hdu 4651 Partition（公式）

解题思路

代码

#include <cstdio>
#include <cstring>
#include <algorithm>

/*
* 五边形数：f(n) = sum( (-1)^(k+1) [ P(n-k(3k-1)/2) + P(n-k(3k+1)/2)] )
*/

using namespace std;
typedef long long ll;
const int maxn = 1e5;
const int mod = 1e9 + 7;

ll f[maxn + 5];

void presolve() {
memset(f, 0, sizeof(f));
f[0] = 1;
for (int i = 1; i <= maxn; i++) {
int bit = 1;
for (int j = 1; j <= i; j++) {
int v1 = i - j * (3 * j - 1) / 2;
int v2 = i - j * (3 * j + 1) / 2;

if (v1 < 0 && v2 < 0) break;

if (v1 >= 0)
f[i] = (f[i] + bit * f[v1]) % mod;
if (v2 >= 0)
f[i] = (f[i] + bit * f[v2]) % mod;
bit *= -1;
}
f[i] = (f[i] + mod) % mod;
}
}

int main () {
presolve();

int cas, n;
scanf("%d", &cas);
while (cas--) {
scanf("%d", &n);
printf("%lld\n", f
);
}
return 0;
}