矩阵 uva 12037

来源：互联网发布：3w咖啡盈利模式知乎编辑：程序博客网时间：2024/06/05 04:11
自动机构造矩阵注意初值与解状态取舍
#include <stdio.h>#include <iostream>using namespace std;const int mod = 34830;const int maxn = 10;typedef long long ll;int n,k;struct mat{  ll e[maxn][maxn];  int step;  void init (int flag, int s)  {    step = s;    for (int i = 1; i <= s; i++)    {      for (int j = 1; j <= s; j++)      {          if (i == j) e[i][j] = flag;          else e[i][j] = 0;      }    }  }  void output_mat()  {    for (int i = 1; i <= step; i++)    {      for (int j = 1; j <= step; j++)      {        cout << e[i][j] << " ";      }      cout<<endl;    }  }} op;mat mul (mat a, mat b){  mat ret;  ret.init (0, a.step);  for (int i = 1; i <= ret.step; i++)  {    for (int j = 1; j <= ret.step; j++)    {      if (a.e[i][j])      {        for (int k = 1; k <= ret.step; k++)        {          ret.e[i][k] += (a.e[i][j] * b.e[j][k]) % mod;          ret.e[i][k] %= mod;        }      }    }  }  return ret;}mat qpow (mat a,int p){  mat ret;  ret.init (1, a.step);  for (; p; p >>= 1)  {    if (p & 1) ret = mul(ret, a);    a = mul(a, a);  }  return ret;}void init_op(){  op.init(0,7);  op.e[1][1] = (k - 4) % mod; op.e[1][4] = (k - 3) % mod;  op.e[1][5] = (k - 3) % mod;  op.e[2][1] =             1; op.e[2][4] =             1;  op.e[3][1] =             1; op.e[3][5] =             1;  op.e[4][3] = (k - 3) % mod; op.e[4][7] = (k - 2) % mod;  op.e[5][2] = (k - 3) % mod; op.e[5][6] = (k - 2) % mod;  op.e[6][3] =             1;  op.e[7][2] =             1;}ll fuct (ll x,int t){  ll ans = 1;  for (int i = 0; i < t; i++)  {      ans *= (x - i) % mod;      ans %= mod;  }  return ans;}ll meow(){  if (n <= 3) return fuct(k, n);  if (k < 3) return 0;  init_op();  op = qpow (op, n - 4);  ll ans = 0;  ans = (ans + op.e[1][1] * fuct (k, 4)) % mod;  ans = (ans + op.e[1][3] * fuct (k, 3)) % mod;  ans = (ans + op.e[5][1] * fuct (k, 4)) % mod;  ans = (ans + op.e[5][3] * fuct (k, 3)) % mod;  return ans;}int main(){  int n_case;  scanf ("%d", &n_case);  for (int i_case = 1; i_case <= n_case; i_case++)  {      scanf ("%d%d", &n, &k);      printf ("Case %d: %lld\n", i_case, meow ());  }  return 0;}
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