【FCS NOI2018】福建省冬摸鱼笔记 day1

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。

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中午划水

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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和@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。

#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cmath>
#include<cstring>
using namespace std;
long long db[1001]={0ll,4126246193160ll,12378728639758ll,20631171412037ll,28883635629265ll,37136106727534ll,45388534571542ll,53641029590780ll,61893450343725ll,70145939882670ll,78398314522564ll,86650906615396ll,94903251693489ll,103155721252391ll,111408151342220ll,119660677157336ll,127913087049852ll,136165567668553ll,144417970434463ll,152670398028287ll,160922963597770ll,169175312295969ll,177427680650599ll,185680460766117ll,193932650163658ll,202185176961496ll,210437541301111ll,218690115627072ll,226942486289180ll,235194942080358ll,243447495675021ll,251699799516949ll,259952394940665ll,268204695273212ll,276457252222829ll,284709622036265ll,292962015904071ll,301214665538349ll,309467086512465ll,317719457852396ll,325971946736178ll,334224451664188ll,342476792512463ll,350729348954642ll,358981705820952ll,367234133799499ll,375486666486722ll,383739264009402ll,391991117300691ll,400244011032328ll,408496574863862ll,416748807652817ll,425001435374479ll,433253880717281ll,441506236356385ll,449758526618126ll,458011169792727ll,466263743492592ll,474515781733944ll,482768535461101ll,491021202744901ll,499273194350303ll,507525966605171ll,515778154479056ll,524030722845805ll,532283516302184ll,540535501723841ll,548788043558658ll,557040717591692ll,565292937838426ll,573545603889411ll,581797717040707ll,590050362090575ll,598302979698892ll,606555124683247ll,614807927249441ll,623059608785879ll,631312600962465ll,639565241647958ll,647817472963535ll,656070199278377ll,664322088355244ll,672575067134735ll,680827284961412ll,689079890210004ll,697332008730881ll,705584639010052ll,713837712288471ll,722089316408170ll,730341725563046ll,738594505418893ll,746846835981219ll,755099583270599ll,763351864888613ll,771603710033399ll,779856976763962ll,788109207052402ll,796361174622565ll,804614420822359ll,812866591976123ll,821118851080778ll,829372204248270ll,837623474425889ll,845876927637946ll,854128436542735ll,862381009647939ll,870633753994368ll,878886439323054ll,887138401182421ll,895391028877154ll,903643602429997ll,911895426257868ll,920148576694384ll,928400863241610ll,936653167437912ll,944905350159692ll,953158718292359ll,961410349110812ll,969663171666091ll,977915396915438ll,986168202061453ll,994419463152938ll,1002673635435969ll,1010924920684017ll,1019178082375547ll,1027430133354405ll,1035682568863422ll,1043934760662113ll,1052187976648438ll,1060440793106895ll,1068692261743516ll,1076944900567338ll,1085197297761257ll,1093449721607556ll,1101702394376349ll,1109954235112313ll,1118207029673161ll,1126460508129417ll,1134712036579317ll,1142964370246743ll,1151217008530707ll,1159469475456289ll,1167721757923135ll,1175974090868977ll,1184227282851390ll,1192478706186883ll,1200732563131593ll,1208984180940840ll,1217236305634235ll,1225488947632331ll,1233741871517893ll,1241993958571201ll,1250246088181101ll,1258499194833254ll,1266751869692086ll,1275003341569934ll,1283256504415517ll,1291508484922880ll,1299760151731961ll,1308014221805983ll,1316265856124619ll,1324518483557648ll,1332770251302124ll,1341022911721461ll,1349276565829502ll,1357528406229662ll,1365779744761484ll,1374033915528551ll,1382285388655225ll,1390537540980637ll,1398791249871999ll,1407042240544114ll,1415296385539158ll