Good Bye 2018-D. New Year and the Permutation Concatenation

本文解析了Codeforces竞赛中一道关于数学规律的问题,通过观察序列找出递推公式,使用C++实现并考虑到大数问题,采取了模运算保证数值范围。

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地址:http://codeforces.com/contest/1091/problem/D

思路:规律题,比赛时一看就想到是规律题,但是一直没找到规律,看了别人的代码才发现是和前一个值有关

    i=1  f[i]=1

       i=2  f[i]=2=2!+0                0=2*(1-1) 

       i=3  f[i]=9=3!+3                 3=3*(2-1);

  i=4  f[i]=56=4!+32             32=4*(9-1);

  i=5   f[i]=395=5!+275         275=5*(56-1);

  i=n : f[i]=n!+t                      t=n*(f[n-1]-1);

Code:

#include<iostream>
using namespace std;
typedef long long LL;

const LL MOD=998244353;
LL n;

int main()
{
	ios::sync_with_stdio(false);
	cin>>n;
	LL ans=1,dd=1,pre=1;
	for(LL i=2;i<=n;++i)
	{
		dd=dd*i%MOD;
		ans=(dd+(pre-1+MOD)%MOD*i)%MOD;
		pre=ans;
	}
	cout<<ans<<endl;
	
	return 0;
}

 

with_progress({ + # 初始化进度条 + p <- progressor(along = 1:2) + + # 执行100次置换 + placebo_dist <- manual_placebo(data, n_permute = 2) + }) One outcome and one treatment time found. Running single_augsynth. One outcome and one treatment time found. Running single_augsynth. Warning message: In handle_progression(condition, debug = debug) : Received a progression ‘update’ request (amount=1; msg=‘character(0)’) but is not listening to this progressor. This can happen when code signals more progress updates than it configured the progressor to do. When the progressor completes all steps, it shuts down resulting in the global progression handler to no longer listen to it. To troubleshoot this, try with progressr::handlers("debug") > # 清理内存碎片 > gc() used (Mb) gc trigger (Mb) max used (Mb) Ncells 2983096 159.4 5026872 268.5 5026872 268.5 Vcells 10326783 78.8 36845423 281.2 112127404 855.5 > # 5. 结果查看 ------------------------------------------------------------------ > # 查看前10次置换结果 > print(head(placebo_dist, 10)) Time Estimate lower_bound upper_bound p_val permutation pseudo_unit 2016-04-01...1 2016-04-01 -0.18368508 NA NA NA 1 1 2016-04-02...2 2016-04-02 -0.31366935 NA NA NA 1 1 2016-04-03...3 2016-04-03 -0.49916072 NA NA NA 1 1 2016-04-04...4 2016-04-04 0.30554081 NA NA NA 1 1 2016-04-05...5 2016-04-05 -0.33573735 NA NA NA 1 1 2016-04-06...6 2016-04-06 0.07909620 NA NA NA 1 1 2016-04-07...7 2016-04-07 -0.21757939 NA NA NA 1 1 2016-04-08...8 2016-04-08 -0.45763920 NA NA NA 1 1 2016-04-09...9 2016-04-09 0.07273611 NA NA NA 1 1 2016-04-10...10 2016-04-10 0.17557989 NA NA NA 1 1 >
03-25
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