Added LongestPalindromeSubsequence using bottom up approach

src/main/cpp/algorithms/dp/LongestPalindromeSubsequenceTabular.h

@@ -0,0 +1,71 @@
+/*
+ * @file   LongestPalindromeSubsequence.h
+ * @author (original JAVA) William Fiset, [email protected]
+ *         (conversion to C++) Armin Zare Zadeh, [email protected]
+ * @date   14 July 2020
+ * @version 0.1
+ * @brief   Implementation of finding the longest paldindrome subsequence Time complexity: O(n^2)
+ */
+
+#ifndef D_LONGESTPALINDROMSUBSEQUENCETABULAR_H
+#define D_LONGESTPALINDROMSUBSEQUENCETABULAR_H
+
+#include <vector>
+#include <deque>
+#include <list>
+#include <set>   // set and multiset
+#include <map>   // map and multimap
+#include <unordered_set>  // unordered set/multiset
+#include <unordered_map>  // unordered map/multimap
+#include <iterator>
+#include <algorithm>
+#include <numeric>    // some numeric algorithm
+#include <functional>
+#include <stack>
+
+#include <sstream>
+#include <memory>
+#include <iostream>
+#include <cmath>
+
+namespace dsa {
+
+
+class LongestPalindromeSubsequenceTabular {
+public:
+  // Returns the length of the longest palindrome subsequence
+  // Using Bottom up Approach
+  static int lps(const std::string& s) {
+    if (s.length() == 0) return 0;
+    std::vector<std::vector<int>> dp(s.length(), std::vector<int>(s.length(), 0));
+
+    for(int l = 1; l <= s.length(); l++) {
+      for(int i = 0; i <= s.length() - l; i++) {
+        int j = i + l - 1;
+        char c1 = s.at(i), c2 = s.at(j);
+
+        //extra case for equal indices
+        if(i == j) dp[i][j] = 1;
+        //Handle out of bounds using ternary operator
+        // Both end characters match 
+        else if(c1 == c2) dp[i][j] = 2 + ((i + 1 < s.length() && j > 0) ? dp[i + 1][j - 1] : 0);
+        // Consider both possible substrings and take the maximum
+        else dp[i][j] = max((i + 1 < s.length()) ? dp[i + 1][j] : 0, (j > 0) ? dp[i][j - 1] : 0);
+      }
+    }
+
+    return dp[0][s.length() - 1];
+  }
+};
+
+
+void LongestPalindromeSubsequenceTabular_test()
+{
+  std::cout << LongestPalindromeSubsequenceTabular::lps("bbbab") << std::endl; // Outputs 4 since "bbbb" is valid soln
+  std::cout << LongestPalindromeSubsequenceTabular::lps("bccd") << std::endl; // Outputs 2 since "cc" is valid soln
+}
+
+
+} // namespace dsa
+
+#endif /* D_LONGESTPALINDROMSUBSEQUENCETABULAR_H */