結果

問題 No.2795 Perfect Number
コンテスト
ユーザー 矢澤式WINTER
提出日時 2024-06-28 21:28:03
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,732 bytes
コンパイル時間 2,900 ms
コンパイル使用メモリ 255,868 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-06-28 21:28:07
合計ジャッジ時間 3,909 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 35
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
/*/
#include <atcoder/all>
using namespace atcoder;
#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector,fast-math")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#pragma GCC target("avx,avx2,fma")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
//*/
#define rep(i,n) for(int i=0;i<n;i++)
#define Rep(i,a,b) for(int i=a;i<b;i++)
#define ALL(x) (x).begin(),(x).end()
#define dbgv(x); for(auto now : x) cout << now << " "; cout << endl;
//using P = pair<int,int>;
using ll = long long;
using ull = unsigned long long;
//*/
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<int> vint;
random_device rnd;
mt19937 rng(rnd());

namespace nachia{

bool IsPrime(unsigned long long x) noexcept {
    if(x <= 1) return false;
    if(x % 2 == 0) return x == 2;
    using u64 = unsigned long long;
    using u128 = __uint128_t;
    u64 d = x-1;
    int s = 0;
    int q = 63;
    while(!(d&1)){ d >>= 1; s++; }
    while(!(d >> q)) q--;
    u64 r = x; for(int t=0; t<6; t++) r*=2-r*x;
    u128 n2 = -(u128)x % x;
    auto red = [=](u128 t) noexcept -> u64 {
        t = (t + (u128)((u64)t*-r)*x) >> 64;
        return (t >= x) ? t-x : t;
    };
    u64 one = red(n2);
    for(u64 base : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }){
        if(base%x==0) continue;
        u64 a = base = red(base%x*n2);
        for(int e=q-1; e>=0; e--){ a = red((u128)a*a); if((d>>e)&1) a = red((u128)a*base); }
        if(a == one) continue;
        for(int t=1; t<s&&a!=x-one; t++) a = red((u128)a*a);
        if(a != x-one) return false;
    }
    return true;
}

} // namespace nachia
#line 1 "nachia\\misc\\bit-operations.hpp"

#include <vector>
#include <algorithm>


namespace nachia{

    int Popcount(unsigned long long c) noexcept {
    #ifdef __GNUC__
        return __builtin_popcountll(c);
    #else
        c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
        c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
        c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
        c = (c * (~0ull/257)) >> 56;
        return c;
    #endif
    }

    // please ensure x != 0
    int MsbIndex(unsigned long long x) noexcept {
    #ifdef __GNUC__
        return 63 - __builtin_clzll(x);
    #else
        int res = 0;
        for(int d=32; d>=0; d>>=1) if(x >> d){ res |= d; x >>= d; }
        return res;
    #endif
    }

    // please ensure x != 0
    int LsbIndex(unsigned long long x) noexcept {
    #ifdef __GNUC__
        return __builtin_ctzll(x);
    #else
        return msb_idx(x & -x);
    #endif
    }

}

#line 5 "nachia\\math\\factorize.hpp"
#include <utility>

namespace nachia{

std::vector<std::pair<unsigned long long, int>> Factorize(unsigned long long x){
    if(x == 1) return {};
    if(IsPrime(x)) return {{x,1}};
    using u64 = unsigned long long;
    using u128 = __uint128_t;
    u64 X = x;
    std::vector<u64> p;
    for(u64 i=2; i<100; i+=1+i%2) if(x%i==0){ p.push_back(i); while(x%i==0) x/=i; }
    u64 r=1; u128 n2=1;
    auto updX = [&](){
        r = x; for(int t=0; t<6; t++) r*=2-r*x;
        n2 = -(u128)x % x;
    };
    auto red = [&](u128 t) noexcept -> u64 {
        t = (t + (u128)((u64)t*-r)*x) >> 64;
        return (t >= x) ? t-x : t;
    };
    auto mult = [&](u64 a, u64 b) noexcept { return red((u128)red((u128)a*n2)*b); };
    auto f = [&](u64 a) noexcept -> u64 { return red((u128)a*a+1); };
    auto gcd = [](u64 a, u64 b) noexcept {
        if(!a || !b) return a|b;
        int q = LsbIndex(a|b);
        b >>= LsbIndex(b);
        a >>= LsbIndex(a);
        while(a!=b){
            if(a<b){ b-=a; b>>=LsbIndex(b); }
            else{ a-=b; a>>=LsbIndex(a); }
        }
        return a<<q;
    };
    static u64 v = 7001;
    p.push_back(x);
    for(int pi=p.size()-1; pi<(int)p.size(); pi++) while(p[pi] != 1 && !IsPrime(p[pi])){
        x = p[pi]; updX();
        while(p[pi] == x){
            v^=v<<13; v^=v>>7; v^=v<<17; // Xorshift https://www.jstatsoft.org/article/download/v008i14/916
            u64 a = v%x, b = f(a);
            u64 buf = a, sz = 1, nx = 10;
            while(true){
                while(nx != sz && a != b){
                    buf = mult(buf, a<=b?b-a:a-b); sz++;
                    a = f(a); b = f(f(b));
                }
                u64 g = gcd(buf, x);
                if(g != 1){
                    while(p[pi] % g == 0) p[pi] /= g;
                    p.push_back(g);
                    break;
                }
                if(a == b) break;
                nx = sz * 3 / 2;
            }
        }
    }
    std::vector<std::pair<u64, int>> res;
    for(u64 q : p) if(q != 1){
        int e=0; while(X%q == 0){ e++; X/=q; }
        if(e) res.push_back({ q, e });
    }
    return res;
}

unsigned long long Totient(unsigned long long x){
    auto F = Factorize(x);
    for(auto f : F) x -= x / f.first;
    return x;
}

}

void solve(){
  ull n; cin >> n;
  auto v = nachia::Factorize(n);
  auto f = [&](pair<ull,int> &p)->ull{
    ull now = 0,base = 1;
    for(int x = 0;x <= p.second;x++){
      now += base;
      base *= p.first;
    }
    return now;
  };
  ull s = 1;
  for(auto p : v){
    ull now = f(p);
    cerr << p.first << " " << p.second << " " << now << endl; 
    if(s > 2*n/now){
      cout << "No\n";
      return;
    }
    s *= now;
  }
  if(s == 2*n) cout << "Yes\n";
  else cout << "No\n";
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int t = 1; //cin >> t;
  rep(testcase,t) solve();
}
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