7.22 鲜花
Arghariza
2024-07-22 15:47:54
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我们的模拟赛正在蒸蒸日上!
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### T1
![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)![](https://cdn.luogu.com.cn/upload/image_hosting/3bl2a62a.png)
CF1924D:
$$S_k=(n-2k+1)\left(\dbinom{n}{k}-\dbinom{n}{k-1}\right)$$
### T2
![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)![](https://cdn.luogu.com.cn/upload/image_hosting/83kz46rz.png)
既然 $n\le 10^5$,是不是就能二分答案然后在 Top Tree 上做修改了。
没有更好写的做法的话,谁改谁傻逼。
### T3
$r=1$ 的部分分意义不明。
容斥!先把最后一段扔掉:
$$f_i=-\sum\limits_{j=0}^{i-1}f_j\frac{(-1)^{i-j}}{((i-j)k)!^r}$$
显然是半在线卷积,求逆然后单独考虑最后一段即可。
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