));

  j = lps[j - 1];

  }

  else if (i < N && pat[j] != txt[i]) {

  if (j != 0)

  j = lps[j - 1];

  else

  i = i + 1;

  }

  }

  }

  void computeLPSArray( string pat, int M, int [] lps)

  {

  int len = 0;

  int i = 1;

  lps[0] = 0;

  while (i < M) {

  if (pat[i] == pat[len]) {

  len++;

  lps[i] = len;

  i++;

  }

  else

  {

  if (len != 0) {

  len = lps[len - 1];

  }

  else

  {

  lps[i] = len;

  i++;

  }

  }

  }

  }

  public static void Main()

  {

  string txt = "ABABDABACDABABCABAB" ;

  string pat = "ABABCABAB" ;

  new GFG().KMPSearch(pat, txt);

  }

  }

  PHP

  <?php

  function KMPSearch( $pat , $txt )

  {

  $M = strlen ( $pat );

  $N = strlen ( $txt );

  $lps = array_fill (0, $M ,0);

  computeLPSArray( $pat , $M , $lps );

  $i = 0;

  $j = 0;

  while ( $i < $N ) {

  if ( $pat [ $j ] == $txt [ $i ]) {

  $j ++;

  $i ++;

  }

  if ( $j == $M ) {

  printf( "Found pattern at index " .( $i - $j ));

  $j = $lps [ $j - 1];

  }

  else if ( $i < $N && $pat [ $j ] != $txt [ $i ]) {

  if ( $j != 0)

  $j = $lps [ $j - 1];

  else

  $i = $i + 1;

  }

  }

  }

  function computeLPSArray( $pat , $M , & $lps )

  {

  $len = 0;

  $lps [0] = 0;

  $i = 1;

  while ( $i < $M ) {

  if ( $pat [ $i ] == $pat [ $len ]) {

  $len ++;

  $lps [ $i ] = $len ;

  $i ++;

  }

  else

  {

  if ( $len != 0) {

  $len = $lps [ $len - 1];

  }

  else

  {

  $lps [ $i ] = 0;

  $i ++;

  }

  }

  }

  }

  $txt = "ABABDABACDABABCABAB" ;

  $pat = "ABABCABAB" ;

  KMPSearch( $pat , $txt );

  ?>

  
  Output:

  Found pattern at index 10

  Preprocessing Algorithm:
  In the preprocessing part, we calculate values in lps[]. To do that, we keep track of the length of the longest prefix suffix value (we use len variable for this purpose) for the previous index. We initialize lps[0] and len as 0. If pat[len] and pat[i] match, we increment len by 1 and assign the incremented value to lps[i]. If pat[i] and pat[len] do not match and len is not 0, we update len to lps[len-1]. See computeLPSArray () in the below code for details.

  Illustration of preprocessing (or construction of lps[])

  pat[] = "AAACAAAA"  len = 0, i  = 0.              lps[0] is always 0, we move  to i = 1  len = 0, i  = 1. Since pat[len] and pat[i] match, do len++,  store it in lps[i] and do i++. len = 1,              lps[1] = 1, i = 2  len = 1, i  = 2. Since pat[len] and pat[i] match, do len++,  store it in lps[i] and do i++. len = 2,              lps[2] = 2, i = 3  len = 2, i  = 3. Since pat[len] and pat[i] do not match, and len > 0,  set len = lps[len-1] = lps[1] = 1  len = 1, i  = 3. Since pat[len] and pat[i] do not match and len > 0,  len = lps[len-1] = lps[0] = 0  len = 0, i  = 3. Since pat[len] and pat[i] do not match and len = 0,  Set              lps[3] = 0              and i = 4. We know that characters pat len = 0, i  = 4. Since pat[len] and pat[i] match, do len++,  store it in lps[i] and do i++. len = 1,              lps[4] = 1, i = 5  len = 1, i  = 5. Since pat[len] and pat[i] match, do len++,  store it in lps[i] and do i++. len = 2,              lps[5] = 2, i = 6  len = 2, i  = 6. Since pat[len] and pat[i] match, do len++,  store it in lps[i] and do i++. len = 3,              lps[6] = 3, i = 7  len = 3, i  = 7. Since pat[len] and pat[i] do not match and len > 0, set len = lps[len-1] = lps[2] = 2  len = 2, i  = 7. Since pat[len] and pat[i] match, do len++,  store it in lps[i] and do i++. len = 3,              lps[7] = 3, i = 8  We stop here as we have constructed the whole lps[].            

  Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

  
  

design aalgorithm to make the assignment of reviewers to papers

Source: https://www.geeksforgeeks.org/kmp-algorithm-for-pattern-searching/

Share :