Bear in the Field CodeForces - 385E
思路:根据所给条件写出递推式。
fxn=f(xn-1)+d(xn-1)+k
k=xn-1+yn-1+2+t(n-1)
tn-1=t(n-2)+1
为了方便计算将1-n 变为0-n-1,初始时将x-1,y-1,又由于求k时候是原始位置x+y,所以为x+y+2;
得出递推矩阵
#include<cstdio>
#include<iostream>
#include<cstring>
using namespace std;
typedef long long ll;
ll mod;
struct matrix{
ll x[7][7];
};
matrix multi(matrix a,matrix b){
matrix temp;
memset(temp.x,0,sizeof(temp.x));
for(int i=0;i<6;i++)
for(int j=0;j<6;j++)
for(int k=0;k<6;k++)
{
temp.x[i][j]+=a.x[i][k]*b.x[k][j];
temp.x[i][j]%=mod;
if(temp.x[i][j]<0) temp.x[i][j]=(temp.x[i][j]+mod)%mod;
}
return temp;
}
matrix quick_multi(matrix a,ll n)//矩阵快速幂
{
matrix temp=a;
n--;
while(n){
if(n&1)
temp=multi(temp,a);
a=multi(a,a);
n>>=1;
}
return temp;
}
int main()
{
ll x,y,dx,dy,t;
while(scanf("%lld%lld%lld%lld%lld%lld",&mod,&x,&y,&dx,&dy,&t)!=EOF)
{
matrix A,B;
if(t==0) printf("%lld %lld\n",x,y);
else
{
memset(A.x,0,sizeof(A.x));
memset(B.x,0,sizeof(B.x));
A.x[0][0]=A.x[0][5]=2,A.x[0][1]=A.x[0][2]=A.x[0][4]=1;
A.x[1][0]=A.x[1][3]=A.x[1][4]=1;A.x[1][1]=A.x[1][5]=2;
A.x[2][0]=A.x[2][1]=A.x[2][2]=A.x[2][4]=1;A.x[2][5]=2;//速度可能时负的
A.x[3][0]=A.x[3][1]=A.x[3][3]=A.x[3][4]=1;A.x[3][5]=2;
A.x[4][4]=A.x[4][5]=A.x[5][5]=1;
A=quick_multi(A,t);
B.x[0][0]=x-1;B.x[1][0]=y-1;B.x[2][0]=dx;B.x[3][0]=dy;B.x[5][0]=1;
B=multi(A,B);
printf("%lld %lld\n",B.x[0][0]+1,B.x[1][0]+1);
}
}
return 0;