Common templates and conclusions in ACM number theory

1: The method of greatest common divisor

Euclidean algorithm implementation. Recursive implementation

1#include <stdio.h>2#include <string.h>3#include <algorithm>4#include <iostream>5 using namespacestd;6 __int64 gcd (__int64 y,__int64 x)7 {8__int64 ans=0;9     if(x==0)Tenans=y; One      Else AANS=GCD (x,y%x); -      returnans; - }  the intMain () - { -     intT; - __int64 A, b; +scanf"%d",&t); -scanf"%i64d%i64d",&a,&B); +         if(a>B) A Swap (A, b); atprintf"%i64d\n", gcd (A, b)); -     } -     return 0; -}

2: The relationship between least common multiple and greatest common divisor

Set N and M greatest common divisor is p, least common multiple is q, then there are the following relationships

P*q=n*m, so the greatest common divisor of two numbers can be converted into the greatest common divisor of two numbers and then the relationship between the two to seek least common multiple =

3: Determination of Prime number

1> Trial Business Law

int Is_prime () {for (int i=2; i*i<=n;i++) {    if(n%i==0  )    return0return1;}

2> Screening Method

Array a[] The number of primes within 1000000 is stored

intGet_prme () {intk=0;  for(intI=2; i<=1000000; i++)    {        if(!Chick[i]) a[k++]=i;  for(intj=0; j<k;j++)        {            if(i*a[j]>1000000)              Break; CHICK[A[J]*i]=1; if(i%a[j]==0)             Break; }    }    return 0;} //To find prime numbers by filtering method

3: Decomposition of a number of the qualitative factor, wherein a[] is a prime, f[] is a number of the mass factor = =

intGET_FX (intx) {     intj,k=0;  for(j=0; a[j]*a[j]<=x;j++)      {         if(x%a[j]==0) f[K++]=A[j];  while(x%a[j]==0) {x=x/A[j]; F[k++]=A[j]; }        if(x==1)         Break; }     if(x!=1) F[k++]=x; return 0}

4: The number that can be divisible by 11 he satisfies the absolute value of the singular number and-even number of digits and can be divisible by 11 = =

To be continued~~~

Common templates and conclusions in ACM number theory