hihocoder 1297 : 数论四·扩展欧几里德

线性同余方程求解，可以把同余方程转化成线性丢番图方程，根据扩展欧几里德算法求出一组特解，然后再求出最小正整数解。

#include <iostream>#include <algorithm>using namespace std;typedef long long LL;LL s1,s2,v1,v2,m;long long extend_gcd(long long a,long long b,long long &x,long long &y){    if(a==0&&b==0) return -1;//无最大公约数    if(b==0)    {        x=1;        y=0;        return a;    }    long long d=extend_gcd(b,a%b,y,x);    y-=a/b*x;    return d;}int main(){    ios::sync_with_stdio(false);    cin.tie(0);    cin >> s1 >> s2 >> v1 >> v2 >> m;    LL A,B,C;    A = v1-v2;    B = m;    C = s2 - s1;    LL gcd = __gcd(A,B);    if(C%gcd || v1 == v2)    {        cout << "-1" << endl;        return 0;    }    LL x,y;    LL d = extend_gcd(A,B,x,y);    x = x*(C/d);    LL mod = abs(B/d);    x = (x%mod + mod)%mod;    cout <<  x << endl;    return 0;}