#884087 (C++23) No.2358 xy+yz+zx=N

提出ソース
結果

問題	No.2358 xy+yz+zx=N
ユーザー	eQe
提出日時	2023-06-23 22:23:32
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	23 ms / 2,000 ms
コード長	13,190 bytes
コンパイル時間	7,166 ms
コンパイル使用メモリ	335,264 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-07-01 17:36:28
合計ジャッジ時間	8,212 ms
ジャッジサーバーID （参考情報）	judge5 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	3 ms 5,376 KB
testcase_08	AC	23 ms 5,376 KB
testcase_09	AC	23 ms 5,376 KB
testcase_10	AC	13 ms 5,376 KB
testcase_11	AC	15 ms 5,376 KB
testcase_12	AC	10 ms 5,376 KB
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ソースコード

raw source code
#include<bits/stdc++.h>
#include<atcoder/all>
#define all(a) begin(a),end(a)
#define eb emplace_back
#define ep emplace
#define ef(...) else if(__VA_ARGS__)
#define wh(...) while(__VA_ARGS__)
#define fin(...) rr pp(__VA_ARGS__)
#define RD(T,...) T __VA_ARGS__;li(__VA_ARGS__)
#define LL(...) RD(ll,__VA_ARGS__)
#define ST(...) RD(str,__VA_ARGS__)
#define UL(n,...) u1 __VA_ARGS__;resize({n},__VA_ARGS__);li(__VA_ARGS__)
#define UV(n,...) u1 __VA_ARGS__;resize({n},__VA_ARGS__);vi(__VA_ARGS__)
#define SS(n,...) strs __VA_ARGS__;resize({n},__VA_ARGS__);li(__VA_ARGS__)
#define U2(n,m,...) u2 __VA_ARGS__;resize({n,m},__VA_ARGS__);li(__VA_ARGS__)
#define fe(v,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__)__VA_OPT__(]):v)
#define fo(i,...) for(ll i=rng_fo(__VA_ARGS__)[0],i##stop=rng_fo(__VA_ARGS__)[1],i##step=rng_fo(__VA_ARGS__)[2];i<i##stop;i+=i##step)
#define of(i,...) for(ll i=rng_of(__VA_ARGS__)[0],i##stop=rng_of(__VA_ARGS__)[1],i##step=rng_of(__VA_ARGS__)[2];i>=i##stop;i-=i##step)
#define debug(...) pp(#__VA_ARGS__,__VA_ARGS__)
#define I(...) template<__VA_ARGS__>
#define J typename
#define O operator
#define ce constexpr
#define cs const
#define rr return
#define uu using
uu vo=void;vo solve();uu std::cin;uu std::cout;uu std::swap;uu std::lower_bound;uu std::upper_bound;uu std::vector;uu std::multiset;
uu std::deque;uu std::tuple;uu std::array;uu std::begin;uu std::end;uu is=std::istream;uu os=std::ostream;
uu bo=bool;uu dd=long double;uu ll=long long;uu i64=ll;uu i128=__int128_t;uu ul=unsigned long long;uu u64=ul;uu u128=__uint128_t;
I(J T)uu v1=vector<T>;I(J T)uu v2=v1<v1<T>>;uu u1=v1<ll>;uu u2=v2<ll>;uu str=std::string;uu strs=v1<str>;str sp=" ",nc="",nl="\n";
uu ml=atcoder::modint998244353;is&O>>(is&i,ml&x){ll t;i>>t;x=t;rr i;}os&O<<(os&o,cs ml&x){rr o<<x.val();}uu m1=v1<ml>;uu m2=v2<ml>;
I(J A,J B=A)struct cp{A a;B b;cp():a(),b(){}cp(A a,B b):a(a),b(b){}cp(std::pair<A,B>p):a(p.first),b(p.second){}
  cp&O+=(cs cp&c){a+=c.a,b+=c.b;rr*this;}cp O+(cs cp&c)cs{rr cp{*this}+=c;}bo O==(cs cp&c)cs{rr a==c.a&&b==c.b;}
  cp&O-=(cs cp&c){a-=c.a,b-=c.b;rr*this;}cp O-(cs cp&c)cs{rr cp{*this}-=c;}bo O!=(cs cp&c)cs{rr a!=c.a||b!=c.b;}cp O-()cs{rr cp(-a,-b);}
  bo O<(cs cp&c)cs{rr a!=c.a?a<c.a:b<c.b;}friend is&O>>(is&i,cp&c){rr i>>c.a>>c.b;}
  bo O>(cs cp&c)cs{rr a!=c.a?a>c.a:b>c.b;}friend os&O<<(os&o,cs cp&c){rr o<<c.a<<sp<<c.b;}
};uu cl=cp<ll>;uu cls=v1<cl>;I(J T)uu qmax=std::priority_queue<T>;I(J T)uu qmin=std::priority_queue<T,v1<T>,std::greater<T>>;
I(J T)struct mset:multiset<T>{uu multiset<T>::multiset;vo erase(cs T&x){if(auto p=this->find(x);p!=this->end())multiset<T>::erase(p);}};
I(J T)uu set=std::set<T>;I(J T)uu uset=std::unordered_set<T>;I(J T,J U=T)uu map=std::map<T,U>;I(J T,J U=T)uu umap=std::unordered_map<T,U>;
ce ll oo=3e18;dd ee=1e-12,pi=acosl(-1);str Yes(bo y=1){rr y?"Yes":"No";}str No(){rr"No";}ll ppc(ll x){rr __builtin_popcountll(x);}
ll rnd(ll l,ll r=oo){static ul x=76,y=53,z=20,w=41;ul t=x^(x<<11);x=y,y=z,z=w,w=(w^(w>>19))^(t^(t>>8));if(r==oo)r=l,l=0;rr w%(r-l)+l;}
ll l2(u128 x){x|=1;ll r=0;wh(x)x>>=1,++r;rr r;}bo odd(ll x){rr x&1;}bo eve(ll x){rr~x&1;}ll pm1(ll x){rr 1-2*(x&1);}ll pw2(ll n){rr 1LL<<n;}
I(J T)bo at(T x,ll i){rr x>>i&1;}I(J T,J U,J V)bo in(T l,U m,V r){rr l<=m&&m<r;}I(J T)T sq(cs T&a){rr a*a;}I(J T)T cb(cs T&a){rr a*a*a;}
I(J T)T flo(T x,T y){rr y<0?x=-x,y=-y:x>=0?x/y:(x+1)/y-1;}array<ll,3>rng_fo(ll a,ll b=oo,ll c=0){if(b==oo)b=a,a=0;if(!c)c=1;rr{a,b,c};}
I(J T)T cei(T x,T y){rr y<0?x=-x,y=-y:x<=0?x/y:(x-1)/y+1;}array<ll,3>rng_of(ll a,ll b=0,ll c=0){if(!c)c=1;rr{a-1,b,c};}

