Binomial Coefficient

Number Theory/Dp_nCr.cpp

@@ -0,0 +1,41 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+vector<vector<int>> nCr;
+void binomialCoefficient(int n,int k){
+
+	nCr.resize(n+1,vector<int>(k+1,0));
+
+	nCr[1][0] = nCr[1][1] = 1;
+
+	for(int i = 2 ; i <= n ; i++ ){
+		for(int j = 0 ; j <= min(i,k) ; j++ ){
+			
+			if( j == 0 ){
+				nCr[i][j] = 1;
+				continue;
+			}
+
+			if( j == 1 || j == 0 ){
+				nCr[i][j] = i;
+				continue;
+			}
+
+			nCr[i][j] = nCr[i-1][j]+nCr[i-1][j-1];
+		}
+	}
+}
+
+int main(int argc,char* argv[]){
+
+	binomialCoefficient(5,5);
+
+	for(int i = 0 ; i <= 5 ; i++ ){
+		for(int j = 0 ; j <= 5 ; j++ ){
+			cout << nCr[i][j] << " ";
+		}
+		cout << endl;
+	}
+	return 0;
+}

Number Theory/Fast_Multiply.cpp

@@ -1,19 +1,19 @@
-#include <bits/stdc++.h>
-
-using namespace std;
-
-int binary_multiplication(int a , int b,int M=(int)1e9+7){
-    int res = 0;
-    while( b ){
-        if( b&1 ) res += a , res %= M;
-        a = 2 * a ; a %= M:
-        b >>= 1;
-    }
-
-    return res;
-}
-
-int main(){
-
-    return 0;
-}
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int binary_multiplication(int a , int b,int M=(int)1e9+7){
+    int res = 0;
+    while( b ){
+        if( b&1 ) res += a , res %= M;
+        a = 2 * a ; a %= M:
+        b >>= 1;
+    }
+
+    return res;
+}
+
+int main(){
+
+    return 0;
+}

