feat: add longest palindromic subsequence algorithm (#1185)

* feat: add longest palindromic subsequence algorithm

* feat: add longest palindromic subsequence algorithm

* feat: add longest palindromic subsequence algorithm

* feat: add longest palindromic subsequence algorithm

dynamic_programming/longest_palindromic_subsequence.cpp

@@ -0,0 +1,90 @@
+/**
+ * @file
+ * @brief Program to find the Longest Palindormic
+ * Subsequence of a string
+ *
+ * @details
+ * [Palindrome](https://en.wikipedia.org/wiki/Palindrome) string sequence of
+ * characters which reads the same backward as forward
+ * [Subsequence](https://en.wikipedia.org/wiki/Subsequence)  is a sequence that
+ * can be derived from another sequence by deleting some or no elements without
+ * changing the order of the remaining elements.
+
+ * @author [Anjali Jha](https://github.com/anjali1903)
+ */
+
+#include <algorithm>
+#include <cassert>
+#include <iostream>
+#include <vector>
+
+/**
+ * Function that returns the longest palindromic
+ * subsequence of a string
+ */
+std::string lps(std::string a) {
+    std::string b = a;
+    reverse(b.begin(), b.end());
+    int m = a.length();
+    std::vector<std::vector<int> > res(m + 1);
+
+    // Finding the length of the longest
+    // palindromic subsequence and storing
+    // in a 2D array in bottoms-up manner
+    for (int i = 0; i <= m; i++) {
+        for (int j = 0; j <= m; j++) {
+            if (i == 0 || j == 0) {
+                res[i][j] = 0;
+            } else if (a[i - 1] == b[j - 1]) {
+                res[i][j] = res[i - 1][j - 1] + 1;
+            } else {
+                res[i][j] = std::max(res[i - 1][j], res[i][j - 1]);
+            }
+        }
+    }
+    // Length of longest palindromic subsequence
+    int idx = res[m][m];
+    // Creating string of index+1 length
+    std::string ans(idx + 1, '\0');
+    int i = m, j = m;
+
+    // starting from right-most bottom-most corner
+    // and storing them one by one in ans
+    while (i > 0 && j > 0) {
+        // if current characters in a and b are same
+        // then it is a part of the ans
+        if (a[i - 1] == b[j - 1]) {
+            ans[idx - 1] = a[i - 1];
+            i--;
+            j--;
+            idx--;
+        }
+        // If they are not same, find the larger of the
+        // two and move in that direction
+        else if (res[i - 1][j] > res[i][j - 1]) {
+            i--;
+        } else {
+            j--;
+        }
+    }
+
+    return ans;
+}
+
+/** Test function */
+void test() {
+    // lps("radar") return "radar"
+    assert(lps("radar") == "radar");
+    // lps("abbcbaa") return "abcba"
+    assert(lps("abbcbaa") == "abcba");
+    // lps("bbbab") return "bbbb"
+    assert(lps("bbbab") == "bbbb");
+}
+
+/**
+ * Main Function
+ */
+int main() {
+    test();  // execute the tests
+    return 0;
+}