結果

問題 No.2358 xy+yz+zx=N
ユーザー 蜜蜂
提出日時 2023-06-23 21:40:11
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 79 ms / 2,000 ms
コード長 5,296 bytes
コンパイル時間 2,681 ms
コンパイル使用メモリ 197,480 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-01 17:27:40
合計ジャッジ時間 3,593 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 10
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function 'std::vector<long long int> divisor(std::vector<std::pair<long long int, int> >&)':
main.cpp:209:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  209 |     auto [a,b]=fac[i];
      |          ^
main.cpp: In function 'int main()':
main.cpp:257:12: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  257 |   for(auto [x,y,z]:v){
      |            ^
main.cpp:268:12: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  268 |   for(auto [x,y,z]:ans){
      |            ^

ソースコード

diff #
プレゼンテーションモードにする

// g++ 1.cpp -std=c++17 -O2 -I .
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
 
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vld = vector<ld>;
using vvld = vector<vld>;
using vst = vector<string>;
using vvst = vector<vst>;
 
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define pq_big(T) priority_queue<T,vector<T>,less<T>>
#define pq_small(T) priority_queue<T,vector<T>,greater<T>>
#define all(a) a.begin(),a.end()
#define rep(i,start,end) for(ll i=start;i<(ll)(end);i++)
#define per(i,start,end) for(ll i=start;i>=(ll)(end);i--)
#define uniq(a) sort(all(a));a.erase(unique(all(a)),a.end())
//https://atcoder.jp/contests/arc122/submissions/24436348
//https://judge.yosupo.jp/submission/53811
//https://yukicoder.me/submissions/680896
//https://atcoder.jp/contests/abc180/submissions/24436784
#include <cassert>
#include <cmath>
#include <initializer_list>
#include <random>
#include <iostream>
#include <algorithm>
std::mt19937_64 mt{std::random_device{}()};
long long rnd(long long n) { return std::uniform_int_distribution<long long>(0, n-1)(mt); }
bool is_prime(long long x){
  using u128=__uint128_t;
  
  if(x==2||x==3||x==5||x==7)return true;
  if(x%2==0||x%3==0||x%5==0||x%7==0)return false;
  if(x<121){
    return x>1;
  }
  long long d = (x-1) >> __builtin_ctzll(x-1);
  long long one=1,minus_one=x-1;
  auto pow = [](long long x,long long n,long long mod){
    u128 res;
    x%=mod;
    if(n==0){
      res=1;return res;
    }
    res=1;
    u128 now=x;
    for(;n;n>>=1,now=(now*now)%mod){
      if(n&1){
        res=res*now%mod;
      }
    }
    return res;
  };
  auto ok = [&](long long a){
    auto y=pow(a,d,x);
    long long t=d;
    while(y!=one&&y!=minus_one&&t!=x-1){
      y=y*y%x;
      t<<=1;
    }
    if(y!=minus_one&&t%2==0)return false;
    return true;
  };
  if(x<(1ull<<32)){
    for(long long a:{2,7,61}){
      if(!ok(a))return false;
    }
  }
  else{
    for(long long a:{2,325,9375,28178,450775,9780504,1795265022}){
      if(x<=a)return true;
      if(!ok(a))return false;
    }
  }
  return true;
}
long long GCD(long long a,long long b){
  if(b==0){
    return a;
  }
  else{
    return GCD(b,(a%b));
  }
}
long long rho(long long n,long long c){
  using u128=__uint128_t;
  assert(n>1);
  long long cc=c;
  auto f = [&](long long x){
    long long res;
    res=(((u128)x)*x+cc)%n;
    return res;
  };
  long long x=1,y=2,z=1,q=1;
  long long g=1;
  long long m= 1LL<<((64-__builtin_ctzll(n))/5);
  for(long long r=1;g==1;r<<=1){
    x=y;
    for(int i=0;i<r;i++){
      y=f(y);
    }
    for(long long k=0;k<r&&g==1;k+=m){
      z=y;
      for(long long i=0;i<std::min(m,r-k);i++){
        y=f(y);
        long long w=(x-y)%n;
        if(w<0)w+=n;
        q=((u128)q*w)%n;
      }
      g=GCD(q,n);
    }
  }
  if(g==n){
    do{
      z=f(z);
      long long w=(x-z)%n;
      if(w<0)w+=n;
      g=GCD(w,n);
    }while(g==1);
  }
  return g;
}
long long prime_factor(long long n){
  assert(n>1);
  if(is_prime(n)) return n;
  for(int i=0;i<100;i++){
    long long m=rho(n,rnd(n));
    if(is_prime(m))return m;
    n=m;
  }
  std::cerr<<"failed\n";
  assert(false);
  return -1;
}
//nを素因数分解 {素因数,個数} で管理 (1は空配列)
std::vector<std::pair<long long,int>> factor(long long n){
  static std::vector<std::pair<long long,int>> res;
  res.clear();
  for(long long i=2;i<=100&&i*i<=n;++i){
    if(n%i==0){
      int cnt=0;
      do{
        cnt++;
        n/=i;
      }while(n%i==0);
      res.emplace_back(i,cnt);
    }
  }
  while(n>1){
    long long p=prime_factor(n);
    int cnt=0;
    do{
      cnt++;
      n/=p;
    }while(n%p==0);
    res.emplace_back(p,cnt);
  }
  std::sort(res.begin(),res.end());
  return res;
}
//nの約数配列(昇順) 引数はfactor(n)
std::vector<long long> divisor(std::vector<std::pair<long long,int>> &fac){
  int sz=fac.size();
  //n=1の時
  if(sz==0){
    return {1};
  }
  
  std::vector<std::vector<long long>> x(sz);
  for(int i=0;i<sz;i++){
    auto [a,b]=fac[i];
    long long now=1;
    for(int j=0;j<=b;j++){
      x[i].emplace_back(now);
      now*=a;
    }
  }
  
  std::vector<std::vector<long long>> res(sz);
  res[0]=x[0];
  
  for(int i=1;i<sz;i++){
    for(int j=0;j<res[i-1].size();j++){
      for(int k=0;k<x[i].size();k++){
        res[i].emplace_back(res[i-1][j]*x[i][k]);
      }
    }
  }
  std::sort(res[sz-1].begin(),res[sz-1].end());
  return res[sz-1];
}
int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  ll n;cin>>n;
  // x <= y <= z
  // yz + xy + xz = n
  // (y+x)(z+x) = n + x^2
  vector<tuple<ll,ll,ll>> v;
  rep(i,0,5000){
    if(i*i>n)break;
    auto f=factor(n+i*i);
    auto d=divisor(f);
    for(ll d2:d){
      ll d3=(n+i*i)/d2;
      ll y=d2-i,z=d3-i;
      if(i<=y&&y<=z){
        v.emplace_back(i,y,z);
      }
    }
  }
  vector<tuple<ll,ll,ll>> ans;
  for(auto [x,y,z]:v){
    ans.emplace_back(x,y,z);
    ans.emplace_back(x,z,y);
    ans.emplace_back(y,x,z);
    ans.emplace_back(y,z,x);
    ans.emplace_back(z,x,y);
    ans.emplace_back(z,y,x);
  }
  uniq(ans);
  cout<<ans.size()<<endl;
  for(auto [x,y,z]:ans){
    cout<<x<<" "<<y<<" "<<z<<endl;
  }
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0