feat: added z_algorithm in strings (#1581)

* feat: added z_algorithm in strings

* Updated z_function.cpp 

Updated z_function.cpp as per contribution guidelines.
Fixed Link using github markdown syntax
Created a separate function for tests and covered the corner case

* Apply suggestions from code review

More comments added to the code

Co-authored-by: David Leal <halfpacho@gmail.com>

* Apply suggestions from code review

Some more documentation added as per contribution guidelines.

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update strings/z_function.cpp

comments added

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update strings/z_function.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for 0c7515e9

* Updated int -> uint64_t 

Updated int -> uint64_t for non-negative values

* clang-format and clang-tidy fixes for 12d51239

* Update strings/z_function.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update strings/z_function.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* More comments added

* clang-format and clang-tidy fixes for 8a627ac9

* Update strings/z_function.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update strings/z_function.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -334,3 +334,4 @@
   * [Knuth Morris Pratt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/knuth_morris_pratt.cpp)
   * [Manacher Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp)
   * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp)
+  * [Z Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/z_function.cpp)

strings/z_function.cpp

@@ -0,0 +1,96 @@
+/**
+ * @file
+ * @brief The [Z function](https://cp-algorithms.com/string/z-function.html) for
+ * finding occurences of a pattern within a piece of text with time and space
+ * complexity O(n + m)
+ * @details
+ * 1. The Z-function for a string is an array of length n where the
+ * i-th element is equal to the greatest number of characters starting
+ * from the position i that coincide with the first characters of s.
+ * 2. E.g.: string: ababb then z[2]=2 as s[2]=s[0] and s[3]=s[1] and s[4]!=s[2]
+ * @author [Ritika Gupta](https://github.com/RitikaGupta8734)
+ */
+
+#include <iostream>  /// for IO operations
+#ifdef _MSC_VER
+#include <string>  /// for string (use this for MS Visual C++)
+#else
+#include <cstring>  /// for string
+#endif
+#include <cassert>  /// for assert
+#include <vector>   /// for std::vector
+
+/**
+ * @brief Generate the Z-function for the inputted string.
+ * \param[in] pattern text on which to apply the Z-function
+ * \returns the Z-function output as a vector array
+ */
+std::vector<uint64_t> Z_function(const std::string &pattern) {
+    uint64_t pattern_length = pattern.size();
+    std::vector<uint64_t> z(pattern_length, 0);
+
+    for (uint64_t i = 1, l = 0, r = 0; i < pattern_length; i++) {
+        if (i <= r) {
+            z[i] = std::min(r - i + 1, z[i - l]);
+        }
+        while (i + z[i] < pattern_length &&
+               pattern[z[i]] == pattern[i + z[i]]) {
+            z[i]++;
+        }
+        if (i + z[i] - 1 > r) {
+            r = i + z[i] - 1;
+        }
+    }
+    return z;
+}
+
+/**
+ * @brief Using Z_function to find a pattern in a text
+ * \param[in] pattern string pattern to search
+ * \param[in] text text in which to search
+ * \returns a vector of starting indexes where pattern is found in the text
+ */
+std::vector<uint64_t> find_pat_in_text(const std::string &pattern,
+                                       const std::string &text) {
+    uint64_t text_length = text.size(), pattern_length = pattern.size();
+    std::vector<uint64_t> z = Z_function(pattern + '#' + text);
+    std::vector<uint64_t> matching_indexes;
+
+    for (uint64_t i = 0; i < text_length; i++) {
+        if (z[i + pattern_length + 1] == pattern_length) {
+            matching_indexes.push_back(i);
+        }
+    }
+    return matching_indexes;
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // usual case
+    std::string text1 = "alskfjaldsabc1abc1abcbksbcdnsdabcabc";
+    std::string pattern1 = "abc";
+
+    // matching_indexes1 gets the indexes where pattern1 exists in text1
+    std::vector<uint64_t> matching_indexes1 = find_pat_in_text(pattern1, text1);
+    assert((matching_indexes1 == std::vector<uint64_t>{10, 14, 18, 30, 33}));
+
+    // corner case
+    std::string text2 = "greengrass";
+    std::string pattern2 = "abc";
+
+    // matching_indexes2 gets the indexes where pattern2 exists in text2
+    std::vector<uint64_t> matching_indexes2 = find_pat_in_text(pattern2, text2);
+    assert((matching_indexes2 == std::vector<uint64_t>{}));
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}