「BZOJ3028」食物-生成函数

Description

链接

Solution

构造出八种食物的生成函数。

相乘结果为$\frac{x}{(1-x{)}^4}=x(1+x+x^2+x^3+...{)}^4$

考虑组合意义，第$n$项的答案为在$4$种物品中选若干个组成$n-1$个物品的方案数。答案为$C_{n+2}^3$

#include 
using namespace std;

typedef long long lint;
const int mod = 10007;

int n;

inline int gi()
{
	char c = getchar();
	while (c < '0' || c > '9') c = getchar();
	int sum = 0;
	while ('0' <= c && c <= '9') sum = (sum * 10 + c - 48) % mod, c = getchar();
	return sum;
}

int main()
{
	freopen("food.in", "r", stdin);
	freopen("food.out", "w", stdout);

	n = gi() + 2;
	printf("%lld\n", (lint)n * (n - 1) / 2 * (n - 2) / 3 % mod);
	
	return 0;
}