Z-Algorithm

@z

Z-Algorithm is a string searching algorithm that uses a preprocessed array to find all occurrences of a pattern within a main string. It is particularly useful for finding all occurrences of a pattern in a long string, as it allows for efficient searching and multiple match detection.

Pseudo-code
function Z(string T):
  T := Preprocess string T to create a Z array.
  for i from 0 to n-1:
    for j from i+1 to n-1:
      if P[j] matches P[i] and the remaining characters match:
        update the Z array to record the longest match.
  return the Z array.
function Preprocess(string T):
  Z := Initialize an empty Z array of size n.
  for i from 0 to n-1:
    Z[i] := Find the longest substring ending at i that matches a prefix of T.
  return Z.
  • T The main string being searched.
  • P The pattern string that is being searched for.
  • m The length of the main string T.
  • n The length of the pattern string P.
Recipe Steps
1

Imagine you have a long string of letters and a shorter string of letters that you want to find inside the long string. First, write down the long string and the shorter string.

2

Then, create a new table next to the long string and fill it with zeros. This table will help us find where the shorter string appears in the long string.

3

Now, go through the long string and the shorter string one letter at a time. When the letters match, fill in the corresponding cell in the table with a value that indicates how many letters match so far.

4

If the letters don't match, reset the value in the table to zero and start checking again from the beginning of the shorter string.

5

Repeat steps 3 and 4 until you have checked all letters in the long string.

6

Finally, examine the table to find where the shorter string appears in the long string.

Questions & Answers

The Z-Algorithm is used to find all occurrences of a pattern within a main string.

The Z array is used to record the longest match of the pattern string within the main string.

The Z-Algorithm allows for efficient searching and multiple match detection.
- The Z-Algorithm can be slow for very large strings and patterns. Consider using other algorithms like Knuth-Morris-Pratt or Rabin-Karp for larger inputs.
- The Z-Algorithm assumes that the pattern string is a substring of the main string. If this is not the case, you may need to modify the algorithm or use a different approach.

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