I(J T)auto&O++(v1<T>&v,int){fe(v,e)++e;rr v;}I(J T)auto&O^=(v1<T>&v,cs v1<T>&u){copy(all(u),back_inserter(v));rr v;}
I(J T)auto&O--(v1<T>&v,int){fe(v,e)--e;rr v;}I(J T)auto O^(v1<T>v,cs v1<T>&u){rr v^=u;}
I(J T)T&srt(T&a){sort(all(a));rr a;}I(J T)T&rv(T&a){reverse(all(a));rr a;}I(J T)T slice(cs T&a,ll l,ll r){rr T(begin(a)+l,begin(a)+r);}
I(J T)T&rsr(T&a){srt(a),rv(a);rr a;}I(J T)T&uq(T&a){srt(a),a.erase(unique(all(a)),end(a));rr a;}I(J T)uu ilis=std::initializer_list<T>;
I(J T)decltype(auto)bg(T&a){rr*begin(a);}I(J T)T pof(deque<T>&q){T r=bg(q);q.pop_front();rr r;}I(J T)ce bo is_vec=0;
I(J T)decltype(auto)rb(T&a){rr*rbegin(a);}I(J T)T pob(deque<T>&q){T r=rb(q);q.pop_back();rr r;}I(J T)ce bo is_vec<v1<T>> =1;
I(J T)auto pop(T&a){if ce(is_vec<T>||std::is_same_v<T,str>){auto r=rb(a);a.pop_back();rr r;}else{auto r=a.top();a.pop();rr r;}}
I(J...A)auto max(cs A&...a){rr std::max(ilis<std::common_type_t<A...>>{a...});}I(J T,J U=T)vo af(v1<T>&a,U e={}){a.ep(begin(a),e);}
I(J...A)auto min(cs A&...a){rr std::min(ilis<std::common_type_t<A...>>{a...});}I(J T)vo df(T&a){a.erase(begin(a));}
I(J T,J U)bo amax(T&a,cs U&b){rr a<b?a=b,1:0;}I(J T,J U)ll arglb(cs v1<T>&a,cs U&b){rr lower_bound(all(a),b)-begin(a);}
I(J T,J U)bo amin(T&a,cs U&b){rr a>b?a=b,1:0;}I(J T,J U)ll argub(cs v1<T>&a,cs U&b){rr upper_bound(all(a),b)-begin(a);}
I(J V)auto vec_defval(cs v1<V>&){if ce(is_vec<V>)rr vec_defval(V());else rr V();}I(J T)bo add(T&a,cs T&b){rr a+=b,1;}
I(J S,bo f(S&,cs S&),J V)cp<S,bo>scan(cs v1<V>&v){//semigroup
  S r{};bo b=0;if ce(std::is_same_v<V,S>)fe(v,x)b?f(r,x):(r=x,b=1);else fe(v,x)if(auto[y,c]=scan<S,f>(x);c)b?f(r,y):(r=y,b=1);rr{r,b};}
I(J V,J T=decltype(vec_defval(V())))T max(cs V&v){rr scan<T,amax<T>>(v).a;}I(J T)ll len(cs T&a){rr a.size();}
I(J V,J T=decltype(vec_defval(V())))T min(cs V&v){rr scan<T,amin<T>>(v).a;}u1 io(ll n,ll x=0){u1 a(n);iota(all(a),x);rr a;}
I(J V,J T=decltype(vec_defval(V())))T sum(cs V&v){rr scan<T,add<T>>(v).a;}I(J F,J...A)vo swl(cs F&f,A&...a){(vo)ilis<ll>{(vo(f(a)),0)...};}
I(J T=ll,ll k=0,ll n)auto vec(cs ll(&s)[n],cs T&x={}){if ce(k==n-1)rr vector(s[k],x);else rr vector(s[k],vec<T,k+1,n>(s,x));}
I(ll n,J...A)vo resize(cs ll(&s)[n],A&...a){swl([&](auto&u){u=vec(s,vec_defval(u));},a...);}
I(J V,J T=decltype(vec_defval(V())))vo fill(v1<V>&v,T x={}){if ce(is_vec<V>)fe(v,e)fill(e,x);else fe(v,e)e=x;}