Number Theory/Matrix_Exponentiation.cpp

@@ -1,92 +1,92 @@
-#include <bits/stdc++.h>
-#define ll long long int
-
-using namespace std;
-
-const int M = (int)1e9+7;
-struct Mat{
-    ll m[2][2];
-
-    Mat(){
-        memset(m,0,sizeof(m));
-    }
-
-    void identity(){
-        for(int idx = 0 ; idx < 2 ; idx++ ){
-            m[idx][idx] = 1;
-        }
-    }
-};
-
-Mat operator* (Mat m1,Mat m2){
-    Mat res;
-
-    for(int i = 0 ; i < 2 ; i++ ){
-        for(int j = 0 ; j < 2 ; j++ ){
-            for(int k = 0 ; k < 2 ; k++ ){
-                res.m[i][j] += m1.m[i][k]*m2.m[k][j];
-                res.m[i][j] %= M;
-            }
-        }
-    }
-
-    return res;
-}
-
-Mat power(Mat X,ll n){
-    Mat res;
-    res.identity();
-
-    ll b = n;
-    while(b){
-        if( b&1 ) res = res*X;
-        X = X*X;
-        b >>= 1;
-    }
-
-    return res;
-}
-
-ll fibo(ll n){
-
-    if( n < 2 ) return n;
-    Mat res;
-
-    Mat X;
-    X.m[0][1] = 1 , X.m[1][0] = 1 , X.m[1][1] = 1;
-
-    res = power(X,n);
-
-    ll fn[2][1];
-    fn[0][0]=0,fn[1][0]=1;
-
-    ll fn1[2][1];
-
-    for(int i = 0 ; i < 2 ; i++ ){
-        for(int j = 0 ; j < 1 ; j++ ){
-            for(int k = 0 ; k < 2 ; k++ ){
-                fn1[i][j] = res.m[i][k]*fn[k][j];
-                fn1[i][j]%=M;
-            }
-        }
-    }
-
-    return fn1[0][0];
-}
-
-ll modSub(ll a,ll b){
-    return ((a%M)-(b%M)+M)%M;
-}
-
-int main(){
-    int t;
-    cin>>t;
-
-    while(t--){
-        ll n,m;
-        cin>>n>>m;
-
-        cout << modSub(fibo(m+2),fibo(n+1)) << '\n';
-    }
-    return 0;
-}
+#include <bits/stdc++.h>
+#define ll long long int
+
+using namespace std;
+
+const int M = (int)1e9+7;
+struct Mat{
+    ll m[2][2];
+
+    Mat(){
+        memset(m,0,sizeof(m));
+    }
+
+    void identity(){
+        for(int idx = 0 ; idx < 2 ; idx++ ){
+            m[idx][idx] = 1;
+        }
+    }
+};
+
+Mat operator* (Mat m1,Mat m2){
+    Mat res;
+
+    for(int i = 0 ; i < 2 ; i++ ){
+        for(int j = 0 ; j < 2 ; j++ ){
+            for(int k = 0 ; k < 2 ; k++ ){
+                res.m[i][j] += m1.m[i][k]*m2.m[k][j];
+                res.m[i][j] %= M;
+            }
+        }
+    }
+
+    return res;
+}
+
+Mat power(Mat X,ll n){
+    Mat res;
+    res.identity();
+
+    ll b = n;
+    while(b){
+        if( b&1 ) res = res*X;
+        X = X*X;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+ll fibo(ll n){
+
+    if( n < 2 ) return n;
+    Mat res;
+
+    Mat X;
+    X.m[0][1] = 1 , X.m[1][0] = 1 , X.m[1][1] = 1;
+
+    res = power(X,n);
+
+    ll fn[2][1];
+    fn[0][0]=0,fn[1][0]=1;
+
+    ll fn1[2][1];
+
+    for(int i = 0 ; i < 2 ; i++ ){
+        for(int j = 0 ; j < 1 ; j++ ){
+            for(int k = 0 ; k < 2 ; k++ ){
+                fn1[i][j] = res.m[i][k]*fn[k][j];
+                fn1[i][j]%=M;
+            }
+        }
+    }
+
+    return fn1[0][0];
+}
+
+ll modSub(ll a,ll b){
+    return ((a%M)-(b%M)+M)%M;
+}
+
+int main(){
+    int t;
+    cin>>t;
+
+    while(t--){
+        ll n,m;
+        cin>>n>>m;
+
+        cout << modSub(fibo(m+2),fibo(n+1)) << '\n';
+    }
+    return 0;
+}

Number Theory/extended_gcd_recursive.cpp

@@ -1,12 +1,12 @@
-//Extended gcd -> Recursive
-
-tuple<int,int,int> extended_gcd( int a, int b){
-	
-	if( b == 0 ){
-		return {1,0,a};
-	}
-	
-	int x,y,g;
-	tie(x,y,g) = extended_gcd( b , a%b );
-	return {y , x - (a/b)*y , g};
+//Extended gcd -> Recursive
+
+tuple<int,int,int> extended_gcd( int a, int b){
+	
+	if( b == 0 ){
+		return {1,0,a};
+	}
+	
+	int x,y,g;
+	tie(x,y,g) = extended_gcd( b , a%b );
+	return {y , x - (a/b)*y , g};
 }

Number Theory/inverse_factorial.cpp

@@ -1,9 +1,9 @@
-int invFac[MAX_N];
-void inverse_factorial(){
-
-	invFac[0] = invFac[1] = 1;
-
-	for(int i = 2 ; i <= MAX_N ; i++ ){
-		invFac[i] = (inverse(i)*invFac[i-1])%M;
-	}
+int invFac[MAX_N];
+void inverse_factorial(){
+
+	invFac[0] = invFac[1] = 1;
+
+	for(int i = 2 ; i <= MAX_N ; i++ ){
+		invFac[i] = (inverse(i)*invFac[i-1])%M;
+	}
 }

