Catalan Number

dynamic_programming/catalanumber.cpp

@@ -0,0 +1,40 @@
+#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; 
+
+    // Since C(n, k) = C(n, n-k) 
+    if (k > n - k) 
+        k = n - k; 
+
+    // Calculate value of [n*(n-1)*---*(n-k+1)] / [k*(k-1)*---*1] 
+    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) 
+{ 
+    // Calculate value of 2nCn 
+    unsigned long int c = binomialCoeff(2*n, n); 
+
+    // return 2nCn/(n+1) 
+    return c/(n+1); 
+} 
+
+// Driver program to test above functions 
+int main() 
+{ 
+    for (int i = 0; i < 10; i++) 
+        cout << catalan(i) << " "; 
+    return 0; 
+}