struct fio{fio(){cin.tie(0)->sync_with_stdio(0);cout<<std::fixed<<std::setprecision(12);}}fio;
os&O<<(os&o,cs u128&x){if(x<10)rr o<<char(x+'0');rr o<<x/10<<char(x%10+'0');}os&O<<(os&o,cs i128&x){if(x<0)o<<'-';rr o<<u128(x<0?-x:x);}
I(J V)os&O<<(os&o,cs v1<V>&v){str s=nl;if ce(is_vec<V>){if ce(is_vec<J V::value_type>)s+=nl;}else s=sp;fe(v,e)o<<e<<(&e==&rb(v)?nc:s);rr o;}
I(J T)os&O<<(os&o,cs set<T>&v){fe(v,e)o<<e<<sp;rr o;}I(J T,J U)os&O<<(os&o,cs map<T,U>&m){fe(m,e)o<<cp(e)<<nl;rr o;}
I(J T)os&O<<(os&o,cs mset<T>&v){fe(v,e)o<<e<<sp;rr o;}I(J T)is&O>>(is&i,v1<T>&v){fe(v,e)i>>e;rr i;}
I(J T)vo pp(cs T&a){cout<<a<<nl;}I(J...A)vo li(A&...a){(cin>>...>>a);}I(J...A)vo vi(ll i,A&...a){(cin>>...>>a[i]);}
I(J T,J...A)vo pp(cs T&a,cs A&...b){cout<<a;((cout<<sp<<b),...);pp(nc);}I(J T,J...A)vo vi(v1<T>&a,A&...b){fo(i,len(a))vi(i,a,b...);}

