FCS NOI2018福建省冬摸鱼笔记 day1
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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
【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。
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 }
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