BZOJ 3028

直接推生成函数,即

$$\begin{align}
F(z)&=\frac{1}{1-z^2}\cdot(1+z)\cdot(1+z+z^2)\cdot\frac{z}{1-z^2}\cdot\frac{1}{1-z^4}\cdot(1+z+z^2+z^3)\cdot(1+z)\cdot\frac{1}{1-z^3}\\
&=(\frac{1}{1-z})^3\cdot\frac{z}{1-z}\\
&=\frac{z}{(1-z)^4}
\end{align}$$

$$[z^n]F(z)=\binom{n+2}{n-1}=\binom{n+2}{3}=\frac{n(n+1)(n+2)}{6}$$

直接算就行了

const int MAXN = 500 + 5, MOD = 10007, INV_6 = 1668;

IL int add(int a, int b) {
  a += b;
  return a >= MOD ? a - MOD : a;
}

IL int mul(int a, int b) {
  return a * b % MOD;
}

char str[MAXN];

int main() {
  scanf("%s", str + 1);
  int len = strlen(str + 1), result = 0;
  For(i, 1, len) {
    result = add(mul(result, 10), str[i] - '0');
  }
  printf("%d\n", mul(INV_6, mul(result, mul(result + 1, result + 2))));
  return 0;
}

 

posted @ 2019-01-03 01:24  sjkmost  阅读(172)  评论(0编辑  收藏  举报