結果

問題 No.2244 Integer Complete
ユーザー 👑 Nachia
提出日時 2023-03-09 03:52:33
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 9 ms / 2,000 ms
コード長 4,682 bytes
コンパイル時間 1,101 ms
コンパイル使用メモリ 88,576 KB
最終ジャッジ日時 2025-02-11 07:03:24
ジャッジサーバーID
(参考情報)
judge1 / judge4
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ファイルパターン 結果
other AC * 60
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ソースコード

diff #
プレゼンテーションモードにする

#line 1 "Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <atcoder/modint>
#line 2 "nachia\\math\\prime-sieve-explicit.hpp"
#line 5 "nachia\\math\\prime-sieve-explicit.hpp"
#include <cassert>
#line 7 "nachia\\math\\prime-sieve-explicit.hpp"
namespace nachia{
namespace prime_sieve_explicit_internal{
std::vector<bool> isprime = { false }; // a[x] := isprime(2x+1)
void CalcIsPrime(int z){
if((int)isprime.size() *2+1 < z+1){
int new_z = isprime.size();
while(new_z*2+1 < z+1) new_z *= 2;
z = new_z-1;
isprime.resize(z+1, true);
for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){
for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false;
}
}
}
std::vector<int> prime_list = {2};
int prime_list_max = 0;
void CalcPrimeList(int z){
while((int)prime_list.size() < z){
if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1);
for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
if(isprime[p]) prime_list.push_back(p*2+1);
}
prime_list_max = isprime.size() - 1;
}
}
void CalcPrimeListUntil(int z){
if(prime_list_max < z){
CalcIsPrime(z);
for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
if(isprime[p]) prime_list.push_back(p*2+1);
}
prime_list_max = isprime.size() - 1;
}
}
}
bool IsprimeExplicit(int n){
using namespace prime_sieve_explicit_internal;
if(n == 2) return true;
if(n % 2 == 0) return false;
CalcIsPrime(n);
return isprime[(n-1)/2];
}
int NthPrimeExplicit(int n){
using namespace prime_sieve_explicit_internal;
CalcPrimeList(n);
return prime_list[n];
}
int PrimeCountingExplicit(int n){
using namespace prime_sieve_explicit_internal;
if(n < 2) return 0;
CalcPrimeListUntil(n);
auto res = std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin();
return (int)res;
}
// [l, r)
std::vector<bool> SegmentedSieveExplicit(long long l, long long r){
assert(0 <= l); assert(l <= r);
long long d = r - l;
if(d == 0) return {};
std::vector<bool> res(d, true);
for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){
long long il = (l+p-1)/p, ir = (r+p-1)/p;
if(il <= p) il = p;
for(long long i=il; i<ir; i++) res[i*p-l] = false;
}
if(l < 2) for(long long p=l; p<2 && p<r; p++) res[l-p] = false;
return res;
}
} // namespace nachia
#line 8 "Main.cpp"
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;
using Modint = atcoder::static_modint<998244353>;
int main(){
// n p in range (n^2, (n+1)^2) p
// 10^9 281 ( Wikipedia )
int N, M; cin >> N >> M;
vector<int> A(40000);
vector<int> B(40000);
rep(i,N){ int a; cin >> a; A[a] = 1; }
rep(i,M){ int a; cin >> a; B[a] = 1; }
if(A[1] == 0 || B[1] == 0){ cout << "1\n"; return 0; }
i64 mex = 1;
while(A[mex] == 1 || B[mex]) mex++;
i64 ans = INF;
i64 ansmin = mex * mex;
auto tab = nachia::SegmentedSieveExplicit(mex*mex, (mex+1)*(mex+1));
rep(i,tab.size()) if(tab[i]){ ans = mex*mex+i; break; }
// ans
// ans - ansmin <= 281
// ans <= 9x10^8
vector<int> Flag(ans - ansmin + 1);
vector<i64> sq(40000);
rep(i,40000) sq[i] = (i64)i * i;
auto checkPlayable = [&](i64 a, i64 b) -> void {
int a1 = upper_bound(sq.begin(), sq.end(), a) - sq.begin(); a1--;
int b1 = upper_bound(sq.begin(), sq.end(), b) - sq.begin(); b1--;
// if playable
if((A[a1] && B[b1]) || (A[b1] && B[a1])) Flag[a*b-ansmin] = 1;
};
for(i64 d=2; d*d<=ans; d++){
// ansmin <= d * e < ans
i64 el = (ansmin - 1) / d + 1;
i64 er = (ans - 1) / d;
for(i64 e=el; e<=er; e++) checkPlayable(d, e);
}
for(int i=0; i<(int)Flag.size(); i++) if(Flag[i] == 0){ ans = ansmin + i; break; }
cout << ans << '\n';
return 0;
}
struct ios_do_not_sync{
ios_do_not_sync(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
}
} ios_do_not_sync_instance;
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