矩阵快速幂 专题

poj 3233 Matrix Power Series　　http://poj.org/problem?id=3233

/**************************************************************
    Problem:poj 3233
    User: youmi
    Language: C++
    Result: Accepted
    Time:1735MS
    Memory:3880K
****************************************************************/
//#pragma comment(linker, "/STACK:1024000000,1024000000")
//#include<bits/stdc++.h>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <map>
#include <stack>
#include <set>
#include <sstream>
#include <cmath>
#include <queue>
#include <deque>
#include <string>
#include <vector>
#define zeros(a) memset(a,0,sizeof(a))
#define ones(a) memset(a,-1,sizeof(a))
#define sc(a) scanf("%d",&a)
#define sc2(a,b) scanf("%d%d",&a,&b)
#define sc3(a,b,c) scanf("%d%d%d",&a,&b,&c)
#define scs(a) scanf("%s",a)
#define sclld(a) scanf("%I64d",&a)
#define pt(a) printf("%d\n",a)
#define ptlld(a) printf("%I64d\n",a)
#define rep0(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define rep_1(i,n) for(int i=n;i>=1;i--)
#define rep_0(i,n) for(int i=n-1;i>=0;i--)
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
#define lson (step<<1)
#define rson (lson+1)
#define esp 1e-6
#define oo 0x3fffffff
#define TEST cout<<"*************************"<<endl

using namespace std;
typedef long long ll;

int n,tot,mod;

const int maxn=50;
typedef struct T
{
    int mat[maxn][maxn];
}matrix;
matrix org,ans,unit;
matrix operator+(matrix a,matrix b)
{
    matrix c;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++)
            c.mat[i][j]=(a.mat[i][j]+b.mat[i][j])%mod;
    return c;
}
matrix operator*(matrix a,matrix b)
{
    matrix c;
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++)
        {
            c.mat[i][j]=0;
            for(int k=1;k<=n;k++)
                c.mat[i][j]=(c.mat[i][j]+(a.mat[i][k]*b.mat[k][j])%mod)%mod;
        }
    return c;
}
matrix q_pow(int k)
{
    matrix res=unit,p=org;
    while(k)
    {
        if(k&1)
            res=res*p;
        k>>=1;
        p=p*p;
    }
    return res;
}
matrix solve(int k)
{
    if(k==1)
        return org;
    int half=k>>1;
    matrix temp=solve(half);
    matrix t;
    if(k&1)
    {
        t=q_pow(half+1);
        temp=t+temp+temp*t;
    }
    else
    {
        t=q_pow(half);
        temp=temp+temp*t;
    }
    return temp;
}
void init()
{
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=n;j++)
        {
            org.mat[i][j]%=mod;
            unit.mat[i][j]=(i==j);
        }
    }
}
int main()
{
    //freopen("in.txt","r",stdin);
    while(~sc3(n,tot,mod))
    {
        for(int i=1;i<=n;i++)
            for(int j=1;j<=n;j++)
                scanf("%d",&org.mat[i][j]);
        init();
        ans=solve(tot);
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
                printf("%d%c",ans.mat[i][j],j==n?‘\n‘:‘ ‘);
        }
    }
    return 0;
}