From 5650a04893d9a3fc7c4beda6f743cf2c16835614 Mon Sep 17 00:00:00 2001
From: fulcrum999 <114816542+fulcrum999@users.noreply.github.com>
Date: Sat, 1 Oct 2022 19:42:29 +0530
Subject: [PATCH] catalan_number.cpp

C++ program to find the nth Catalan Number
---
 Arrays/catalan_number.cpp | 37 +++++++++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)
 create mode 100644 Arrays/catalan_number.cpp

diff --git a/Arrays/catalan_number.cpp b/Arrays/catalan_number.cpp
new file mode 100644
index 0000000..e3ef670
--- /dev/null
+++ b/Arrays/catalan_number.cpp
@@ -0,0 +1,37 @@
+// 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;
+}