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Number Theory Part 1 Added
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‎Algorithm/18 Power.cpp

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/** Which of the favors of your Lord will you deny ? **/
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#include<bits/stdc++.h>
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using namespace std;
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#define LL long long
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#define PII pair<int,int>
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#define PLL pair<LL,LL>
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#define MP make_pair
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#define F first
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#define S second
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#define INF INT_MAX
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#define ALL(x) (x).begin(), (x).end()
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#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
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#define READ freopen("alu.txt", "r", stdin)
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#define WRITE freopen("vorta.txt", "w", stdout)
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#include <ext/pb_ds/assoc_container.hpp>
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#include <ext/pb_ds/tree_policy.hpp>
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using namespace __gnu_pbds;
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template<class TIn>using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;
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/**
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PBDS
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-------------------------------------------------
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1) insert(value)
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2) erase(value)
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3) order_of_key(value) // 0 based indexing
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4) *find_by_order(position) // 0 based indexing
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**/
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template<class T1, class T2>
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ostream &operator <<(ostream &os, pair<T1,T2>&p);
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template <class T>
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ostream &operator <<(ostream &os, vector<T>&v);
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template <class T>
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ostream &operator <<(ostream &os, set<T>&v);
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inline void optimizeIO()
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{
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ios_base::sync_with_stdio(false);
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cin.tie(NULL);
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}
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const int nmax = 2e5+7;
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const LL LINF = 1e17;
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template <class T>
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string to_str(T x)
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{
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stringstream ss;
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ss<<x;
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return ss.str();
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}
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//bool cmp(const PII &A,const PII &B)
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//{
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//
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//}
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template <class T>
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T po(T x,T n)
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{
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if(n==0)
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return 1;
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T u = po(x,n/2);
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u = u*u;
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if(n%2==1)
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u = u*x;
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return u;
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}
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template <class T>
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T po_iter(T b, T p) /// Faster than recursive one
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{
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T res = 1, x = b;
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while ( p ) {
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if ( p & 1 ) res = ( res * x );
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x = ( x * x );
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p >>= 1;
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}
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return res;
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}
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int main()
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{
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optimizeIO();
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cout<<po(3LL,25LL)<<endl;
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cout<<po_iter(3LL,25LL)<<endl;
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return 0;
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}
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/**
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**/
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template<class T1, class T2>
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ostream &operator <<(ostream &os, pair<T1,T2>&p)
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{
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os<<"{"<<p.first<<", "<<p.second<<"} ";
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return os;
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}
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template <class T>
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ostream &operator <<(ostream &os, vector<T>&v)
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{
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os<<"[ ";
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for(int i=0; i<v.size(); i++)
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{
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os<<v[i]<<" " ;
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}
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os<<" ]";
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return os;
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}
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template <class T>
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ostream &operator <<(ostream &os, set<T>&v)
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{
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os<<"[ ";
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for(T i:v)
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{
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os<<i<<" ";
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}
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os<<" ]";
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return os;
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}
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‎Algorithm/19 BigMod.cpp

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/** Which of the favors of your Lord will you deny ? **/
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#include<bits/stdc++.h>
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using namespace std;
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#define LL long long
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#define PII pair<int,int>
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#define PLL pair<LL,LL>
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#define MP make_pair
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#define F first
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#define S second
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#define INF INT_MAX
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#define ALL(x) (x).begin(), (x).end()
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#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
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#define READ freopen("alu.txt", "r", stdin)
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#define WRITE freopen("vorta.txt", "w", stdout)
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#include <ext/pb_ds/assoc_container.hpp>
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#include <ext/pb_ds/tree_policy.hpp>
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using namespace __gnu_pbds;
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template<class TIn>using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;
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/**
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PBDS
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-------------------------------------------------
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1) insert(value)
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2) erase(value)
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3) order_of_key(value) // 0 based indexing
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4) *find_by_order(position) // 0 based indexing
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**/
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template<class T1, class T2>
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ostream &operator <<(ostream &os, pair<T1,T2>&p);
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template <class T>
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ostream &operator <<(ostream &os, vector<T>&v);
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template <class T>
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ostream &operator <<(ostream &os, set<T>&v);
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inline void optimizeIO()
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{
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ios_base::sync_with_stdio(false);
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cin.tie(NULL);
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}
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const int nmax = 2e5+7;
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const LL LINF = 1e17;
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template <class T>
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string to_str(T x)
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{
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stringstream ss;
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ss<<x;
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return ss.str();
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}
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//bool cmp(const PII &A,const PII &B)
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//{
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//
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//}
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template <class T>
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T bigMod(T x,T n,T mo)
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{
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if(n==0)
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return 1;
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T u = bigMod(x,n/2,mo);
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u = ((u%mo)*(u%mo))%mo;
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if(n%2==1)
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u = ((u%mo)*(x%mo))%mo;
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return u;
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}
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template <class T>
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T bigMod_iter(T b, T p, T m ) /// Faster than recursive one
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{
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T res = 1 % m, x = b % m;
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while ( p )
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{
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if ( p & 1 )
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res = ( res * x ) % m;
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x = ( x * x ) % m;
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p >>= 1;
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}
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return res;
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}
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int main()
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{
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optimizeIO();
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LL mod = 1e9+7;
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cout<<bigMod(3LL,25LL,mod)<<endl;
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cout<<bigMod_iter(3LL,25LL,mod)<<endl;
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return 0;
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}
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/**
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**/
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template<class T1, class T2>
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ostream &operator <<(ostream &os, pair<T1,T2>&p)
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{
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os<<"{"<<p.first<<", "<<p.second<<"} ";
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return os;
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}
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template <class T>
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ostream &operator <<(ostream &os, vector<T>&v)
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{
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os<<"[ ";
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for(int i=0; i<v.size(); i++)
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{
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os<<v[i]<<" " ;
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}
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os<<" ]";
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return os;
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}
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template <class T>
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ostream &operator <<(ostream &os, set<T>&v)
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{
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os<<"[ ";
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for(T i:v)
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{
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os<<i<<" ";
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}
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os<<" ]";
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return os;
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}
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