POJ 3233 Matrix Power Series 求S = A + A2 + A3 + … + Ak.

求：S = A + A2 + A3 + … +Ak.

第一次代碼：二分直接遞迴，很好理解。1250MS

#include <cstdio>#define SIZE (1<<10)#define MAX_SIZE 32#define lint __int64using namespace std;class CMatrix{     public:         int element[MAX_SIZE][MAX_SIZE];         void setSize(int);         void setModulo(int);         CMatrix operator* (CMatrix);         CMatrix operator+ (CMatrix);         CMatrix power( lint );         CMatrix sum_exp ( lint );     private:         int size;         int modulo;};void CMatrix::setSize ( int x ){     for ( int i = 0; i < x; i++ )         for ( int j = 0; j < x; j++ )             element[i][j]=0;     size = x;}void CMatrix::setModulo ( int x ){     modulo = x;}CMatrix CMatrix::operator+ ( CMatrix param ){    CMatrix ret;    ret.setSize ( size );    ret.setModulo ( modulo );    for ( int i = 0; i < size; i++ )        for ( int j = 0; j < size; j++ )            ret.element[i][j] = ( element[i][j] + param.element[i][j] ) % modulo;    return ret;}CMatrix CMatrix::operator* ( CMatrix param ){     CMatrix product;     product.setSize ( size );     product.setModulo ( modulo );     for ( int i = 0; i < size; i++ )         for ( int j = 0; j < size; j++ )             for ( int k = 0; k < size; k++ )             {                 product.element[i][j] += element[i][k]*param.element[k][j];                 product.element[i][j] %= modulo;             }     return product;}CMatrix CMatrix::power( lint exp ){     CMatrix tmp = (*this) * (*this);     if ( exp == 1 ) return *this;     else if (exp & 1) return tmp.power(exp/2) * (*this);     else return tmp.power( exp / 2 );}CMatrix CMatrix::sum_exp ( lint exp ){    if ( exp == 1 ) return *this;    lint mid = exp / 2;    CMatrix tmps = sum_exp ( mid );    CMatrix tmpp = power ( mid );    if ( exp & 1 )        return tmps + tmpp * ( tmps + tmpp * (*this) );    else return tmps + tmpp * tmps;}int main(){    lint n, k, m;    scanf("%I64d%I64d%I64d",&n,&k,&m);    CMatrix obj, res;    obj.setSize(n);    obj.setModulo(m);    int i, j;    for ( i = 0; i < n; i++ )        for ( j = 0; j < n; j++ )            scanf("%d",&obj.element[i][j]);    res = obj.sum_exp(k);    for ( i = 0; i < n; i++ )    {        for ( j = 0; j < n; j++ )            printf("%d ",res.element[i][j]);        printf("\n");    }    return 0;}

第二次代碼：

利用 直接對矩陣快速求冪。

但是比較納悶還是 719MS

#include <cstdio>#define SIZE 100#define MAX_SIZE 100using namespace std;class CMatrix{     public:         int element[MAX_SIZE][MAX_SIZE];         void setSize(int);         void setModulo(int);         CMatrix operator* (CMatrix);         CMatrix operator+ (CMatrix);         CMatrix power( int );         CMatrix sum_exp ( int );     private:         int size;         int modulo;};void CMatrix::setSize ( int x ){     for ( int i = 0; i < x; i++ )         for ( int j = 0; j < x; j++ )             element[i][j]=0;     size = x;}void CMatrix::setModulo ( int x ){     modulo = x;}CMatrix CMatrix::operator+ ( CMatrix param ){    CMatrix ret;    ret.setSize ( size );    ret.setModulo ( modulo );    for ( int i = 0; i < size; i++ )        for ( int j = 0; j < size; j++ )            ret.element[i][j] = ( element[i][j] + param.element[i][j] ) % modulo;    return ret;}CMatrix CMatrix::operator* ( CMatrix param ){     CMatrix product;     product.setSize ( size );     product.setModulo ( modulo );     for ( int i = 0; i < size; i++ )         for ( int j = 0; j < size; j++ )             for ( int k = 0; k < size; k++ )             {                 product.element[i][j] += element[i][k]*param.element[k][j];                 product.element[i][j] %= modulo;             }     return product;}/*CMatrix CMatrix::power( int exp ){     CMatrix tmp = (*this) * (*this);     if ( exp == 1 ) return *this;     else if (exp & 1) return tmp.power(exp/2) * (*this);     else return tmp.power( exp / 2 );}*/CMatrix CMatrix::power ( int exp ){    CMatrix ret;    ret.setSize(size);    ret.setModulo(modulo);    CMatrix tmp = *this;    for ( int i = 0; i < size; i++ )        ret.element[i][i] = 1;    while ( exp >= 1 )    {        if ( exp & 1 )            ret = ret * tmp;        tmp = tmp * tmp;        exp >>= 1;    }    return ret;}CMatrix CMatrix::sum_exp ( int exp ){    if ( exp == 1 ) return *this;    int mid = exp / 2;    CMatrix tmps = sum_exp ( mid );    CMatrix tmpp = power ( mid );    if ( exp & 1 )        return tmps + tmpp * ( tmps + tmpp * (*this) );    else return tmps + tmpp * tmps;}void print ( int n, CMatrix res ){    for ( int i = 0; i < n; i++ )    {        for ( int j = 0; j < n; j++ )            printf("%d ",res.element[i][j]);        printf("\n");    }}int main(){    int n, k, m;    scanf("%d%d%d",&n,&k,&m);    CMatrix obj, tmp, res;    obj.setSize(2*n);    obj.setModulo(m);    int i, j;    for ( i = 0; i < n; i++ )        for ( j = 0; j < n; j++ )            scanf("%d",&obj.element[i][j]);    if ( k == 1 ) { print( n, obj ); return 0; }    for ( i = 0; i < n; i++ )        obj.element[i+n][i+n] = obj.element[i][i+n] = 1;    for ( i = 0; i < n; i++ )        for ( j = 0; j < n; j++ )            tmp.element[i][j] = tmp.element[i+n][j] = obj.element[i][j];    res = obj.power(k-1) * tmp;    print ( n, res );    return 0;}