CodeForces 7C Line

扩展欧几里德算法：

已知a, b求解一组x，y，使它们满足等式： ax+by = gcd(a, b) =d（解一定存在，根据数论中的相关定理）。

扩展欧几里德常用在求解模线性方程及方程组中。

ax+by+c=0可以转化为ax+by=-c；

可以用扩展欧几里德算法来求ax1+by1=gcd(a,b)来求出x1，y1

此时gcd(a,b)不一定等于-c，假设-c=gcd(a,b)*z,可得z=-c/gcd(a,b);

则ax+by=-c <==> (ax1+by1)*z=gcd(a,b)z;

<==> ax1*z+bx2*z=gcd(a,b)z;

因此可以得知x与x1的关系，y与y1的关系：

x=x1*z，y = y1*z（z上面已经求出来了）

时间： 2024-10-24 09:49:18

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