,1423547429013263ll,1431800462368597ll,1440052337629769ll,1448305632012050ll,1456558276107036ll,1464809655951319ll,1473062914412690ll,1481314756967827ll,1489567362230863ll,1497820324948255ll,1506070964389182ll,1514324955290500ll,1522577865690641ll,1530830106935135ll,1539081694793857ll,1547335918438050ll,1555586420051109ll,1563839820474230ll,1572092368606447ll,1580344034678732ll,1588595860213855ll,1596850670612261ll,1605100106681656ll,1613354897926284ll,1621607310143153ll,1629859232761564ll,1638111057078298ll,1646363045338683ll,1654617259483886ll,1662868196559047ll,1671120919901352ll,1679373915658212ll,1687625643310699ll,1695879680251068ll,1704130712168994ll,1712383981938390ll,1720635847170218ll,1728888769219544ll,1737141308617387ll,1745393827514876ll,1753645829064356ll,1761898237936909ll,1770149877526034ll,1778403083075087ll,1786656187825069ll,1794907216427108ll,1803160869233978ll,1811412861084890ll,1819665697313207ll,1827917581067464ll,1836170352615014ll,1844422872364856ll,1852675227343068ll,1860927821683761ll,1869181407009959ll,1877433105952955ll,1885685435450589ll,1893938202260706ll,1902188139115598ll,1910443306681314ll,1918694955467222ll,1926947711739837ll,1935197857656708ll,1943453131796200ll,1951705160391135ll,1959956495848252ll,1968209847055867ll,1976461969711557ll,1984715635835030ll,1992966124436530ll,2001219663785650ll,2009471480847824ll,2017725104191343ll,2025977283904286ll,2034228228313111ll,2042481800056284ll,2050733629245479ll,2058986717014352ll,2067239201164281ll,2075491149005751ll,2083742724373623ll,2091997048458561ll,2100248931002962ll,2108501755892471ll,2116754135888405ll,2125005595567988ll,2133257441387098ll,2141512200368743ll,2149762870497800ll,2158015001725590ll,2166270167126305ll,2174519725845254ll,2182774082798822ll,2191025083937208ll,2199278134597698ll,2207531378356192ll,2215782665731750ll,222403486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long long l,r;
int c;
long long ans;
bool com[100001]={1,1};
int pri[100001],tot;
int com2[10000001];
void init(){
    long long sq=sqrt(r);
    while((sq+1)*(sq+1)<=r) sq++;
    while((sq-1)*(sq-1)>=r) sq--;
    if(sq*sq>r) sq--;
    int Sq=sq;
    for(int i=2;i<=Sq;++i){
        if(!com[i]) pri[++tot]=i;
        for(int j=1;j<=tot&&i*pri[j]<=Sq;++j){
            com[i*pri[j]]=true;
            if(i%pri[j]==0) break;
        }
    }
}
int main(){
    freopen("factor.in","r",stdin);
    freopen("factor.out","w",stdout);
    cin>>l>>r;
    init();
    if(r-l<=6000000){
        c=r-l;
        for(int i=tot;i>=1;--i){
            for(long long j=max((l-1)/pri[i]+1,2ll)*pri[i];j<=r;j+=pri[i]){
                com2[j-l+1]=pri[i];
            }
        }
        for(int i=1;i<=c+1;++i){
            if(com2[i]) ans+=(i+l-1)/com2[i];
        }
        cout<<ans;
        return 0;
    }
    long long L=l,R=r;
    l=L, r=((L-1)/5000000+1)*5000000;
    c=r-l;
    for(int i=tot;i>=1;--i){
        for(long long j=max((l-1)/pri[i]+1,2ll)*pri[i];j<=r;j+=pri[i]){
            com2[j-l+1]=pri[i];
        }
    }
    for(int i=1;i<=c+1;++i){
        if(com2[i]) ans+=(i+l-1)/com2[i];
    }
//===========
    int l1=r/5000000+1;
//===========
    r=R, l=(R-1)/5000000*5000000+1;
    c=r-l;
    memset(com2,0,sizeof com2);
    for(int i=tot;i>=1;--i){
        for(long long j=max((l-1)/pri[i]+1,2ll)*pri[i];j<=r;j+=pri[i]){
            com2[j-l+1]=pri[i];
        }
    }
    for(int i=1;i<=c+1;++i){
        if(com2[i]) ans+=(i+l-1)/com2[i];
    }
//===========
    int r1=(l-1)/5000000;
    for(int i=l1;i<=r1;++i) ans+=db[i];
    cout<<ans;
    return 0;
}