省冬的第一天。

帶了本子，筆，一本《算法導論》就去了。驚訝於為什麽同學不帶本子記筆記。

他們說：“都學過了。”，果然這才是巨神吧。

第一天：數論，講師：zzx

前幾頁的課件挺水，瞎記了點筆記。後面直接就講了兩道題，我就沒想出來，真的菜。

然後學了波原根，又聽不太懂。

莫比烏斯反演，又聽不太懂。然而我自己瞎推式子好像就能反演出來，沒想法XD。

杜教篩，又聽不太懂。

線性代數，zzx幹脆不講了，沒想法。反正也不是數論範疇。

第一天的早晨就這麽過去了，@qrc去AMC10了，沒想法。

中午劃水

下午毒瘤題開始做了，福一中的題面就是好看。

T1正解洲閣篩，我們都是分段打表的XD。——100

T2瞎推後就變成二維數點cdq分治了，沒想法。——40

T3就是劇毒，處理表達式還要推式子算組合數，沒想法。——0

結果@lh和@qrc居然就比我高了3分，沒想法。

【T1】

題面：計算[l,r]中所有合數的最大真因數之和，對於一個合數，其最大真因數為它的正因數中除了它本身最大的一個。

題解：洲閣篩都沒聽懂。我的做法是：對於\(r-l\leq 5,000,000\)的數據，可以處理\(\sqrt{r}\)中的質數，把\([l,r]\)中的數篩出來。

對於更大的數據，分段打表即可。

 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 }

【FCS NOI2018】福建省冬摸魚筆記 day1