結果
| 問題 | No.2620 Sieve of Coins |
| ユーザー |
👑  Nachia
|
| 提出日時 | 2024-01-15 01:01:19 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 86 ms / 2,000 ms |
| コード長 | 6,024 bytes |
| コンパイル時間 | 1,633 ms |
| コンパイル使用メモリ | 113,496 KB |
| 最終ジャッジ日時 | 2025-02-18 20:08:06 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 53 |
ソースコード
// 00:32:43#ifdef NACHIA#define _GLIBCXX_DEBUG#else#define NDEBUG#endif#include <iostream>#include <string>#include <vector>#include <algorithm>#include <utility>#include <queue>#include <array>#include <cmath>#include <cassert>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 * 2 + 10);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 nachianamespace nachia{template<class Elem>void DivisorZeta(std::vector<Elem>& a){using namespace prime_sieve_explicit_internal;int n = a.size() - 1;for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i*d] += a[i];}template<class Elem>void DivisorInvZeta(std::vector<Elem>& a){using namespace prime_sieve_explicit_internal;int n = a.size() - 1;for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i] += a[i*d];}template<class Elem>void DivisorMobius(std::vector<Elem>& a){using namespace prime_sieve_explicit_internal;int n = a.size() - 1;for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i*d] -= a[i];}template<class Elem>void DivisorInvMobius(std::vector<Elem>& a){using namespace prime_sieve_explicit_internal;int n = a.size() - 1;for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i] -= a[i*d];}template<class Elem>std::vector<Elem> GcdConvolution(std::vector<Elem> a, std::vector<Elem> b){assert(a.size() == b.size());assert(1 <= a.size());DivisorInvZeta(a);DivisorInvZeta(b);for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];DivisorInvMobius(a);return a;}template<class Elem>std::vector<Elem> LcmConvolution(std::vector<Elem> a, std::vector<Elem> b){assert(a.size() == b.size());assert(1 <= a.size());DivisorZeta(a);DivisorZeta(b);for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];DivisorMobius(a);return a;}}using namespace std;using i64 = long long;using u64 = unsigned long long;#define rep(i,n) for(i64 i=0; i<(i64)(n); i++)#define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--)const i64 INF = 1001001001001001001;const char* yn(bool x){ return x ? "Yes" : "No"; }template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }template<typename A> using nega_queue = priority_queue<A,vector<A>,greater<A>>;int main(){i64 L, N; cin >> L >> N;vector<i64> A(N); rep(i,N) cin >> A[i];vector<vector<i64>> pow23(1);pow23[0].push_back(1);while(pow23.back()[0] * 3 <= L){i64 l = pow23.back()[0];pow23.emplace_back(1);pow23.back()[0] = l * 3;}for(auto& a : pow23) while(a.back() * 2 <= L) a.push_back(a.back() * 2);int H = (int)max(pow23.size(), pow23[0].size());vector<vector<int>> coins(H, vector<int>(H));for(i64 a : A){int p2 = 0; while(a%2 == 0){ p2++; a /= 2; }int p3 = 0; while(a%3 == 0){ p3++; a /= 3; }coins[p3][p2] = 1;}rep(y,H) rep(x,H) if(coins[y][x]){for(int yy=y; yy<H; yy++) for(int xx=x; xx<H; xx++) if(xx != x || yy != y) coins[yy][xx] ^= 1;}i64 ans = 0;rep(y,H) rep(x,H) if(coins[y][x]) if(y<(int)pow23.size()) if(x<(int)pow23[y].size()){i64 mp = pow23[y][x];i64 smallL = L / mp;i64 sz = 1; while((sz+1)*(sz+1) <= smallL) sz++;vector<i64> Q(sz+1);for(i64 i=1; i<=sz; i++) if(i%2 != 0 && i%3 != 0){Q[i] += smallL / (i * i);Q[i] -= smallL / (i * i) / 2;Q[i] -= smallL / (i * i) / 3;Q[i] += smallL / (i * i) / 6;}nachia::DivisorInvMobius(Q);ans += Q[1];}cout << ans << endl;return 0;}