hdu 4651 - Partition(五边形数定理)

定理详见维基百科。。。。http://zh.wikipedia.org/wiki/%E4%BA%94%E9%82%8A%E5%BD%A2%E6%95%B8%E5%AE%9A%E7%90%86

代码如下：

#include <cstdio>
#include <cstring>
#include <algorithm>
#define LL long long
#define INF 0x7fffffff
#define MOD 1000000007
#define M 100005

using namespace std;

int p[M];
LL ans[M];
void presolve()
{
    int c = 0;
    for(int i = 1; ; i++)
    {
        p[c++] = (3*i*i-i)/2;
        p[c++] = (3*i*i+i)/2;
        if((3*i*i-i)/2>M) break;
    }
}
LL solve(int n)
{
    if(ans[n]) return ans[n];
    LL temp = 0;
    for(int i = 0; p[i] <= n; ++i)
    {
        if((i/2)&1) temp -= solve(n-p[i]);
        else temp += solve(n-p[i]);
    }
    if(temp<0) temp+=(-temp/MOD+1)*MOD;
    return ans[n] = temp%MOD;
}
int main ()
{
    int t, n;
    scanf("%d",&t);
    presolve();
    memset(ans,0,sizeof(ans));
    while(t--)
    {
        scanf("%d",&n);
        ans[0] = 1; ans[1] = 1; ans[2] = 2;
        for(int i = 3; i <= n; ++i)
            solve(i);
        printf("%I64d\n",solve(n));
    }
    return 0;
}