计数百题整理

https://www.luogu.com.cn/problem/P6146

3.P6075 [JSOI2015]子集选取
https://www.luogu.com.cn/problem/P6075
$$1~n$$的每个数字显然可以分开单独考虑

4.P6008 [USACO20JAN]Cave Paintings P
https://www.luogu.com.cn/problem/P6008

5.Game of Death
https://ac.nowcoder.com/acm/contest/11261/G

6.P6773 [NOI2020] 命运
https://www.luogu.com.cn/problem/P6773

f[x][k]

7.bytedance camp D

$$n$$$$1*2$$多米诺骨牌

1.全$$00$$
2.全$$11$$
3.$$cnt_{01}=cnt_{10}>0$$

8.玲珑杯 Round 17 B
https://blog.csdn.net/qq_33183401/article/details/73694890

9.P3214 [HNOI2011] 卡农
https://www.luogu.com.cn/problem/P3214

$$f_i$$=$$A_{2^n-1}^{i-1}-f_{i-1}-(i-1)*(2^n-i+1)*f_{i-2}$$

10.P3746 [六省联考 2017] 组合数问题
https://www.luogu.com.cn/problem/P3746

11.P2490 [SDOI2011]黑白棋
$$k-nim$$博弈计数

12.CF961G Partitions
https://www.luogu.com.cn/problem/CF961G

1.自己单走，拿到的贡献为$$w_x$$，方案数$$s(n-1,k-1$$
2.放到一个已有集合，有$$k$$种放置方法，每种放置方法的权值为$$\sum w_y+w_x$$

$ans=S*S_{n}^{k}+(n-1)*S*S_{n-1}^{k}$

13.[2018雅礼集训1-16]方阵
https://www.cnblogs.com/hchhch233/p/10016522.html

14.ABC231G Balls in Boxes

$f_n(x)=\sum \frac{(a_n+k)*x^k}{k!}=a_n*e^x+1+x*e^x=(x+a_n+1)*e^x$

15.长度为$$n$$的环,$$m$$种颜色的环，相邻不相同的方案数。

$(m-1)^n-(-1)^{n-1}$

posted @ 2021-12-05 23:24  Creed-qwq  阅读(41)  评论(0编辑  收藏  举报