矩阵相关

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ACM模版

矩阵乘法

/* *  矩阵乘法 n*n矩阵乘法 */#define MAXN 111#define mod(x) ((x) % MOD)#define MOD 1000000007#define LL long longint n;struct mat{    int m[MAXN][MAXN];};//  矩阵乘法mat operator * (mat a, mat b){    mat ret;    LL x;    for (int i = 0; i < n; i++)    {        for (int j = 0; j < n; j++)        {            x = 0;            for (int k = 0; k < n; k++)            {                x += mod((LL)a.m[i][k] * b.m[k][j]);            }            ret.m[i][j] = mod(x);        }    }    return ret;}

矩阵乘法 + 判等

/* *  AB == C ??? */struct Matrix{    Type mat[MAXN][MAXN];    int n, m;    Matrix()    {        n = m = MAXN;        memset(mat, 0, sizeof(mat));    }    Matrix(const Matrix &a)    {        set_size(a.n, a.m);        memcpy(mat, a.mat, sizeof(a.mat));    }    Matrix & operator = (const Matrix &a)    {        set_size(a.n, a.m);        memcpy(mat, a.mat, sizeof(a.mat));        return *this;    }    void set_size(int row, int column)    {        n = row;        m = column;    }    friend Matrix operator * (const Matrix &a, const Matrix &b)    {        Matrix ret;        ret.set_size(a.n, b.m);        for (int i = 0; i < a.n; ++i)        {            for (int k = 0; k < a.m; ++k)            {                if (a.mat[i][k])                {                    for (int j = 0; j < b.m; ++j)                    {                        if (b.mat[k][j])                        {                            ret.mat[i][j] = ret.mat[i][j] + a.mat[i][k] * b.mat[k][j];                        }                    }                }            }        }        return ret;    }    friend bool operator == (const Matrix &a, const Matrix &b)    {        if (a.n != b.n || a.m != b.m)        {            return false;        }        for (int i = 0; i < a.n; ++i)        {            for (int j = 0; j < a.m; ++j)            {                if (a.mat[i][j] != b.mat[i][j])                {                    return false;                }            }        }        return true;    }};

矩阵快速幂

/* *  矩阵快速幂 n*n矩阵的x次幂 */#define MAXN 111#define mod(x) ((x) % MOD)#define MOD 1000000007#define LL long longint n;struct mat{    int m[MAXN][MAXN];} unit; //  单元矩阵//  矩阵乘法mat operator * (mat a, mat b){    mat ret;    LL x;    for (int i = 0; i < n; i++)    {        for (int j = 0; j < n; j++)        {            x = 0;            for (int k = 0; k < n; k++)            {                x += mod((LL)a.m[i][k] * b.m[k][j]);            }            ret.m[i][j] = mod(x);        }    }    return ret;}void init_unit(){    for (int i = 0; i < MAXN; i++)    {        unit.m[i][i] = 1;    }    return ;}mat pow_mat(mat a, LL n){    mat ret = unit;    while (n)    {        if (n & 1)        {//            n--;            ret = ret * a;        }        n >>= 1;        a = a * a;    }    return ret;}int main(){    LL x;    init_unit();    while (cin >> n >> x)    {        mat a;        for (int i = 0; i < n; i++)        {            for (int j = 0; j < n; j++)            {                cin >> a.m[i][j];            }        }        a = pow_mat(a, x);  //  a矩阵的x次幂        //  输出矩阵        for (int i = 0; i < n; i++)        {            for (int j = 0; j < n; j++)            {                if (j + 1 == n)                {                    cout << a.m[i][j] << endl;                }                else                {                    cout << a.m[i][j] << " ";                }            }        }    }    return 0;}

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