HDU 5015 233 Matrix（西安网络赛I题, 构造矩阵)

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网络赛的时候看出来 A(n,m) = sigma(A(i,m-1)) + A(0,m) (1<=i<=n), 但是没构造出来矩阵。。。

详细的题解这里已经有了

http://blog.csdn.net/u013654696/article/details/39273405

B为一个列矩阵, (a0-an)初始为第一列系数矩阵为A 答案为 A^(m-1)*B

B = | 0 |

| a0 |

| a1 |

...

| an |

#include <iostream>#include <cstdio>#include <cstdlib>#include <cstring>#include <vector>#include <queue>#include <stack>#include <cassert>#include <algorithm>#include <cmath>#include <set>#include <limits>using namespace std;#define MIN(a, b) a < b ? a : b#define MAX(a, b) a > b ? a : b#define F(i, n) for (int i=0;i<(n);++i)#define REP(i, s, t) for(int i=s;i<=t;++i)#define UREP(i, s, t) for(int i=s;i>=t;--i)#define REPOK(i, s, t, o) for(int i=s;i<=t && o;++i)#define MEM0(addr, size) memset(addr, 0, size)#define LBIT(x) x&-x#define PI 3.1415926535897932384626433832795#define HALF_PI 1.5707963267948966192313216916398#define MAXN 15#define MAXM 10000#define MOD 10000007typedef long long LL;const double maxdouble = numeric_limits<double>::max();const double eps = 1e-10;const int INF = 0x7FFFFFFF;#define DEBUGconst int max_matrix_size = 15;struct Matrix{    long long mat[max_matrix_size][max_matrix_size];    int _size;    Matrix(int n):_size(n) {memset(mat, 0, sizeof(mat));};    Matrix operator*(const Matrix &b)const{        Matrix ret(_size);        for(int i = 0;i < _size;i++)            for(int j = 0;j < _size;j++){                ret.mat[i][j] = 0;                for(int k = 0;k < _size;k++)                    ret.mat[i][j] += mat[i][k]*b.mat[k][j]%MOD;            }        return ret;    }};Matrix pow_M(Matrix a,long long n) {    Matrix ret(a._size);    memset(ret.mat,0,sizeof(ret.mat));    for (int i=0;i<ret._size;++i)        ret.mat[i][i] = 1;    Matrix tmp = a;    while(n){        if(n&1) ret = ret*tmp;        tmp = tmp*tmp;        n >>= 1;    }    return ret;}int main() {    //freopen("input.in", "r", stdin);    int n, m;    while(scanf("%d%d",&n,&m) != EOF) {        Matrix A(n+2), B(n+2);        A.mat[0][0] = 1;        REP(i, 1, n+1) {            A.mat[i][0] = 3;            A.mat[i][1] = 10;            REP(j, 2, i)                A.mat[i][j] = 1;        }        B.mat[0][0] = 1;        B.mat[1][0] = 233;        REP(i, 2, n+1)            scanf("%d", &B.mat[i][0]);        if (m == 0) {            if (n == 0)                printf("0\n");            else                printf("%d\n",B.mat[n+1][0]);            continue;        }        REP(i, 2, n+1)            B.mat[i][0] = (B.mat[i-1][0]+B.mat[i][0])%MOD;        A = pow_M(A, m-1);        Matrix C = A * B;        cout << C.mat[n+1][0]%MOD << endl;    }    return 0;}

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