Difference between revisions of "2018 Multi-University, HDU Day 6"

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ultmaster: 除了我签了个到,全是 kblack 做的。可能 kblack 1v3 结局也差不多吧。。。
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== Problem A ==
 
== Problem A ==
  
 
Solved by ultmaster. 00:39 (+4)
 
Solved by ultmaster. 00:39 (+4)
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题意:小学积分题。
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题解:不会积分,上了个 Wolfram Alpha。没想到漏除一个 $b$(纸上是有的,抄上去就没有了)。对着一个明显不对的答案调了好久,还仔细考虑有没有精度问题。答案是 $\pi a + 2b$。注意输出要去尾。根本不需要什么 long double...
  
 
== Problem B ==
 
== Problem B ==

Revision as of 10:32, 8 August 2018

ultmaster: 除了我签了个到,全是 kblack 做的。可能 kblack 1v3 结局也差不多吧。。。

Problem A

Solved by ultmaster. 00:39 (+4)

题意:小学积分题。

题解:不会积分,上了个 Wolfram Alpha。没想到漏除一个 $b$(纸上是有的,抄上去就没有了)。对着一个明显不对的答案调了好久,还仔细考虑有没有精度问题。答案是 $\pi a + 2b$。注意输出要去尾。根本不需要什么 long double...

Problem B

Solved by kblack. 02:12 (+2)

Problem C

Solved by kblack. 04:12 (+5)

Problem D

Problem E

Problem F

Problem G

Unsolved. (-6)

Problem H

Problem I

Problem J

Solved by kblack. 01:01 (+1)

Problem K

Upsolved by ultmaster. (-5)

题意:$M_n(i,j) = 1 \text{ if} \binom{i}{j} \bmod p > 0 \text{ else } 0$. $F(n,k) = \sum_{i = 0}^{p^n-1}\sum_{j=0}^{p^n-1}M_n^k(i,j)$. 求 $(\sum_{n=1}^N\sum_{k=1}^K F(n,k)) \bmod (10^9 + 7)$.

题解:打表找规律,最后发现如果枚举 $k$ 的话,是一个首项为 $q=p(p+1)\cdots(p+k)/(k+1)!$,公比也为 $q$ 的等比数列。求前 $N$ 项和即可。

ultmaster: 小学生常犯错误:等比数列求和直接套公式,从来不考虑公比为 $1$ 的情况,到最后都没看出来。(差点就有贡献了啊。。。心痛。。。

Problem L

Solved by kblack. 00:23 (+)

温暖的签到。