matrix multiplication example.cpp

// UVa10870 Recurrences
// Rujia Liu
#include<iostream>
#include<string>
#include<cstring>
using namespace std;

const int maxn = 20;
typedef long long Matrix[maxn][maxn];// declare Matrix as the alias of an 2d array with maxn * maxn as its dimension.
typedef long long Vector[maxn];

int sz, mod;
void matrix_mul(Matrix A, Matrix B, Matrix res) {// when array is passed into the function, only the pointer is passed in. 
  Matrix C;
  memset(C, 0, sizeof(C));//So memset and memcpy is revising the original array.
  for(int i = 0; i < sz; i++)
    for(int j = 0; j < sz; j++)
      for(int k = 0; k < sz; k++) C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % mod;
  memcpy(res, C, sizeof(C));
}

void matrix_pow(Matrix A, int n, Matrix res) {
  Matrix a, r;
  memcpy(a, A, sizeof(a));
  memset(r, 0, sizeof(r));
  for(int i = 0; i < sz; i++) r[i][i] = 1;//initialize r matrix to identity matrix
  while(n) {
    if(n&1) matrix_mul(r, a, r);//if n is odd, r *= a;
    n >>= 1;//r /= 2
    matrix_mul(a, a, a);//a = a^2
  }
  memcpy(res, r, sizeof(r));
}

void transform(Vector d, Matrix A, Vector res) {
  Vector r;
  memset(r, 0, sizeof(r));
  for(int i = 0; i < sz; i++)
    for(int j = 0; j < sz; j++)
      r[j] = (r[j] + d[i] * A[i][j]) % mod;
  memcpy(res, r, sizeof(r));
}

int main() {
  int d, n, m;
  while(cin >> d >> n >> m && d) {
    Matrix A;
    Vector a, f;

    for(int i = 0; i < d; i++) { cin >> a[i]; a[i] %= m; }
    for(int i = d-1; i >= 0; i--) { cin >> f[i]; f[i] %= m; }

    memset(A, 0, sizeof(A));
    for(int i = 0; i < d; i++) A[i][0] = a[i];
    for(int i = 1; i < d; i++) A[i-1][i] = 1;

    sz = d;
    mod = m;
    matrix_pow(A, n-d, A);
    transform(f, A, f);

    cout << f[0] << endl;
  }
  return 0;
}