z Algorithm
The Z algorithm, also known as the Z-function algorithm, is a linear time complexity algorithm used for string matching and pattern searching within a given text. This powerful technique is particularly effective in solving problems related to string processing, as it is able to identify all occurrences of a pattern within a text string in a highly efficient manner. The fundamental concept behind the Z algorithm is the construction of a Z-array or Z-table, which stores the length of the longest common prefix between the main string and its substrings, helping to quickly identify matches between the pattern and the text.
In essence, the Z algorithm preprocesses the given pattern and text by concatenating them with a unique separator, which is not a part of the input strings. Following this, it calculates the Z-values for each character in the concatenated string. These Z-values represent the longest common prefix lengths between the main string and its corresponding substrings. By iterating through the Z-array, the algorithm can efficiently identify all positions where the pattern occurs in the text, as the Z-values at these positions will be equal to the length of the pattern. This preprocessing step enables the Z algorithm to perform pattern searching in linear time, making it a highly effective and practical solution for various string matching problems.
#include <iostream>
#include <string>
#include <vector>
/**
* Function to fill in zvalues vector of ztext
*/
std::vector<size_t> fillZvalues(const std::string & ztext) {
size_t n = ztext.length();
std::vector<size_t> zvals(n, 0);
size_t L = 0, R = 0; // s[L..R] represent the prefix string.
for (size_t i = 1; i < n; ++i) {
if ( i > R ) {
L = R = i;
while( R < n && ztext[R-L] == ztext[R] ) {
++R;
}
zvals[i] = R-L;
--R;
} else {
size_t K = i - L;
if( zvals[K] < R-i+1 ) {
zvals[i] = zvals[K];
} else {
L = R = i;
while( R < n && ztext[R-L] == ztext[R] ) {
++R;
}
zvals[i] = R-L;
--R;
}
}
}
return zvals;
}
/**
* This function returns index of text where pattern matches using z algorithm
*/
std::vector<size_t> search( const std::string & text, const std::string & pattern ) {
std::string ztext = pattern + '$' + text;
std::vector<size_t> zvalues = fillZvalues(ztext);
std::vector<size_t> indices;
for ( size_t i = 1; i < zvalues.size(); ++i ) {
if (zvalues[i] == pattern.length()) {
indices.push_back(i - pattern.length() -1 );
}
}
return indices;
}
int main()
{
std::string text, pattern;
std::cout << "String searching using Z algorithm:\n";
std::cout << "Enter text:";
std::getline(std::cin, text);
std::cout << "Pattern :";
std::getline(std::cin, pattern);
std::vector<size_t> indices = search(text, pattern);
for (auto i : indices ) {
std::cout << pattern << " occurs in given text starting at index " << i << std::endl;
}
return 0;
}
