Created catalan_numbers.cpp

C++ program to find the nth Catalan Number

catalan_numbers.cpp

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+// C++ program to find the nth Catalan Number
+#include <iostream>
+using namespace std;
+
+// Returns value of Binomial Coefficient C(n, k)
+unsigned long int binomialCoeff(unsigned int n,
+								unsigned int k)
+{
+	unsigned long int res = 1;
+
+	if (k > n - k)
+		k = n - k;
+
+	for (int i = 0; i < k; ++i) {
+		res *= (n - i);
+		res /= (i + 1);
+	}
+
+	return res;
+}
+
+// A Binomial coefficient based function to find nth catalan
+// number in O(n) time
+unsigned long int catalan(unsigned int n)
+{
+	unsigned long int c = binomialCoeff(2 * n, n);
+
+	return c / (n + 1);
+}
+
+// Driver code
+int main()
+{
+	for (int i = 0; i < 10; i++)
+		cout << catalan(i) << " ";
+	return 0;
+}