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  • Codeforces Round #257(Div. 2) B. Jzzhu and Sequences(矩阵高速幂)

    题目链接http://codeforces.com/problemset/problem/450/B

    
    

    B. Jzzhu and Sequences
    time limit per test
    1 second
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    Jzzhu has invented a kind of sequences, they meet the following property:

    You are given x and y, please calculate fn modulo 1000000007 (109 + 7).

    Input

    The first line contains two integers x and y (|x|, |y| ≤ 109). The second line contains a single integer n (1 ≤ n ≤ 2·109).

    Output

    Output a single integer representing fn modulo 1000000007 (109 + 7).

    Sample test(s)
    input
    2 3
    3
    
    output
    1
    
    input
    0 -1
    2
    
    output
    1000000006
    
    Note

    In the first sample, f2 = f1 + f33 = 2 + f3f3 = 1.

    In the second sample, f2 =  - 1 - 1 modulo (109 + 7) equals (109 + 6).


    代码例如以下:

    #include <iostream>
    #include <cstdio>
    #include <cstring>
    using namespace std;
    struct A
    {
        int mat[2][2];
    };
    A d,f;
    __int64 n,mod;
    A mul(A a,A b)
    {
        A t;
        memset(t.mat,0,sizeof(t.mat));
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n;j++)
            {
               // if(a.mat[i][k])
                    for(int k = 0; k < n; k++)
                    {
                        t.mat[i][j]+=a.mat[i][k]*b.mat[k][j];
                        t.mat[i][j]%=mod;
                    }
            }
        }
        return t;
    }
    A quickP(int k)
    {
        A p = d ,m;
        memset(m.mat,0,sizeof(m.mat));
        for(int i=0;i<n;++i)//单位矩阵
        {
            m.mat[i][i]=1;
        }
        while(k)
        {
            if(k & 1)
                m=mul(m,p);
            p=mul(p,p);
            k >>= 1 ;
        }
        return m;
    }
    int main()
    {
        n=2;
        int k,t;__int64 x,y,z;
        while(scanf("%I64d%I64d",&x,&y)!=EOF)
        {
            int s=0;
            scanf("%I64d",&z);
            mod=1000000007;
            if(z == 1)
            {
                if(x < 0)
                    printf("%I64d
    ",x+mod);
                else
                    printf("%I64d
    ",x);
                continue;
            }
            d.mat[0][1]=-1;d.mat[1][1] = 0;
            d.mat[0][0]=d.mat[1][0]=1;
            A ret=quickP(z-2);//z-2 乘的次数
            __int64 ans=(ret.mat[0][0]*y%mod+ret.mat[0][1]*x%mod)%mod;
            if(ans < 0)
                ans+=mod;
            printf("%I64d
    ",ans);
        }
        return 0;
    }
    


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  • 原文地址:https://www.cnblogs.com/yjbjingcha/p/7227673.html
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