Number Theory/inverse_modulo_array.cpp

@@ -1,24 +1,24 @@
-vector<int> invs( vi& a , int m ){
-	int n = (int)a.size();
-	
-	if( n == 0 ) return {};
-	
-	vector<int> b(n);
-	
-	int v = 1;
-	for(int i = 0 ; i < n ; i++ ){
-		b[i] = v;
-		v = ((long long)v * a[i] ) % m; 
-	}
-	
-	int x = power( v , m - 2 , m ) ;
-	
-	x = (x % m + m ) % m;
-	
-	for(int i = n - 1 ; i >= 0 ; i-- ){
-		b[i] = x * b[i] %m;
-		x = x * a[i] % m;
-	}
-	
-	return b;
+vector<int> invs( vi& a , int m ){
+	int n = (int)a.size();
+	
+	if( n == 0 ) return {};
+	
+	vector<int> b(n);
+	
+	int v = 1;
+	for(int i = 0 ; i < n ; i++ ){
+		b[i] = v;
+		v = ((long long)v * a[i] ) % m; 
+	}
+	
+	int x = power( v , m - 2 , m ) ;
+	
+	x = (x % m + m ) % m;
+	
+	for(int i = n - 1 ; i >= 0 ; i-- ){
+		b[i] = x * b[i] %m;
+		x = x * a[i] % m;
+	}
+	
+	return b;
 }

Number Theory/modAdd.cpp

@@ -1,4 +1,4 @@
-template<typename T>
-T modAdd(T a,T b,T M=(T)1e9+7){
-	return ((M+a%M)%M+(M+b%M)%M)%M;
-}
+template<typename T>
+T modAdd(T a,T b,T M=(T)1e9+7){
+	return ((M+a%M)%M+(M+b%M)%M)%M;
+}

Number Theory/modMul.cpp

@@ -1,4 +1,4 @@
-template<typename T>
-T modMul(T a,T b,T M=(int)1e9+7){
-	return ((a%M)*(b%M))%M;
+template<typename T>
+T modMul(T a,T b,T M=(int)1e9+7){
+	return ((a%M)*(b%M))%M;
 }

Number Theory/modSub.cpp

@@ -1,4 +1,4 @@
-template<typename T>
-T modSub(T a,T b,T M=(T)1e9+7){
-	return (M+((M+a%M)%M-(M+b%M)%M))%M;
+template<typename T>
+T modSub(T a,T b,T M=(T)1e9+7){
+	return (M+((M+a%M)%M-(M+b%M)%M))%M;
 }

Number Theory/prime_sieve.cpp

@@ -1,18 +1,18 @@
-#define MAX_N 5000001
-bool is_prime[MAX_N];
-
-bool is_sieve_eval = false;
-
-void sieve_erathosis(){
-	if( is_sieve_eval ) return;
-	is_sieve_eval = true;
-	memset(is_prime,0,sizeof(is_prime));
-	is_prime[0] = true , is_prime[1] = true;
-	for(int num = 2 ; num*num < MAX_N ; num++ ){
-		if( !is_prime[num] ){
-			for(int val = num*num ; val < MAX_N ; val += num ){
-				is_prime[val] = true;
-			}
-		}
-	}
+#define MAX_N 5000001
+bool is_prime[MAX_N];
+
+bool is_sieve_eval = false;
+
+void sieve_erathosis(){
+	if( is_sieve_eval ) return;
+	is_sieve_eval = true;
+	memset(is_prime,0,sizeof(is_prime));
+	is_prime[0] = true , is_prime[1] = true;
+	for(int num = 2 ; num*num < MAX_N ; num++ ){
+		if( !is_prime[num] ){
+			for(int val = num*num ; val < MAX_N ; val += num ){
+				is_prime[val] = true;
+			}
+		}
+	}
 }

Number Theory/string_mod_int.cpp

@@ -1,11 +1,11 @@
-int operator%(string& a , int b){
-
-    int sz = (int)a.size();
-    int val = 0;
-    for(int idx = 0 ; idx < sz ; idx++ ){
-        val = 10*val + (a[idx]-'0');
-        val %= b;
-    }
-
-    return val;
+int operator%(string& a , int b){
+
+    int sz = (int)a.size();
+    int val = 0;
+    for(int idx = 0 ; idx < sz ; idx++ ){
+        val = 10*val + (a[idx]-'0');
+        val %= b;
+    }
+
+    return val;
 }