hdu4686 Arc of Dream 矩阵快速幂

Posted 2020-09-05 奚政

An Arc of Dream is a curve defined by following function:

where
a₀ = A0
a_i = a_i-1*AX+AY
b₀ = B0
b_i = b_i-1*BX+BY
What is the value of AoD(N) modulo 1,000,000,007?

 

矩阵快速幂

 1 #include<stdio.h>
 2 #include<string.h>
 3 typedef long long ll;
 4 const int mod=1000000007;
 5 
 6 struct mat{
 7     int r,c;
 8     ll m[6][6];
 9     void clear(){
10         for(int i=1;i<=r;i++)memset(m[i],0,sizeof(m[i]));
11     }
12 };
13 
14 mat MatMul(mat &m1,mat &m2){
15     mat tmp;
16     tmp.r=m1.r;
17     tmp.c=m2.c;
18     int i,j,k;
19     for(i=1;i<=tmp.r;i++){
20         for(j=1;j<=tmp.c;j++){
21             ll t=0;
22             for(k=1;k<=m1.c;k++){
23                 t=(t+(m1.m[i][k]*m2.m[k][j])%mod)%mod;
24             }
25             tmp.m[i][j]=t;
26         }
27     }
28     return tmp;
29 }
30 
31 mat MatQP(mat &a,ll n){
32     mat ans,tmp=a;
33     ans.r=ans.c=a.r;
34     memset(ans.m,0,sizeof(ans.m));
35     for(int i=1;i<=ans.r;i++){
36         ans.m[i][i]=1;
37     }
38     while(n){
39         if(n&1)ans=MatMul(ans,tmp);
40         n>>=1;
41         tmp=MatMul(tmp,tmp);
42     }
43     return ans;
44 }
45 
46 int main(){
47     ll n;
48     mat a;
49     a.r=5,a.c=1;
50     mat tmp;
51     tmp.c=tmp.r=5;
52     ll a0,b0,ax,ay,bx,by;
53     while(scanf("%lld",&n)!=EOF){
54         scanf("%lld%lld%lld%lld%lld%lld",&a0,&ax,&ay,&b0,&bx,&by);
55         a0%=mod;
56         ax%=mod;
57         ay%=mod;
58         b0%=mod;
59         bx%=mod;
60         by%=mod;
61         a.clear();
62         a.m[1][1]=0;
63         a.m[2][1]=(a0*b0)%mod;
64         a.m[3][1]=b0;
65         a.m[4][1]=a0;
66         a.m[5][1]=1;
67         tmp.clear();
68         tmp.m[1][1]=tmp.m[1][2]=tmp.m[5][5]=1;
69         tmp.m[2][2]=(ax*bx)%mod;
70         tmp.m[2][3]=(ay*bx)%mod;
71         tmp.m[2][4]=(ax*by)%mod;
72         tmp.m[2][5]=(ay*by)%mod;
73         tmp.m[3][3]=bx;
74         tmp.m[3][5]=by;
75         tmp.m[4][4]=ax;
76         tmp.m[4][5]=ay;
77 //        tmp.m[1][3]=tmp.m[1][4]=tmp.m[1][5]=tmp.m[2][1]=tmp.m[3][1]=tmp.m[3][2]=tmp.m[3][4]=tmp.m[4][1]=tmp.m[4][2]=tmp.m[4][3]=tmp.m[5][1]=tmp.m[5][2]=tmp.m[5][3]=tmp.m[5][4]=0;
78         tmp=MatQP(tmp,n);
79         a=MatMul(tmp,a);
80         printf("%lld\\n",a.m[1][1]);
81     }
82     return 0;
83 }

View Code