题目大意

直接看题面吧。

思路

感觉挺水的一道题啊？怎么评到紫色的啊?考试的时候LJS出了这个题的加强版我就只想出这个思路，然后就爆了。。。

不难发现，我们可以构造矩阵：

x 2x 4x 6x ...

3x 6x 12x 24x 48x ...

9x 18x 36x ...

然后实际上就相当于在这个矩阵中选出一些数使得两两不相邻。因为行数列数都是 \(\log\) 级别的，所以直接状压就好了。

\(\texttt{Code}\)

#include <bits/stdc++.h>

using namespace std;

#define Int register int

#define mod 1000000001

#define MAXN 1000005

template <typename T> void read (T &x){char c = getchar ();x = 0;int f = 1;while (c < '0' || c > '9') f = (c == '-' ? -1 : 1),c = getchar ();while (c >= '0' && c <= '9') x = x * 10 + c - '0',c = getchar ();x *= f;}

template <typename T,typename ... Args> void read (T &x,Args& ... args){read (x),read (args...);}

template <typename T> void write (T x){if (x < 0) x = -x,putchar ('-');if (x > 9) write (x / 10);putchar (x % 10 + '0');}

template <typename T> void Mx (T &a,T b){a = max (a,b);}

template <typename T> void Mi (T &a,T b){a = min (a,b);}

bool mark[MAXN];

int n,a[25][25],lim[25];

void init (int x){

	a[1][1] = x;

	for (Int i = 1;i <= 15;++ i){

		if (i > 1) a[i][1] = a[i - 1][1] * 3;

		if (a[i][1] > n) break;

		for (Int j = 2;j <= 20;++ j){

			a[i][j] = a[i][j - 1] * 2;

			if (a[i][j] > n){

				lim[i] = j - 1;

				break;

			}

		}

		for (Int j = 1;j <= lim[i];++ j) mark[a[i][j]] = 1;

	}

} 

bool chk[1 << 21];

int dp[2][1 << 22];

int WorkDP (){

	int endl = 0;

	for (Int i = 0;i < (1 << lim[1]);++ i) dp[1][i] = chk[i];

	for (Int i = 2;i <= 15;++ i){

		if (a[i][1] > n){

			endl = i - 1;

			break;

		}

		for (Int S = 0;S < (1 << lim[i]);++ S) if (chk[S]){

			dp[i & 1][S] = 0;

			for (Int S1 = 0;S1 < (1 << lim[i - 1]);++ S1)

				if ((S & S1) == 0) dp[i & 1][S] += dp[i - 1 & 1][S1],dp[i & 1][S] %= mod;

		}

		else dp[i & 1][S] = 0;

	}

	int ans = 0;

	for (Int S = 0;S < (1 << lim[endl]);++ S) ans += dp[endl & 1][S],ans %= mod;

	return ans;

}

signed main(){

	read (n);int res = 1;

	for (Int i = 0;i < (1 << 20);++ i) chk[i] = ((i & (i >> 1)) == 0);

	for (Int i = 1;i <= n;++ i) if (!mark[i]) init (i),res = 1ll * res * WorkDP () % mod;

	write (res),putchar ('\n');

	return 0;

}

巴特西

题解 [HNOI2012]集合选数

题目大意

思路

\(\texttt{Code}\)

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