P1707 刷題比賽

明顯的矩陣乘法題。

模數很大，要用龜速乘。

寫法：

矩陣寫在結構體裡，不要用過載運算子，結構體內寫乘法函式。

下面有龜速乘的模板。

//標頭檔案省略
ll n,mod;
#define madd(a,b) {a=((a+b)%mod+mod)%mod;}
#define mmul(a,b) {a=(a*b%mod+mod)%mod;}
inline ll cheng(ll a,ll b){//龜速乘
	ll res=0;
	a%=mod;
	b%=mod;
	while(b){
		if(b&1){
			madd(res,a);
		}
		b>>=1;
		a=(a<<1)%mod;
	}
	return res;
}
struct matrix{
	ll m[11][11];
	matrix mul(matrix x){
		matrix res;
		ll ans;
		For(i,0,10){
			For(j,0,10){
				ans=0;
				For(k,0,10){
					madd(ans,cheng(m[i][k],x.m[k][j]));
				}
				res.m[i][j]=ans;
			}
		}
		return res;
	}
}a,b,c;
void pw(ll x){
	For(i,0,10) b.m[i][i]=1;
	while(x>0){
		if(x&1){
			b=b.mul(a);
		}
		x>>=1;
		a=a.mul(a);
	}
}
signed main(){
	IOS;
	ll p,q,r,t,u,v,w,x,y,z;
	cin>>n>>mod>>p>>q>>r>>t>>u>>v>>w>>x>>y>>z;
	ll t1[11][11]={
	{p,1,1,0,1,0,0,0,0,0,0},
	{q,0,0,0,0,0,0,0,0,0,0},
	{1,0,u,1,1,0,0,0,0,0,0},
	{0,0,v,0,0,0,0,0,0,0,0},
	{1,0,1,0,x,1,0,0,0,0,0},
	{0,0,0,0,y,0,0,0,0,0,0},
	{r,0,0,0,0,0,1,0,0,0,0},
	{t,0,0,0,1,0,2,1,0,0,0},
	{0,0,1,0,0,0,0,0,w,0,0},
	{0,0,0,0,1,0,0,0,0,z,0},
	{1,0,0,0,2,0,1,1,0,0,1}
	};
	For(i,0,10)
		For(j,0,10)
			a.m[i][j]=t1[i][j];
	pw(n-2);
	ll t2[11][11]={
	{3,1,3,1,3,1,1,1,w,z,1},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0},
	{0,0,0,0,0,0,0,0,0,0,0}
	};
	For(i,0,10)
		For(j,0,10)
			c.m[i][j]=t2[i][j];
	c=c.mul(b);
	cout<<"nodgd "<<c.m[0][0]<<"\nCiocio "<<c.m[0][2]<<"\nNicole "<<c.m[0][4]<<"\n";
    return 0;
}
 

本文作者為小蒟蒻：zhangshaojia

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