题面
解法
显然,可以回到初始状态就意味着一定由若干个环组成
假设环的长度为\(l_i\)
那么,我们可以得到\(\sum l_i=n\)
不考虑自环的情况,那么\(\sum l_i≤n\)
将\(n\)以内的质因数全部筛出,强制每一次只取某一个质数的次幂,那么就可以解决重复计数的问题
时间复杂度:\(O(n^2)\)
代码
#include <bits/stdc++.h>
#define int long long
#define N 1010
using namespace std;
template <typename node> void chkmax(node &x, node y) {x = max(x, y);}
template <typename node> void chkmin(node &x, node y) {x = min(x, y);}
template <typename node> void read(node &x) {
x = 0; int f = 1; char c = getchar();
while (!isdigit(c)) {if (c == ‘-‘) f = -1; c = getchar();}
while (isdigit(c)) x = x * 10 + c - ‘0‘, c = getchar(); x *= f;
}
int len, a[N], f[N][N];
bool prime(int x) {
for (int i = 2; i * i <= x; i++)
if (x % i == 0) return false;
return true;
}
void sieve(int n) {
len = 0;
for (int i = 2; i <= n; i++)
if (prime(i)) a[++len] = i;
}
main() {
int n; read(n);
sieve(n); f[0][0] = 1;
for (int i = 1; i <= len; i++)
for (int j = 0; j <= n; j++) {
f[i][j] += f[i - 1][j];
for (int k = a[i]; j + k <= n; k = k * a[i])
f[i][j + k] += f[i - 1][j];
}
int ans = 0;
for (int i = 0; i <= n; i++) ans += f[len][i];
cout << ans << "\n";
return 0;
}
原文地址:https://www.cnblogs.com/copperoxide/p/9472318.html
时间: 2024-10-09 00:58:06