struct edg{ll t,w;edg(){}edg(ll t,ll w=1):t(t),w(w){}};uu graph=v2<edg>;
graph tog(cs u2&a){graph g;fe(a,e){g.eb();fe(e,v)rb(g).eb(v);}rr g;}u2 tou(cs graph&g){u2 a;fe(g,e){a.eb();fe(e,v,w)rb(a).eb(v);}rr a;}
cp<u1>ygi(u2&g,ll m,bo f=1){UV(m,a,b);if(f)a--,b--;fo(i,m)g[a[i]].eb(b[i]);rr{a,b};}
cp<u1>mgi(u2&g,ll m,bo f=1){auto[a,b]=ygi(g,m,f);fo(i,m)g[b[i]].eb(a[i]);rr{a,b};}auto ti(u2&g,bo f=1){rr mgi(g,len(g)-1,f);}
u1 en(cs str&s,cs str&b="a"){ll n=len(s);u1 r(n,-1);fo(i,n)if(len(b)==1)r[i]=s[i]-b[0];else fo(j,len(b))if(s[i]==b[j])r[i]=j;rr r;}
str de(cs u1&a,cs str&b="a"){ll n=len(a);str r(n,'|');fo(i,n)if(len(b)==1)r[i]=a[i]+b[0];else fo(j,len(b))if(a[i]==j)r[i]=b[j];rr r;}
u2 en(cs strs&s,cs str&b="a"){u2 r;fe(s,e)r.eb(en(e,b));rr r;}str ins(){str s;li(s);rr s;}strs inss(ll n){strs s(n);li(s);rr s;}
strs de(cs u2&a,cs str&b="a"){ll n=len(a);strs r(n);fo(i,n)r[i]=de(a[i],b);rr r;}u1 abc(){rr en(ins());}u2 abcs(ll n){rr en(inss(n));}

I(J...A)u1 zp(A&...a){u1 v;fe({a...},e)v^=e;uq(v);swl([&](u1&u){fe(u,e)e=arglb(v,e);},a...);rr v;}
I(J F,J...A)u1 vs(cs F&f,A&...a){ll n;fe({a...},e)n=len(e);u1 o=io(n);sort(all(o),f);swl([&](u1&u){u1 c=u;fo(i,n)u[i]=c[o[i]];},a...);rr o;}
I(J F)ll bsl(cs F&f,ll o,ll n){wh(abs(o-n)>1)(f((o+n)/2)?o:n)=(o+n)/2;rr o;}ll sqr(ll x){ll r=max(sqrtl(x)-1,dd());wh(r+1<=x/(r+1))++r;rr r;}
I(J F)dd bsd(cs F&f,dd o,dd n){fo(t,l2(abs(o-n)/ee)+1)(f((o+n)/2)?o:n)=(o+n)/2;rr o;}I(J T)auto zt(v1<T>a){fo(i,1,len(a))a[i]+=a[i-1];rr a;}
cls rle(cs u1&a){cls r;fe(a,e)len(r)&&e==rb(r).a?++rb(r).b:r.eb(e,1).b;rr r;}cls rce(u1 a){rr rle(srt(a));}
i128 po(i128 x,u128 n,u128 m=0){i128 r=1;wh(n){if(n&1)r*=x;x*=x;if(m)r%=m,x%=m;n>>=1;}rr r;}
u1 divs(ll n){u1 r;for(ll i=1;i*i<=n;i++)if(n%i==0)r.eb(i),r.eb(n/i);rr uq(r);}
cls fact(ll n){umap<ll>m;for(ll i=2;i*i<=n;i++)wh(n%i==0)++m[i],n/=i;if(n>1)++m[n];cls r;fe(m,e)r.eb(e);rr srt(r);}

