快速幂

来源：互联网发布：linux 安装jdk1.7 编辑：程序博客网时间：2024/06/18 09:39

每次除2的快速幂超时了，如果用十进制快速幂的话，会快很多

校赛I题

#include<cstdio>#include<iostream>using namespace std;string s, tmp;const  long long mod=1000000007;class Matrix{public:      int row;      int col;      long long ** element;      Matrix();      ~Matrix();      Matrix(const int , const int);      Matrix(const Matrix &);      Matrix operator = (const Matrix &);      Matrix operator + (const Matrix &);      Matrix operator * (const Matrix &);      void setMatrix();      void print()      {          for(int i=0; i<row; i++)          {              for(int j=0; j<col; j++)                cout<<element[i][j]<<" ";              cout<<endl;          }      }      Matrix quickpow(int n)      {          Matrix result(row, col);          Matrix a=*this;          for(int i=0; i<row; i++)            result.element[i][i]=1;           while(n)           {               if(n%2==1)                result=a*result;               n=n>>1;               a=a*a;           }          return result;      }      Matrix quickpow1()      {          Matrix result(row, col);          for(int i=0; i<row; i++)            result.element[i][i]=1;          Matrix t=*this;          Matrix tmp=t;          for(int i=s.size()-1; i>=0; i--)          {              tmp=t.quickpow(s[i]-'0');              result=result*tmp;              t=t.quickpow(10);          }          return result;      }};Matrix::Matrix(){    row=col=0;    element=NULL;}Matrix::~Matrix(){    for(int i=0; i<row; i++)        delete []element[i];      delete []element;}Matrix::Matrix(const int m_row, const int m_col){    row = m_row;    col = m_col;    element = new long long *[row];    for(int i=0; i<row; i++)        element[i] = new long long[col];    for(int i=0; i<row; i++)        for(int j=0; j<col; j++)        element[i][j]=0;}Matrix::Matrix(const Matrix & temp){    row = temp.row;    col = temp.col;    element = new long long *[row];    for(int i=0; i<row; i++)        element[i] = new long long[col];    for(int i=0; i<row; i++)        for(int j=0; j<col; j++)        element[i][j]=temp.element[i][j];}Matrix Matrix::operator =(const Matrix & right){    for(int i=0; i<row; i++)      delete []element[i];    delete []element;    row = right.row;    col = right.col;    element = new long long *[row];    for(int i=0; i<row; i++)        element[i] = new long long[col];    for(int i=0; i<row; i++)        for(int j=0; j<col; j++)        element[i][j]=right.element[i][j];    return *this;}Matrix Matrix::operator + (const Matrix & right){    Matrix result(row, col);    for(int i=0; i<row; i++)        for(int j=0; j<col; j++)        result.element[i][j] = (element[i][j] + right.element[i][j])%mod;    return result;}Matrix Matrix::operator *(const Matrix & right){    Matrix result(row, right.col);    for(int i=0; i<row; i++)        for(int j=0; j<right.col; j++)        {            result.element[i][j]=0;            for(int k=0; k<col; k++)                {                    result.element[i][j]+=(element[i][k]*right.element[k][j])%mod;                    result.element[i][j]%=mod;                }        }    return result;}int main(){  //  freopen("in.txt", "r", stdin);   // freopen("11.txt", "w", stdout);Matrix tmp(3, 3);tmp.element[0][0]=2;tmp.element[0][1]=1;tmp.element[0][2]=3;tmp.element[1][0]=1;tmp.element[2][1]=1;while(cin>>s){    if(s.size()==1)    {        if(s[0]=='1'){            cout<<1<<endl;continue;            }            else if(s[0]=='2')            {                cout<<2<<endl; continue;            }            else if(s[0]=='0')            {                cout<<0<<endl; continue;            }            else if(s[0]=='3')            {                cout<<5<<endl; continue;            }            else s[0]-=3;    }    else    {        int k = s.size()-1;        if(s[k]>='3') s[k]-=3;        else        {            s[k]+=7;            k--;            while(s[k]=='0')            {                s[k]='9';                k--;            }            s[k]-=1;        }        if(s[0]=='0')        {            s.erase(0, 1);        }    }    Matrix kk=tmp;    kk=kk.quickpow1();    long long ans=(5*kk.element[0][0]+2*kk.element[0][1]+kk.element[0][2])%mod;    printf("%lld\n", ans);}  return 0;}

#include<string.h>#include<cstdio>#include<iostream>#define clr(a) memset(a,0,sizeof(a))using namespace std;string s, tmp;const  long long mod=1000000007;typedef long long ll;struct Ma{    ll a[3][3];}D,E;Ma mul(Ma a,Ma b){    Ma ans;    for(int i=0;i<3;i++){        for(int j=0;j<3;j++){            ans.a[i][j]=0;            for(int k=0;k<3;k++){                ans.a[i][j] += a.a[i][k]*b.a[k][j]%mod;                ans.a[i][j]%=mod;            }        }    }    return ans;}Ma Pow(Ma a,ll b){    Ma d=E,t=a;    while(b){        if(b&1) d=mul(d,t);        b>>=1,t=mul(t,t);    }    return d;}Ma Pow(Ma a){    int l=s.size();    Ma d=E,t=a;    for(int i=l-1;i>=0;i--){        int j=s[i]-'0';        d=mul(d,Pow(t,j));        t=Pow(t,10);    }    return d;}int main(){    //freopen("in.txt", "r", stdin);    //freopen("11.txt", "w", stdout);    clr(D.a),clr(E.a);    for(int i=0;i<=2;i++) E.a[i][i]=1;    D.a[0][0]=2;    D.a[0][2]=3;    D.a[0][1]=D.a[1][0]=D.a[2][1]=1;while(cin>>s){    if(s.size()==1)    {        if(s[0]=='1'){            cout<<1<<endl;continue;            }            else if(s[0]=='2')            {                cout<<2<<endl; continue;            }            else if(s[0]=='0')            {                cout<<0<<endl; continue;            }            else if(s[0]=='3')            {                cout<<5<<endl; continue;            }            else s[0]-=3;    }    else    {        int k = s.size()-1;        if(s[k]>='3') s[k]-=3;        else        {            s[k]+=7;            k--;            while(s[k]=='0')            {                s[k]='9';                k--;            }            s[k]-=1;        }        if(s[0]=='0')        {            s.erase(0, 1);        }    }    Ma kk=D;    kk=Pow(kk);    long long ans=(5*kk.a[0][0]+2*kk.a[0][1]+kk.a[0][2])%mod;    printf("%lld\n", ans);}  return 0;}

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