feat: add palindrome partitioning algorithm (#1319)

* feat: add palindrome partitioning algorithm

* Update palindrome_partitioning.cpp

* updating DIRECTORY.md

* Update palindrome_partitioning.cpp

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

DIRECTORY.md

@@ -67,6 +67,7 @@
   * [Longest Increasing Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence.cpp)
   * [Longest Increasing Subsequence (Nlogn)](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp)
   * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/matrix_chain_multiplication.cpp)
+  * [Palindrome Partitioning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/palindrome_partitioning.cpp)
   * [Searching Of Element In Dynamic Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/searching_of_element_in_dynamic_array.cpp)
   * [Shortest Common Supersequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/shortest_common_supersequence.cpp)
   * [Tree Height](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/tree_height.cpp)

dynamic_programming/palindrome_partitioning.cpp

@@ -0,0 +1,123 @@
+/**
+ * @file
+ * @brief Implements [Palindrome Partitioning](https://leetcode.com/problems/palindrome-partitioning-ii/) algorithm, giving you the minimum number of partitions you need to make
+ *
+ * @details
+ * palindrome partitioning uses dynamic programming and goes to all the possible partitions to find the minimum
+ * you are given a string and you need to give minimum number of partitions needed to divide it into a number of palindromes
+ * [Palindrome Partitioning] (https://www.geeksforgeeks.org/palindrome-partitioning-dp-17/)
+ * overall time complexity O(n^2)
+ * For example: example 1:-
+ * String : "nitik"
+ * Output : 2 => "n | iti | k"
+ * For example: example 2:-
+ * String : "ababbbabbababa"
+ * Output : 3 => "aba | b | bbabb | ababa"
+ * @author [Sujay Kaushik] (https://github.com/sujaykaushik008)
+ */
+
+#include <iostream>   // for io operations
+#include <vector>     // for std::vector
+#include <algorithm>  // for std::min
+#include <cassert>    // for std::assert
+#include <climits>    // for INT_MAX
+
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming {
+
+    /**
+     * @namespace palindrome_partitioning
+     * @brief Functions for [Palindrome Partitioning](https://leetcode.com/problems/palindrome-partitioning-ii/) algorithm
+     */
+    namespace palindrome_partitioning {
+
+        /**
+         * Function implementing palindrome partitioning algorithm using lookup table method.
+         * @param str input string
+         * @returns minimum number of partitions
+         */
+        int pal_part(const std::string &str) {
+
+            int n = str.size();
+
+            // creating lookup table for minimum number of cuts
+            std::vector<std::vector<int> > cuts(n, std::vector<int>(n, 0));
+
+            // creating lookup table for palindrome checking
+            std::vector<std::vector<bool> > is_palindrome(n, std::vector<bool>(n, false));
+
+            // initialization
+            for (int i = 0; i < n; i++) {
+                is_palindrome[i][i] = true;
+                cuts[i][i] = 0;
+            }
+
+            for (int len = 2; len <= n; len++) {
+                for (int start_index = 0; start_index < n - len + 1; start_index++) {
+
+                    int end_index = start_index + len - 1;
+
+                    if (len == 2) {
+                        is_palindrome[start_index][end_index] = (str[start_index] == str[end_index]);
+                    } else {
+                        is_palindrome[start_index][end_index] =
+                                (str[start_index] == str[end_index]) && is_palindrome[start_index + 1][end_index - 1];
+                    }
+
+                    if (is_palindrome[start_index][end_index]) {
+                        cuts[start_index][end_index] = 0;
+                    } else {
+                        cuts[start_index][end_index] = INT_MAX;
+                        for (int partition = start_index; partition <= end_index - 1; partition++) {
+                            cuts[start_index][end_index] = std::min(cuts[start_index][end_index],
+                                                                    cuts[start_index][partition] +
+                                                                    cuts[partition + 1][end_index] + 1);
+                        }
+                    }
+                }
+            }
+
+            return cuts[0][n - 1];
+        }
+    } // namespace palindrome_partitioning
+}  // namespace dynamic_programming
+
+/**
+ * @brief Test Function
+ * @return void
+*/
+static void test() {
+    // custom input vector
+    std::vector<std::string> custom_input{"nitik", "ababbbabbababa", "abdc"};
+
+    // calculated output vector by pal_part Function
+    std::vector<int> calculated_output(3);
+
+    for (int i = 0; i < 3; i++) {
+        calculated_output[i] = dynamic_programming::palindrome_partitioning::pal_part(custom_input[i]);
+    }
+
+    // expected output vector
+    std::vector<int> expected_output{2, 3, 3};
+
+    // Testing implementation via assert function
+    // It will throw error if any of the expected test fails
+    // Else it will give nothing
+    for (int i = 0; i < 3; i++) {
+        assert(expected_output[i] == calculated_output[i]);
+    }
+
+    std::cout << "All tests passed successfully!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // execute the test
+    return 0;
+}