matrix-lib-mr.convict

/*author* Priyanshu Shrivastav (from IIT Palakkad) *
 * *_ __ ___  _ ______ ___  _ ____   ___  ___| |_  *
 * | '_ ` _ \| '__/ __/ _ \| '_ \ \ / / |/ __| __| *
 * | | | | | | | | (_| (_) | | | \ V /| | (__| |_  *
 * |_| |_| |_|_|(_)___\___/|_| |_|\_/ |_|\___|\__| *
When I wrote this, only God and I understood what I was doing
 ** * * * * * * * Now, only God knows * * * * * * */
struct Mat
{
   int sz;
   static const int mxn = 55, inf = (int)1e9;
   int M[mxn][mxn];

   Mat(int n_, int val = 0)
   {
      sz = n_;
      set(val);
   }

   Mat(const Mat& other)
   {
      sz = other.sz;
      for (int i = 0; i < sz; ++i)
         for (int j = 0; j < sz; ++j)
            M[i][j] = other.M[i][j];
   }

   void set(int val)
   {
      for (int i = 0; i < sz; ++i) for (int j = 0; j < sz; ++j)
            M[i][j] = val;
   }

   void make_I()
   {
      for (int i = 0; i < sz; ++i) for (int j = 0; j < sz; ++j)
         M[i][j] = (i == j ? 1 : 0);
   }

   Mat operator+(const Mat &other)  // O(n^2)
   {
      Mat sum(sz);
      for (int i = 0; i < sz; ++i)
         for (int j = 0; j < sz; ++j)
            sum.M[i][j] = add(M[i][j], other.M[i][j]);
      return sum;
   }

   Mat operator*(const Mat &other) // O(n^3)
   {
      Mat prod(sz);
      for (int i = 0; i < sz; ++i)
         for (int j = 0; j < sz; ++j)
            for (int k = 0; k < sz; ++k)
               prod.M[i][j] =
                  add(prod.M[i][j], mul(M[i][k], other.M[k][j]));
      return prod;
   }

   Mat pow(ll k) // O(n^3*logk)
   {
      assert(k >= 0);
      Mat M_cp(*this), res(sz);
      res.make_I();

      while (k)
      {
         if (k & 1) res = res * M_cp;
         M_cp = M_cp * M_cp;
         k >>= 1;
      }
      return res;
   }

   Mat mx_op (const Mat &other)
   {
      Mat res(sz, -inf);
      for (int i = 0; i < sz; ++i) for (int j = 0; j < sz; ++j)
         for (int k = 0; k < sz; ++k)
            res.M[i][j] = max(res.M[i][j], M[i][k] + other.M[k][j]);

      return res;
   }

   Mat mn_op (const Mat &other)
   {
      Mat res(sz, inf);
      for (int i = 0; i < sz; ++i) for (int j = 0; j < sz; ++j)
         for (int k = 0; k < sz; ++k)
            res.M[i][j] = min(res.M[i][j], M[i][k] + other.M[k][j]);

      return res;
   }


   friend istream& operator >> (istream &is, Mat& o)
   {
      for (int i = 0; i < o.sz; ++i) for (int j = 0; j < o.sz; ++j)
            is >> o.M[i][j];
      return is;
   }
   friend ostream& operator << (ostream &os, const Mat& o)
   {
      for (int i = 0; i < o.sz; ++i) for (int j = 0; j < o.sz; ++j)
         os << o.M[i][j] << (j == o.sz -1 ? '\n' : ' ');
      return os;
   }

};