UVA10951 - Polynomial GCD

链接

https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1892

题解

https://www.bilibili.com/video/av34897274?share_medium=android&share_source=qq&bbid=A8C441D0-6780-4427-AB5F-C290ECCA2DAF30201infoc&ts=1540873399429

代码

//多项式最大公约数
#include <bits/stdc++.h>
#define maxn  110
#define cl(x) memset(x,0,sizeof(x))
using namespace std;
struct Polynomial
{
	int a[maxn], D;
	Polynomial(){cl(a);D=0;}
	int& operator[](int index){return a[index];}
}A, B, ans;
int N;
int fastpow(int a, int b, int mod)
{
	int t=a, ans=1;
	for(;b;t=t*t%mod,b>>=1)if(b&1)ans=ans*t%mod;
	return ans;
}
Polynomial operator%(Polynomial a, Polynomial b)
{
	int i, j, k, D;
	D=a.D-b.D;
	for(i=0;i<=D;i++)
	{
		k=a[i]*fastpow(b[0],N-2,N)%N;
		for(j=0;j<=b.D;j++)a[i+j]=((a[i+j]-k*b[j])%N+N)%N;
	}
	for(i=0;i<=a.D and a[i]==0;i++);
	for(j=i;j<=a.D;j++)a[j-i]=a[j];
	a.D-=i;
	return a;
}
Polynomial gcd(Polynomial a, Polynomial b){return b.D==-1?a:gcd(b,a%b);}
int read(int x=0)
{
	int c, f=1;
	for(c=getchar();!isdigit(c) and c!=-1;c=getchar())if(c=='-')f=-1;
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+c-48;
	return f*x;
}
int main()
{
	int i, t, kase=0;
	while(N=read())
	{
		printf("Case %d: ",++kase);
		A.D=read();
		for(i=0;i<=A.D;i++)A[i]=read();
		B.D=read();
		for(i=0;i<=B.D;i++)B[i]=read();
		ans=gcd(A,B);
		t=fastpow(ans[0],N-2,N);
		for(i=0;i<=ans.D;i++)ans[i]=ans[i]*t%N;
		printf("%d",ans.D);
		for(i=0;i<=ans.D;i++)printf(" %d",ans[i]);
		putchar(10);
	}
	return 0;
}