Number theory algorithm templates (not updated regularly)

/**********/#include<iostream>#include<cstdio>#include<cmath>#include<algorithm>#include<cstring>#include<string>#include<cstdlib>#include<vector>#include<stack>#include<map>using namespaceStd;typedefLong Longll;/***********gcd**********************/ll gcd (ll A,ll b) {if(b==0)        returnA; returnGCD (b,a%b);}/************* Fast Ride ***************/ll Mult_mod (ll a,ll b,ll MoD) {a%=mod; b%=MoD; ll Res=0;  while(b) {if(b&1) {res+=A; Res%=MoD; } A<<=1; if(A>=mod) a%=MoD; b>>=1; }    returnRes;}/************* Fast Power **************/ll Pow_mod (ll x,ll n,ll MoD) {if(n==1)returnX%MoD; X%=MoD; ll T=x,res=1;  while(n) {if(n&1) res=Mult_mod (RES,T,MOD); T=Mult_mod (T,T,MOD); N>>=1; }    returnRes;}/************ Extended Euclid ****************/voidEXTEND_GCD (ll a,ll b,ll &x,ll &y) {ll D;//D=GCD (A, b)    if(b==0) {x=1, y=0; D=A; }    Else{d=EXTEND_GCD (b,a%b,y,x); ll xx=x,yy=y; X=yy; Y=xx-(A/b) *yy; }}/****************** of *********** Prime sieve method*/ll L,u,prime[n];inttot;intvis[n],ans[10000005];voidIsPrime () {tot=0; memset (Vis,0,sizeof(VIS)); memset (Prime,0,sizeof(prime));  for(LL i=2; i<n;i++)    {        if(!Vis[i]) {Prime[tot++]=i;  for(LL j=i*i;j<n;j+=i) vis[j]=1; }    }}/********* Prime number Determination miller_rabin***********/BOOLTest (ll a,ll N)//the core of the Miller_rabin algorithm{ll x=n-1, t=0, Res,last;  while((x&1)==0) {x>>=1; T++; } Last=Pow_mod (a,x,n);  for(intI=0; i<t;i++) {res=pow_mod (Last,2, N); if(res==1&&last!=1&&last!=n-1)            return true; Last=Res; }    if(res!=1)return true; return false;}BOOLMillier_rabin (ll N) {if(n==2)return true; if(n==1|| (n&1)==0)return false;  for(intI=0; i<times;i++) {ll a=rand ()% (n1)+1; if(Test (a,n))return false; }    return true;}/********* Large number factor decomposition pollard_rho*************/ll Pollard_rho (ll X,ll c) {ll x0,y,i=1, k=2; X0=rand ()%x; Y=x0;  while(1) {i++; X0= (Mult_mod (x0,x0,x) +c)%x; ll D=GCD (yx0,x); if(d>1&AMP;&AMP;D&LT;X)returnD; if(y==x0) Break; if(i==k) {y=x0; K+=K; }    }    returnx;}voidFIND_FAC (ll N,intc) {    if(n==1)return; if(Millier_rabin (n)) {Factor[tot++]=N; return; } ll P=N;  while(p>=N) P=pollard_rho (p,c--);    FIND_FAC (P,C); FIND_FAC (n/p,c);}/********** Euler function **********************/intEuler (intN) {    intres=N;  for(intI=2; i*i<=n;i++)    {         while(n%i==0) {n/=i; res-= (res/i);  while(n%i==0) n/=i; }    }    if(n>1) Res-= (res/N); returnRes;}/********** Euler function **************/intEuler (intN) {    intres=N;  for(intI=2; i*i<=n;i++)    {         while(n%i==0) {n/=i; res-= (res/i);  while(n%i==0) n/=i; }    }    if(n>1) Res-= (res/N); returnRes;}/** * * * Prime sieve method + Euler hit table **********/ll E[n+5],p[n+5];BOOLvis[n+5];voidinit () {memset (E,0,sizeof(e)); Memset (P,0,sizeof(p)); memset (Vis,false,sizeof(VIS));    ll I,j; p[0]=1;//total number of recorded primesp[1]=2;  for(i=3; i<n;i+=2)    {        if(!Vis[i]) {p[++p[0]]=i;  for(j=i*i;j<n;j+=i) vis[j]=true; }} e[1]=1;  for(i=1; i<=p[0];i++) E[p[i]]=p[i]-1;//Why do you want-1?      for(i=2; i<n;i++)    {        if(!E[i]) {             for(j=1; j<=p[0];j++)            {                if(i%p[j]==0)                {                    if(i/p[j]%P[j]) e[i]=e[i/p[j]]*E[p[j]]; ElseE[i]=e[i/p[j]]*P[j];  Break; }            }        }    }}/************* Euler play table * Faster version ***************/#defineN 1000000inte[n+5];voidinit () {inti,j; Memset (E,0,sizeof(e));  for(i=2; i<=n;i++)    {        if(!E[i]) {             for(j=i;j<=n;j+=i) {if(!E[j]) e[j]=J; E[J]=e[j]/i* (I-1); }        }    }}

Number theory algorithm templates (not updated regularly)