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  • P5175 数列(矩阵加速)

    //minamoto
    #include<bits/stdc++.h>
    #define R register
    #define ll long long
    #define fp(i,a,b) for(R int i=a,I=b+1;i<I;++i)
    #define fd(i,a,b) for(R int i=a,I=b-1;i>I;--i)
    #define go(u) for(int i=head[u],v=e[i].v;i;i=e[i].nx,v=e[i].v)
    using namespace std;
    char buf[1<<21],*p1=buf,*p2=buf;
    inline char getc(){return p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++;}
    ll read(){
        R ll res,f=1;R char ch;
        while((ch=getc())>'9'||ch<'0')(ch=='-')&&(f=-1);
        for(res=ch-'0';(ch=getc())>='0'&&ch<='9';res=res*10+ch-'0');
        return res*f;
    }
    char sr[1<<21],z[20];int C=-1,Z=0;
    inline void Ot(){fwrite(sr,1,C+1,stdout),C=-1;}
    void print(R int x){
        if(C>1<<20)Ot();if(x<0)sr[++C]='-',x=-x;
        while(z[++Z]=x%10+48,x/=10);
        while(sr[++C]=z[Z],--Z);sr[++C]='
    ';
    }
    const int P=1e9+7;
    inline int add(R int x,R int y){return x+y>=P?x+y-P:x+y;}
    inline int dec(R int x,R int y){return x-y<0?x-y+P:x-y;}
    inline int mul(R int x,R int y){return 1ll*x*y-1ll*x*y/P*P;}
    int ksm(R int x,R int y){
    	R int res=1;
    	for(;y;y>>=1,x=mul(x,x))if(y&1)res=mul(res,x);
    	return res;
    }
    struct Matrix{
    	int a[4][4];
    	Matrix(){memset(a,0,sizeof(a));}
    	inline int* operator [](const int &x){return a[x];}
    	Matrix operator *(Matrix b){
    		Matrix res;
    		fp(i,0,3)fp(k,0,3)fp(j,0,3)res[i][j]=add(res[i][j],mul(a[i][k],b[k][j]));
    		return res;
    	}
    }A,B;
    ll n;int a1,a2,x,y;
    signed main(){
    //	freopen("testdata.in","r",stdin);
    	int T=read();
    	while(T--){
    		n=read(),a1=read(),a2=read(),x=read(),y=read();
    		if(n<=2){print(n&1?mul(a1,a1):add(mul(a1,a1),mul(a2,a2)));continue;}
    		fp(i,0,3)fp(j,0,3)A[i][j]=B[i][j]=0;
    		A[0][0]=mul(a2,a2),A[0][1]=mul(a1,a1);
    		A[0][2]=mul(a1,a2),A[0][3]=add(A[0][0],A[0][1]);
    		B[0][0]=B[0][3]=mul(x,x),B[0][1]=B[3][3]=1;
    		B[1][0]=B[1][3]=mul(y,y),B[0][2]=x;
    		B[2][0]=B[2][3]=mul(2,mul(x,y)),B[2][2]=y;
    		for(n-=2;n;n>>=1,B=B*B)if(n&1)A=A*B;
    		print(A[0][3]);
    	}return Ot(),0;
    }
    
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  • 原文地址:https://www.cnblogs.com/bztMinamoto/p/10224253.html
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