poj 3233 Matrix Power Series nyoj 299

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题目来源：http://poj.org/problem?id=3233

题目来源：http://acm.nyist.net/JudgeOnline/problem.php?pid=299

本题用二分，快速幂来求；

A+A^2+A^3+A^4+·······A^k;

当k是奇数时， sum = (A + A^2+······A^(k/2)) + A^(k/2+1)[A + A^2 + ····A^(K/2)] + A^k;

当k是偶数的时候，sum = (A + ·······A^(k/2)) + A^(k/2)[A + A^2 + ····A^(k/2)];

因此可以利用二分的性质求累加和，至于A^k当然是快速幂了。

#include <iostream>#include <cstring>#include <cstdio>using namespace std;const int MAXN = 35;struct Matrix{    int iMatrix[MAXN][MAXN];};int n, iMod;Matrix iPer, A;void Inite_Matrix(){    int i, j;    for(i = 0; i < n; ++i)    {        for(j = 0; j < n; ++j)        {            scanf("%d", &A.iMatrix[i][j]);            A.iMatrix[i][j] %= iMod;            iPer.iMatrix[i][j] = (i == j);//单位矩阵        }    }}Matrix Multi_Matrix(Matrix a, Matrix b)//两个矩阵相乘{    int i, j, k;    Matrix c;    for(i = 0; i < n; ++i)    {        for(j = 0; j < n; ++j)        {            c.iMatrix[i][j] = 0;            for(k = 0; k < n; ++k)                c.iMatrix[i][j] += a.iMatrix[i][k] * b.iMatrix[k][j];            c.iMatrix[i][j] %= iMod;        }    }    return c;}Matrix Add_Matrix(Matrix a, Matrix b)//相加{    int i, j;    Matrix c;    for(i = 0; i < n; ++i)        for(j = 0; j < n; ++j)            c.iMatrix[i][j] = (a.iMatrix[i][j] + b.iMatrix[i][j])%iMod;    return c;}Matrix Quick_Matrix_Power(int k)//矩阵快速幂{    Matrix c, tmp;    c = iPer;    tmp = A;    while(k)    {        if(k&1)        {            c = Multi_Matrix(c, tmp);            k--;        }        else        {            k >>= 1;            tmp = Multi_Matrix(tmp, tmp);        }    }    return c;}Matrix Binary_Search_MatrixSum(int k)//求前k项的和{    if(k == 1)        return A;    Matrix tmp, b;    tmp = Binary_Search_MatrixSum(k>>1);    if(k&1)    {        b = Quick_Matrix_Power((k>>1) + 1);        tmp = Add_Matrix(tmp, Multi_Matrix(tmp, b));        tmp = Add_Matrix(tmp, b);    }    else    {        b = Quick_Matrix_Power(k>>1);        tmp = Add_Matrix(tmp, Multi_Matrix(tmp, b));    }    return tmp;}int main(){    int i, j, k;    Matrix res;    while(~scanf("%d %d %d", &n, &k, &iMod))    {        Inite_Matrix();        res = Binary_Search_MatrixSum(k);        for(i = 0; i < n; ++i)        {            for(j = 0; j < n-1; ++j)                printf("%d ", res.iMatrix[i][j]);            printf("%d\n", res.iMatrix[i][j]);        }    }    return 0;}

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