矩阵相关

最新推荐文章于 2022-07-04 19:16:23 发布

f_zyj

最新推荐文章于 2022-07-04 19:16:23 发布

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分类专栏： ACM模版篇数论 ACM模板-f_zyj 文章标签：矩阵数论

本文链接：https://blog.youkuaiyun.com/f_zyj/article/details/52202169

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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 long

int n;

struct mat
{
    int m[MAXN][MAXN];
};

//  矩阵乘法
mat operator * (mat a, mat &b)
{
    mat ret;
    memset(ret.m, 0, sizeof(ret.m));

    for (int k = 0; k < n; k++)
    {
        for (int i = 0; i < n; i++)
        {
            if (a.m[i][k])
            {
                for (int j = 0; j < n; j++)
                {
                    ret.m[i][j] = mod(ret.m[i][j] + (LL)a.m[i][k] * b.m[k][j]);
                }
            }
        }
    }
    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 long

int n;

struct mat
{
    int m[MAXN][MAXN];
} unit; //  单元矩阵

//  矩阵乘法
mat operator * (mat a, mat &b)
{
    mat ret;
    memset(ret.m, 0, sizeof(ret.m));

    for (int k = 0; k < n; k++)
    {
        for (int i = 0; i < n; i++)
        {
            if (a.m[i][k])
            {
                for (int j = 0; j < n; j++)
                {
                    ret.m[i][j] = mod(ret.m[i][j] + (LL)a.m[i][k] * b.m[k][j]);
                }
            }
        }
    }
    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;
}