The Z algorithm is a powerful string-matching algorithm that is used to efficiently search for a pattern within a larger text string. This algorithm works by precomputing a table of values that represent the longest common prefix between the pattern and each possible suffix of the text string. This table is known as the Z-table, and it allows the algorithm to quickly determine whether or not the pattern appears in the text.

The Z algorithm has several important advantages over other string-matching algorithms, including its simplicity, efficiency, and ability to handle a wide variety of patterns and texts. Unlike some other algorithms that require complex data structures or multiple passes through the input data, the Z algorithm can be implemented in just a few lines of code and typically requires only a single pass through the input.

To illustrate how the Z algorithm works, let's consider an example. Suppose we are searching for the pattern "abab" in the text "abacababab". We can use the Z algorithm to construct the Z-table as follows:

Each row in the Z-table represents the longest common prefix between the pattern and the suffix of the text starting at that position. For example, the value of 2 in row 4 indicates that the longest common prefix between "abab" and "ababab" is "abab".

To use the Z table to search for the pattern in a string, we can append the pattern to the beginning of the search string. Now we just have to calculate the Z table for this resultant string. We can find a match at all the places where the Z value is greater than the pattern length.

The Z algorithm is particularly useful when searching for multiple patterns in the same text since it allows us to construct a single Z-table that can be used to search for all of the patterns simultaneously. This can be much more efficient than constructing a separate table for each pattern.

Overall, the Z algorithm is a powerful and versatile tool for string matching that can be used in a wide range of applications, including text search, data compression, and bioinformatics. Its simplicity and efficiency make it a popular choice for many programming tasks, and it is well worth taking the time to understand how it works and how to implement it in your code.

Time Complexity: O(n) ( for creating the Z array )

Space Complexity: O(n) ( for Storing the Z array )