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【FCS NOI2018】福建省冬摸鱼笔记 day1

时间:2018-02-15 11:06:00      阅读:260      评论:0      收藏:0      [点我收藏+]

标签:targe   最大的   直接   做了   算法   sizeof   long   表达式   cst   

省冬的第一天。

带了本子,笔,一本《算法导论》就去了。惊讶于为什么同学不带本子记笔记。

他们说:“都学过了。”,果然这才是巨神吧。

第一天:数论,讲师:zzx

前几页的课件挺水,瞎记了点笔记。后面直接就讲了两道题,我就没想出来,真的菜。

然后学了波原根,又听不太懂。

莫比乌斯反演,又听不太懂。然而我自己瞎推式子好像就能反演出来,没想法XD。

杜教筛,又听不太懂。

线性代数,zzx干脆不讲了,没想法。反正也不是数论范畴。

第一天的早晨就这么过去了,@qrc去AMC10了,没想法。


中午划水


下午毒瘤题开始做了,福一中的题面就是好看。

T1正解洲阁筛,我们都是分段打表的XD。——100

T2瞎推后就变成二维数点cdq分治了,没想法。——40

T3就是剧毒,处理表达式还要推式子算组合数,没想法。——0

结果@lh@qrc居然就比我高了3分,没想法。

【T1】

题面:计算[l,r]中所有合数的最大真因数之和,对于一个合数,其最大真因数为它的正因数中除了它本身最大的一个。

题解:洲阁筛都没听懂。我的做法是:对于\(r-l\leq 5,000,000\)的数据,可以处理\(\sqrt{r}\)中的质数,把\([l,r]\)中的数筛出来。

对于更大的数据,分段打表即可。

技术分享图片
 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<iostream>
 4 #include<cmath>
 5 #include<cstring>
 6 using namespace std;
 7 long long 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 8 long long l,r;
 9 int c;
10 long long ans;
11 bool com[100001]={1,1};
12 int pri[100001],tot;
13 int com2[10000001];
14 void init(){
15     long long sq=sqrt(r);
16     while((sq+1)*(sq+1)<=r) sq++;
17     while((sq-1)*(sq-1)>=r) sq--;
18     if(sq*sq>r) sq--;
19     int Sq=sq;
20     for(int i=2;i<=Sq;++i){
21         if(!com[i]) pri[++tot]=i;
22         for(int j=1;j<=tot&&i*pri[j]<=Sq;++j){
23             com[i*pri[j]]=true;
24             if(i%pri[j]==0) break;
25         }
26     }
27 }
28 int main(){
29     freopen("factor.in","r",stdin);
30     freopen("factor.out","w",stdout);
31     cin>>l>>r;
32     init();
33     if(r-l<=6000000){
34         c=r-l;
35         for(int i=tot;i>=1;--i){
36             for(long long j=max((l-1)/pri[i]+1,2ll)*pri[i];j<=r;j+=pri[i]){
37                 com2[j-l+1]=pri[i];
38             }
39         }
40         for(int i=1;i<=c+1;++i){
41             if(com2[i]) ans+=(i+l-1)/com2[i];
42         }
43         cout<<ans;
44         return 0;
45     }
46     long long L=l,R=r;
47     l=L, r=((L-1)/5000000+1)*5000000;
48     c=r-l;
49     for(int i=tot;i>=1;--i){
50         for(long long j=max((l-1)/pri[i]+1,2ll)*pri[i];j<=r;j+=pri[i]){
51             com2[j-l+1]=pri[i];
52         }
53     }
54     for(int i=1;i<=c+1;++i){
55         if(com2[i]) ans+=(i+l-1)/com2[i];
56     }
57 //===========
58     int l1=r/5000000+1;
59 //===========
60     r=R, l=(R-1)/5000000*5000000+1;
61     c=r-l;
62     memset(com2,0,sizeof com2);
63     for(int i=tot;i>=1;--i){
64         for(long long j=max((l-1)/pri[i]+1,2ll)*pri[i];j<=r;j+=pri[i]){
65             com2[j-l+1]=pri[i];
66         }
67     }
68     for(int i=1;i<=c+1;++i){
69         if(com2[i]) ans+=(i+l-1)/com2[i];
70     }
71 //===========
72     int r1=(l-1)/5000000;
73     for(int i=l1;i<=r1;++i) ans+=db[i];
74     cout<<ans;
75     return 0;
76 }
View Code

 

【FCS NOI2018】福建省冬摸鱼笔记 day1

标签:targe   最大的   直接   做了   算法   sizeof   long   表达式   cst   

原文地址:https://www.cnblogs.com/PinkRabbit/p/8449312.html

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