Catalan formula and nCr

Number Theory/Catalan_number.cpp

@@ -27,6 +27,6 @@ int catalanNumber( int n ){
 
 int main(int argc, char* argv[] ){
 
-	cout << catalanNumber(3) << '\n';
+	cout << catalanNumber(2) << '\n';
 	return 0;
 }

Number Theory/Catalan_number_formula.cpp

@@ -0,0 +1,69 @@
+typedef long long int ll;
+
+ll mod = 998244353;
+
+vector<ll> factorial;
+void calculateFactorial(ll n){
+	factorial.resize(n+1);
+
+	factorial[0] = factorial[1] = 1;
+
+	for( ll i = 2 ; i <= n ; i++ ){
+		factorial[i] = ( factorial[i-1] * i ) % mod;
+	}
+}
+
+template<typename T>
+T modMul(T a,T b,T M=(ll)1e9+7){
+    return ((a%M)*(b%M))%M;
+}
+
+template<typename T>
+inline T power(T a, T b, T M)
+{
+    T x = 1;
+    while (b)
+    {
+        if (b & 1) x = modMul(x,a,M);
+        a = modMul(a,a,M);
+        b >>= 1;
+    }
+    return x;
+}
+
+/* Using Fermat little Theorem */
+ll inverse(ll n ){
+	return power( n , mod - 2 , mod );
+}
+
+vector<ll> inverse_factorial;
+void calculateInverseFactorial(ll n){
+
+	inverse_factorial.resize(n+1);
+	inverse_factorial[0] = inverse_factorial[1] = 1;
+
+	for( ll i = 2 ; i <= n ; i++ ){
+		inverse_factorial[i] = (inverse(i)*inverse_factorial[i-1])%mod;
+	}
+}
+
+ll nCr( ll n , ll r ){
+
+	// 	-- 		n!       -- 
+	// |   -------------   | % mod
+	//  -- n! * (n - r)! --
+
+	return ( ( ( factorial[n] * inverse_factorial[r] ) % mod
+		) * inverse_factorial[n-r] ) % mod;
+}
+
+/* Catalan Number */
+ll Cn( ll n ){
+
+	//	--	  	2n!			--	
+	// |	---------------	  | % mod
+	// 	--	n! * n! * (n+1)	--
+
+	return ( ( ( ( ( factorial[2*n] * inverse_factorial[n] ) % mod )
+		* inverse_factorial[n] ) % mod ) * inverse( n + 1 ) ) % mod;
+}

Number Theory/nCr_formula.cpp

@@ -0,0 +1,56 @@
+ll mod = 998244353;
+
+vector<ll> factorial;
+void calculateFactorial(ll n){
+	factorial.resize(n+1);
+
+	factorial[0] = factorial[1] = 1;
+
+	for( ll i = 2 ; i <= n ; i++ ){
+		factorial[i] = ( factorial[i-1] * i ) % mod;
+	}
+}
+
+template<typename T>
+T modMul(T a,T b,T M=(ll)1e9+7){
+    return ((a%M)*(b%M))%M;
+}
+
+template<typename T>
+inline T power(T a, T b, T M)
+{
+    T x = 1;
+    while (b)
+    {
+        if (b & 1) x = modMul(x,a,M);
+        a = modMul(a,a,M);
+        b >>= 1;
+    }
+    return x;
+}
+
+/* Using Fermat little Theorem */
+ll inverse(ll n ){
+	return power( n , mod - 2 , mod );
+}
+
+vector<ll> inverse_factorial;
+void calculateInverseFactorial(ll n){
+
+	inverse_factorial.resize(n+1);
+	inverse_factorial[0] = inverse_factorial[1] = 1;
+
+	for( ll i = 2 ; i <= n ; i++ ){
+		inverse_factorial[i] = (inverse(i)*inverse_factorial[i-1])%mod;
+	}
+}
+
+ll nCr( ll n , ll r ){
+
+	// 	-- 		n!       -- 
+	// |   -------------   | % mod
+	//  -- n! * (n - r)! --
+
+	return ( ( ( factorial[n] * inverse_factorial[r] ) % mod
+		) * inverse_factorial[n-r] ) % mod;
+}