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%inverse.cpp

@@ -0,0 +1,32 @@
+#include <bits/stdc++.h>
+#define lli long long int
+using namespace std;
+lli Power(lli a, lli n , lli mod)
+{
+	lli res = 1;
+	while(n)
+		if(!(n & 1))
+		n /= 2, a = (a*a)%mod;
+		else
+		n--, res = (res*a)%mod;
+	return res;
+
+}
+lli ModularMultiplicativeInverse(lli a, lli n)
+{	
+	return Power(a,n-2,n);
+}
+
+int main()
+{
+	lli a, n;
+	scanf("%lld%lld",&a,&n);
+
+	cout<<ModularMultiplicativeInverse(a,n)<<"\n";
+
+    return 0;
+}
+//modular multiplicative inverse of a under modulus n
+//Modular inverse of a under modulo n exist iff GCD(a,n) = 1 // coprime
+//Little fermat's theorem states that if p is prime number then p ^ (n-1) = 1
+//under mods(n) // = here is sign of modular congruency

Binary_exponentioation.cpp

@@ -0,0 +1,34 @@
+#include <bits/stdc++.h>
+#define mod 1000000007
+using namespace std;
+int powerFunc(int a , int n)
+{
+
+    int res = 1;
+    while(n)
+    {
+        if(!(n & 1))
+        {
+            n = n / 2;
+            a = ((a%mod)*(a%mod))%mod;
+        }
+        else
+        {
+            n--;
+            res = ((res%mod) *( a %mod))%mod;
+        }
+
+    }
+    return res%mod;
+
+}
+
+int main()
+{
+    //freopen("input.txt" , "r", stdin);
+    //freopen("outpux.txt","w" , stdout);
+    int a,n;
+    cin>>a>>n;
+    cout<<powerFunc(a,n)<<"\n";
+    return 0;
+}

Binomial_CoefficientUsingModularInverse.cpp

@@ -0,0 +1,48 @@
+#include <bits/stdc++.h> 
+#define MAXN 1000
+using namespace std; 
+int factorial[MAXN+1];
+// this code can  be used when finding combination of large numbers 
+unsigned long long power(unsigned long long a, 
+						int n, int mod) 
+{ 
+	unsigned long long int res = 1;
+	while(n)
+		if(!(n & 1))
+		n /= 2, a = (a*a)%mod;
+		else
+		n--, res = (res*a)%mod;
+	return res;
+} 
+
+unsigned long long modInverse(unsigned long long n, int p) 
+{ 
+	return power(n, p - 2, p); 
+} 
+
+unsigned long long nCrModPFermat(unsigned long long n, 
+								int r, int p) 
+{ 
+
+	if (r == 0) 
+		return 1; 
+
+	return (factorial[n] * modInverse(factorial[r], p) % p * modInverse(factorial[n - r], p) % p) % p; 
+} 
+
+//nCr % p = (factorial[n]* modIverse(factorial[r]) % p *
+               //modIverse(factorial[n-r]) % p) % p;
+int main() 
+{ 
+
+	int n = 10, r = 2, p = 13; 
+	factorial[0] = 1;
+	for (int i = 1; i <= MAXN; i++) {
+    factorial[i] = factorial[i - 1] * i % p;
+	}
+	cout << "Value of nCr % p is "
+		<< nCrModPFermat(n, r, p)<<"\n"; 
+	return 0; 
+} 
+//Here p must always be prime number 
+//coz modular inverse exits if 2 numbers are coprime

EuclidGCD.cpp

@@ -0,0 +1,19 @@
+
+#include <iostream>
+#define lli long long int
+using namespace std;
+
+lli gcd (lli A , lli B)
+{
+    if(B == 0) return A;
+        else return gcd ( B , A%B);
+}
+
+
+int main()
+{
+    lli a , b;
+    cin>>a>>b;
+    cout<<gcd(a,b)<<"\n";
+    return 0;
+}

