added catalan number in cpp in dynamic programming

code/dynamic_programming/src/catalan/catalan_number.cpp

@@ -0,0 +1,61 @@
+#include <iostream>
+#include <vector>
+#include <stdexcept>
+
+namespace dynamic
+{
+
+/*
+ * Error to indicate invalid input
+ */
+const std::invalid_argument errCatalan("can't have a negative n-th catalan number");
+
+/*
+ * NthCatalanNumber returns the n-th Catalan Number
+ * Complexity: O(n^2)
+ */
+long long
+nthCatalanNumber(int n)
+{
+    if (n < 0)
+    {
+        // doesn't accept negative number
+        throw errCatalan;
+    }
+
+    std::vector<long long> catalanNumberList;
+    catalanNumberList.push_back(1); // first value is 1
+
+    for (int i = 1; i <= n; i++)
+    {
+        catalanNumberList.push_back(0); // append 0 and calculate
+
+        for (int j = 0; j < i; j++)
+        {
+            catalanNumberList[i] += catalanNumberList[j] *
+                                     catalanNumberList[i - j - 1];
+        }
+    }
+
+    return catalanNumberList[n];
+}
+
+} // namespace dynamic
+
+int
+main()
+{
+    try
+    {
+        int n = 5;
+        std::cout << "5th Catalan number is: "
+                  << dynamic::nthCatalanNumber(n)
+                  << std::endl;
+    }
+    catch (const std::invalid_argument &e)
+    {
+        std::cerr << "Error: " << e.what() << std::endl;
+    }
+
+    return 0;
+}