//https://nyaannyaan.github.io/library/modint/modint-montgomery64.hpp
//https://yukicoder.me/submissions/794260 (reduce)

struct montgomery64{
  uu ml=montgomery64;
  
  static inline u64 m;
  static inline u64 miv;//m^{-1}
  static inline u64 n2;//n=2^64,n2=n^2%m
  
  static void set_mod(u64 m){
    assert(m<(1ULL<<63));
    assert(m&1);
    ml::m=m;
    n2=-u128(m)%m;
    miv=m;
    fo(t,5)miv*=2-m*miv;//newton's method
    assert(m*miv==1);
  }
  
  static u64 mod(){
    rr m;
  }
  
  u64 a;
  montgomery64(cs i64&a=0):a(reduce((u128)(a%(i64)m+m)*n2)){}
  
  static u64 reduce(cs u128&a){//montgomery reduction
    u128 r=(a+u128(u64(a)*-miv)*m)>>64;
    rr r>=m?r-m:r;
  }
  
  ml&O+=(cs ml&b){if((a+=b.a)>=m)a-=m;rr*this;}
  ml&O-=(cs ml&b){if(i64(a-=b.a)<0)a+=m;rr*this;}
  ml&O*=(cs ml&b){a=reduce(u128(a)*b.a);rr*this;}
  ml&O/=(cs ml&b){*this*=b.inv();rr*this;}
  
  ml O+(cs ml&b)cs{rr ml(*this)+=b;}
  ml O-(cs ml&b)cs{rr ml(*this)-=b;}
  ml O*(cs ml&b)cs{rr ml(*this)*=b;}
  ml O/(cs ml&b)cs{rr ml(*this)/=b;}
  bo O==(cs ml&b)cs{rr a==b.a;}
  bo O!=(cs ml&b)cs{rr a!=b.a;}
  ml O-()cs{rr ml()-ml(*this);}
  
  ml pow(u128 n)cs{
    ml r(1),x(*this);
    wh(n){
      if(n&1)r*=x;
      x*=x;
      n>>=1;
    }
    rr r;
  }
  
  ml inv()cs{
    rr pow(m-2);// if m is a prime number
    /*
     u64 a=this->a,b=m,u=1,v=0;
     wh(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b);
     rr u;
     */
  }
  
  u64 val()cs{
    rr reduce(a);
  }
  
  friend os&O<<(os&o,cs ml&b){
    rr o<<b.val();
  }
};

//https://ja.wikipedia.org/wiki/ミラー–ラビン素数判定法
//https://judge.yosupo.jp/problem/primality_test n<=10^{18}
//https://yukicoder.me/problems/no/3030 n<2^{63}

I(J ml)bo miller_rabin(ll n,u1 as){//n<2^{63}
  ll t=0,d=n-1;
  wh(eve(d))d>>=1;
  
  if(ml::mod()!=n)ml::set_mod(n);
  ml one=1,minus_one=n-1;
  fe(as,a){
    if(a%n==0)continue;
    ll t=d;
    ml y=ml(a).pow(t);
    wh(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1;
    if(y!=minus_one&&eve(t))rr 0;
  }
  rr 1;
}

bo is_prime(ll n){//n<2^{63}
  if(eve(n))rr n==2;
  if(n<=1)rr 0;
  if(n<4759123141LL)rr miller_rabin<montgomery64>(n,{2,7,61});
  rr miller_rabin<montgomery64>(n,{2,325,9375,28178,450775,9780504,1795265022});
}

