Cod sursa(job #467344)

Utilizator katakunaCazacu Alexandru katakuna Data 28 iunie 2010 14:26:37
Problema Pod Scor 30
Compilator cpp Status done
Runda Stelele Informaticii 2010, clasele X-XII, Ziua 2 Marime 2.09 kb
#include <cstdio>
#include <algorithm>
using namespace std;

#define Mmax 1010
#define Nmax 1000010
#define Kmax 22
#define MOD 9901

int n, m, k, i;
int v[Mmax], a[Nmax], X[Kmax];
int A[Kmax][Kmax], B[Kmax][Kmax], S[Kmax][Kmax], C[Kmax][Kmax];

void citire () {
	
	scanf ("%d %d %d", &n, &m, &k);
	for (i = 1; i <= m; i++) 
		scanf ("%d", &v[i]);
	
	sort (v + 1, v + m + 1);
}

void brute1 () {

	a[0] = 1; int p = 1;
	for (i = 1; i <= n; i++) {
		while (p <= m && v[p] < i) p++;
		
		if (v[p] != i) {
			a[i] = a[i-1];
			if (i - k >= 0) {
				a[i]+= a[i - k];
				if (a[i] >= MOD) a[i]-= MOD;
			}
		}
	}
	
	printf ("%d", a[n]);
}

void prod2 () {
	int i, j, l;
	for (i = 1; i <= k; i++) {
		for (j = 1; j <= k; j++) {
			C[i][j] = 0;
			for (l = 1; l <= k; l++) {
				C[i][j]+= S[i][l] * B[l][j];
				C[i][j]%= MOD;
			}
		}
	}
	
	for (i = 1; i <= k; i++)
		for (j = 1; j <= k; j++)
			S[i][j] = C[i][j];
}

void prod () {
	
	int i, j, l;
	for (i = 1; i <= k; i++) {
		for (j = 1; j <= k; j++) {
			C[i][j] = 0;
			for (l = 1; l <= k; l++) {
				C[i][j]+= B[i][l] * B[l][j];
				C[i][j]%= MOD;
			}
		}
	}
	
	for (i = 1; i <= k; i++)
		for (j = 1; j <= k; j++)
			B[i][j] = C[i][j];
}

void brute2 () {
	
	if (n < k) {
		printf ("%d", 1);
		return ;
	}

	if (n == k) {
		printf ("%d", 2);
		return ;
	}
	
	int i, j;
	for (i = 1; i <= k; i++)
		X[i] = 1;
	X[k]++;
	
	for (i = 1; i <= k; i++) 
		for (j = 1; j <= i; j++)
			B[i][j] = B[i][j] = 1;
	
	for (j = 1; j <= k; j++) {
		B[j][k]++;
		A[j][k]++;
	}
	
	int buc = (n - 1) / k;
	for (i = 1; i <= k; i++)
		S[i][i] = 1;
	
	for (i = 0; i <= 30; i++) {
		if (((buc>>i)&1)) {
			prod2 ();
		}
		
		prod ();
	}
	
	int poz = (n - 1) % k + 1, sol = 0;
	for (i = 1; i <= k; i++) {
		sol+= X[i] * S[poz][i];
		sol%= MOD;
	}
	
	printf ("%d", sol);
}

int main () {

	freopen ("pod.in", "r", stdin);
	freopen ("pod.out", "w", stdout);
	
	citire ();
	if (n <= 1000000)
		brute1 ();
	else {
		if (m == 0) 
			brute2 ();
		else
			brute2 ();
	}
	
	return 0;
}