GCDQueries.cpp

@@ -0,0 +1,70 @@
+#include <bits/stdc++.h>
+#define lli long long int
+using namespace std;
+lli pre[100005];
+lli post[100005];
+lli arr[100005];
+lli gcd(lli A , lli B)
+{
+    if(A == B || B == 0)
+        return A;
+    if(A == 0)
+        return B;
+    lli MIN,MAX;
+    if(A < B){
+        MIN = A;
+        MAX = B;
+    }
+    else {MIN = B;MAX=A;}
+    if(!(MAX % MIN))
+        return MIN;
+
+    lli check = 0;
+    for(lli i = 1 ; i*i<=MIN ; ++i)
+        if(!(MIN % i))
+        {
+            lli tmp = (MAX)%i;
+            if(!tmp)
+                check = max(check , i);
+            tmp = MAX%(MIN/i);
+            if(!tmp)
+                check = max(check , MIN/i);
+        }
+    return check;
+}
+void Pre(lli n)
+{
+	pre[0] = 0;
+	for(lli i = 1 ; i<=n ; ++i)
+		pre[i] = gcd(pre[i-1],arr[i]);
+
+}
+void Post(lli n)
+{
+	post[n+1] = 0;
+	for(lli i = n ; i>=1; --i)
+		post[i] = gcd(post[i+1],arr[i]);
+
+}
+int main()
+{
+	lli t;
+	scanf("%lld",&t);
+	while(t--)
+	{
+		lli n,q;
+		scanf("%lld %lld",&n,&q);
+		for(lli i = 1 ; i<=n ; ++i)
+		scanf("%lld",&arr[i]);
+		Pre(n);
+		Post(n);
+		while(q--)
+		{
+			lli l ,r ;
+			scanf("%lld %lld", &l,&r);
+			printf("%lld\n",gcd(pre[l-1],post[r+1]));
+		}
+	}
+
+    return 0;
+}

GcdQuerie.cpp

@@ -0,0 +1,88 @@
+#include <bits/stdc++.h>
+#define lli long long int
+using namespace std;
+
+//c++ 14
+#include <bits/stdc++.h>
+#define lli long long int
+using namespace std;
+
+
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(0);
+    cout.tie(0);
+    int t,n,q,l,r;
+    cin>>t;
+
+    while( t --)
+    {
+        cin>>n>>q;
+
+        vector<int> arr(n);
+        for ( int i =0 ; i < n ; ++ i)
+        cin>>arr[i];
+        int pre[n+1] {0},suf[n+2] {0};
+
+        for ( int i = 0 ; i < n ; ++ i)
+        pre[i+1] = __gcd(arr[i],pre[i]);
+
+        int j = n+1;
+        for ( int i = n-1 ; i >= 0 ; -- i, --j)
+        suf[i+1] = __gcd(arr[i],suf[j]);
+
+        while(q --)
+        {
+            cin>>l>>r;
+            cout<<__gcd(pre[l-1], suf[r+1])<<"\n";
+        }
+    }
+
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+//c++ 17
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(0);
+    cout.tie(0);
+    int t,n,q,l,r;
+    cin>>t;
+
+    while( t --)
+    {
+        cin>>n>>q;
+
+        vector<int> arr(n);
+        for ( int i =0 ; i < n ; ++ i)
+        cin>>arr[i];
+        vector<int> pre(n+1,0);
+        vector<int> suf(n+2,0);
+
+        for ( int i = 0 ; i < n ; ++ i)
+        pre[i+1] = gcd(arr[i],pre[i]);
+
+        int j = n+1;
+        for ( int i = n-1 ; i >= 0 ; -- i, --j)
+        suf[i+1] = gcd(arr[i],suf[j]);
+
+        while(q --)
+        {
+            cin>>l>>r;
+            cout<<gcd(pre[l-1], suf[r+1])<<"\n";
+        }
+    }
+
+    return 0;
+}

KthPrime.cpp

@@ -0,0 +1,35 @@
+#include <bits/stdc++.h>
+using namespace std;
+vector<int> primes;
+void SieveOfEratosthenes(int n)
+{
+
+    vector<bool> prime(n+1,1);
+
+    for (int p=2; p*p<=n; p++)
+    {
+
+        if (prime[p] == true)
+        {
+            for (int i=p*2; i<=n; i += p)
+                prime[i] = false;
+        }
+    }
+
+    for (int p=2; p<=n; p++)
+        if (prime[p])
+            primes.emplace_back(p);
+
+}
+int main() {
+    SieveOfEratosthenes(90000001);
+    int q,n;
+    cin>>q;
+    while(q--)
+    {
+        cin>>n;
+        cout<<primes[n-1]<<"\n";
+    }
+    return 0;
+}
+