//https://nyaannyaan.github.io/library/prime/fast-factorize.hpp.html
I(J ml)ll pollard_rho(ll n){//n<2^{63}．nの因数を一つ返す．
  if(eve(n))rr 2;
  if(is_prime(n))rr n;
  if(ml::mod()!=n)ml::set_mod(n);
  ml R,one=1;
  auto f=[&](ml x){rr x*x+R;};
  wh(1){
    ml x,y,ys,q=one;
    R=rnd(2,n),y=rnd(2,n);
    ll g=1;
    constexpr ll m=128;
    for(ll r=1;g==1;r<<=1){
      x=y;
      fo(i,r)y=f(y);
      for(ll k=0;g==1&&k<r;k+=m){
        ys=y;
        for(ll i=0;i<m&&i<r-k;++i)q*=x-(y=f(y));
        g=std::gcd(q.val(),n);
      }
    }
    if(g==n)do g=std::gcd((x-(ys=f(ys))).val(),n);while(g==1);
    if(g!=n)rr g;
  }
}

u1 inner_factorize(ll n){//n<2^{63}
  if(n<=1)rr{};
  ll d=pollard_rho<montgomery64>(n);
  if(d==n)rr{d};
  rr inner_factorize(d)^inner_factorize(n/d);
}

cls factorize(ll n){//n<2^{63}
  rr rce(inner_factorize(n));
}

u1 divisors(ll n){//n<2^{63}．10^6くらいまではnaiveの方が高速
  cls fa=factorize(n);
  ll K=len(fa);
  
  u1 res;
  deque<cl>q{{0,1}};
  wh(len(q)){
    auto[i,d]=pof(q);
    
    if(i==K){
      res.eb(d);
      continue;
    }
    
    fo(t,fa[i].b+1){
      q.eb(i+1,d);
      d*=fa[i].a;
    }
  }
  rr srt(res);
}

I(J A,J B=A,J C=A)struct tr{
  A a;B b;C c;tr():a(),b(),c(){}tr(A a,B b,C c):a(a),b(b),c(c){}bo O==(cs tr&t)cs{rr a==t.a&&b==t.b&&c==t.c;}
  bo O<(cs tr&t)cs{rr a!=t.a?a<t.a:b!=t.b?b<t.b:c<t.c;}friend is&O>>(is&i,tr&t){rr i>>t.a>>t.b>>t.c;}
  bo O>(cs tr&t)cs{rr a!=t.a?a>t.a:b!=t.b?b>t.b:c>t.c;}friend os&O<<(os&o,cs tr&t){rr o<<t.a<<sp<<t.b<<sp<<t.c;}
};uu tl=tr<ll>;uu tls=v1<tl>;

int main(){ll T=1;fo(t,T)solve();}
vo solve(){
  LL(N);
  tls res;
  fo(x,sqr(N/3)+1){
    u1 div=divisors(N+sq(x));
    
    fo(i,len(div)){
      ll Y=div[i],Z=div[len(div)-1-i];
      ll y=Y-x,z=Z-x;
      if(x<=y&&y<=z){
        if(x==y){
          if(y==z)res.eb(x,x,x);
          else{
            res.eb(x,x,z);
            res.eb(x,z,x);
            res.eb(z,x,x);
          }
        }else{
          if(y==z){
            res.eb(x,y,y);
            res.eb(y,x,y);
            res.eb(y,y,x);
          }else{
            res.eb(x,y,z);
            res.eb(x,z,y);
            res.eb(y,x,z);
            res.eb(y,z,x);
            res.eb(z,x,y);
            res.eb(z,y,x);
          }
        }
      }
    }
  }
  pp(len(res));
  fe(res,e)pp(e);
}