HDU 4602 Partition

矩阵快速幂

#include<cstdio>
#include<cstring>
#include<cmath>
#include<map>
#include<algorithm>
using namespace std;

const long long MOD=1000000000+7;
long long n,k,RR,CC;
map<long long,long long>ans;
struct Matrix
{
    long long A[5][5];
    Matrix operator*(Matrix b);
};

Matrix Matrix::operator*(Matrix b)
{
    Matrix c;
    long long i,j,k;
    memset(c.A,0,sizeof(c.A));
    for(i=1;i<=RR;i++)
        for(j=1;j<=CC;j++)
            for(k=1;k<=3;k++)
                c.A[i][j]=(c.A[i][j]+(A[i][k]*b.A[k][j]+MOD)%MOD)%MOD;
    return c;
}

int main()
{
    ans.clear();
    ans[1]=1;ans[2]=2;ans[3]=5,ans[4]=12;
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%lld%lld",&n,&k);
        if(k>n) {printf("0
");continue;}
        long long u=n-k+1;
        if(ans[u]!=0) printf("%lld
",ans[u]);
        else
        {
            long long i,j;
            long long b=u-4;
            Matrix JZ;
            JZ.A[1][1]=4;JZ.A[1][2]=0;JZ.A[1][3]=0;
            JZ.A[2][1]=-4;JZ.A[2][2]=4;JZ.A[2][3]=1;
            JZ.A[3][1]=0;JZ.A[3][2]=-4;JZ.A[3][3]=0;
            Matrix C;
            for(i=1;i<=3;i++)
                for(j=1;j<=3;j++)
                {
                    if(i==j) C.A[i][j]=1;
                    else C.A[i][j]=0;
                }
            RR=3;CC=3;
            while(b>0)
            {
                if(b%2==1)C=C*JZ,b--;
                else JZ=JZ*JZ,b=b/2;
            }

            RR=1;CC=3;
            Matrix CS;
            CS.A[1][1]=ans[4];
            CS.A[1][2]=ans[3];
            CS.A[1][3]=ans[2];
            CS=CS*C;
            ans[u]=CS.A[1][1];
            printf("%lld
",ans[u]);
        }
    }
    return 0;
}