代码模板之欧拉函数与扩展欧几里得

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欧拉函数

/*
    输入n>1
    输出n的欧拉函数值
    即1~n内与n互素的数的个数

*/

#include<bits/stdc++.h>
using namespace std;
int n;
vector<int> Factor;
void get_Factor()
{
    int temp ,i ,nown=n;
    temp = sqrt(nown)+1;
    Factor.clear();
    for(i = 2; i <= temp; i++)
    {
        if(nown%i == 0)
        {
            Factor.push_back(i);
            while(nown%i == 0)
                nown /= i;
        }
    }
    if(nown != 1)
        Factor.push_back(nown);
}
int euler()
{
    int i ,ans=n ;
    get_Factor();
    int len = Factor.size();
    for(i = 0; i < len; i++)
        ans = (ans/Factor[i])*(Factor[i]-1);
    return ans;
}
int main()
{
    while(~scanf("%d",&n))
        printf("%d\n",euler());
    return 0;
}

扩展欧几里得

/*
    输入a，b
    输出gcd(a,b)=ax+by的解

*/

#include<bits/stdc++.h>
int extend_gcd(int a ,int b ,int &x ,int &y)
{
    if(b == 0)
    {
        x = 1 ;
        y = 0 ;
        return a;
    }
    else
    {
        int gcd = extend_gcd(b, a%b ,y ,x);
        y -= x*(a/b);
        return gcd;
    }
}
int main()
{
    int a ,b ,x ,y;
    while(~scanf("%d%d",&a,&b))
    {
        if(a < b)
            std::swap(a,b);
        printf("%d = ",extend_gcd(a,b,x,y));
        if(x)
            printf("%d*%d ",x,a);
        else printf("0");
        if(y > 0)
            printf(" + %d*%d",y,b);
        else if(y < 0)
            printf(" %d*%d",y,b);
        printf("\n");
    }
    return 0;
}