結果
| 問題 | No.2262 Fractions |
| ユーザー |
 woodywoody
|
| 提出日時 | 2023-04-18 02:29:08 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 10,963 bytes |
| コンパイル時間 | 4,404 ms |
| コンパイル使用メモリ | 241,252 KB |
| 実行使用メモリ | 10,048 KB |
| 最終ジャッジ日時 | 2024-10-13 00:56:07 |
| 合計ジャッジ時間 | 69,048 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 26 TLE * 19 |
ソースコード
#include<bits/stdc++.h>#include<atcoder/all>#define rep(i,b) for(int i=0;i<b;i++)#define rrep(i,b) for(int i=b-1;i>=0;i--)#define rep1(i,b) for(int i=1;i<b;i++)#define repx(i,x,b) for(int i=x;i<b;i++)#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)#define fore(i,a) for(auto i:a)#define fore1(i,a) for(auto &i:a)#define rng(x) (x).begin(), (x).end()#define rrng(x) (x).rbegin(), (x).rend()#define sz(x) ((int)(x).size())#define pb push_back#define fi first#define se second#define pcnt __builtin_popcountllusing namespace std;using namespace atcoder;using ll = long long;using ld = long double;template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}}#define dame { cout << "No" << endl; return;}#define dame1 { cout << -1 << endl; return;}#define cout2(x,y) cout << x << " " << y << endl;#define coutp(p) cout << p.fi << " " << p.se << endl;#define out cout << ans << endl;#define outd cout << fixed << setprecision(20) << ans << endl;#define outm cout << ans.val() << endl;#define outv fore(yans , ans) cout << yans << "\n";#define outdv fore(yans , ans) cout << yans.val() << "\n";#define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}#define coutv2(v) fore(vy , v) cout << vy << "\n";#define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}#define coutvm2(v) fore(vy , v) cout << vy.val() << "\n";using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;using tp = tuple<int ,int ,int>;using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;using mint = modint998244353;//using mint = modint1000000007;//using mint = dynamic_modint<0>;using vm = vector<mint>;using vvm = vector<vector<mint>>;vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}#define yes {cout <<"Yes"<<endl;}#define yesr { cout <<"Yes"<<endl; return;}#define no {cout <<"No"<<endl;}#define nor { cout <<"No"<<endl; return;}const double eps = 1e-10;const ll LINF = 1001002003004005006ll;const int INF = 1001001001;#ifdef MY_LOCAL_DEBUG#define show(x) cerr<<#x<<" = "<<x<<endl#define showp(p) cerr<<#p<<" = "<<p.fi<<" : "<<p.se<<endl#define show2(x,y) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<endl#define show3(x,y,z) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<" : "<<#z<<" = "<<z<<endl#define show4(x,y,z,x2) cerr<<#x<<" = "<<x<<" : "<<#y<<" = "<<y<<" : "<<#z<<" = "<<z<<" : "<<#x2<<" = "<<x2<<endl#define test(x) cout << "test" << x << endl#define showv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}#define showv2(v) fore(vy , v) cout << vy << "\n";#define showvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}#define showvm2(v) fore(vy , v) cout << vy.val() << "\n";#else#define show(x)#define showp(p)#define show2(x,y)#define show3(x,y,z)#define show4(x,y,z,x2)#define test(x)#define showv(v)#define showv2(v)#define showvm(v)#define showvm2(v)#endifstruct Sieve {int n;vector<int> f, primes;Sieve(int n=1):n(n), f(n+1) { //初期化、f[x] = (xの最も小さい素因数)f[0] = f[1] = -1;for (ll i = 2; i <= n; ++i) {if (f[i]) continue;primes.push_back(i);f[i] = i;for (ll j = i*i; j <= n; j += i) {if (!f[j]) f[j] = i;}}}bool isPrime(int x) { return f[x] == x;} //素数判定vector<int> factorList(int x) {//素因数分解、xの素因数を小さいものから個数分列挙vector<int> res;while (x != 1) {res.push_back(f[x]);x /= f[x];}return res;}vector<pii> factor(int x) {//素因数分解その２、xの素因数を小さいものから(素因数、個数)の形で列挙vector<int> fl = factorList(x);if (fl.size() == 0) return {};vector<pii> res(1, pii(fl[0], 0));for (int p : fl) {if (res.back().first == p) {res.back().second++;} else {res.emplace_back(p, 1);}}return res;}vector<pli> factor(ll x) {//素因数分解その２-２、xがllの場合vector<pli> res;for (int p : primes) {int y = 0;while (x%p == 0) x /= p, ++y;if (y != 0) res.emplace_back(p,y);}if (x != 1) res.emplace_back(x,1);return res;}ll totient(ll x){ll den = 1,num = 1;if (x<=n){vpii v = factor((int)x);fore(y , v){den *= y.fi;num *= (y.fi-1);}}else{vpli v = factor(x);fore(y , v){den *= y.fi;num *= (y.fi-1);}}assert(x%den==0);ll ret = x/den*num;return ret;}///////////////// 以下、約数/倍数 ゼータ・メビウス変換 ////////////////// 以下、約数変換template <typename T>void div_zeta_trans(vector<T> &a) {int n = sz(a)-1;fore(p, primes) {if (p > n) break;for (int i = 1; i * p <= n; ++i) a[i * p] += a[i];}}template <typename T>void div_mobius_trans(vector<T> &a) {int n = sz(a)-1;fore(p, primes) {if (p > n) break;for (int i = n / p; i > 0; --i) a[i * p] -= a[i];}}template <typename I, typename T>void div_zeta_trans(map<I, T> &a) {for (auto p = a.rbegin(); p != a.rend(); p++) {fore(y, a) {if (p->fi == y.fi) break;if (p->fi % y.fi == 0) p->se += y.se;}}}template <typename I, typename T>void div_mobius_trans(map<I, T> &a) {fore(y, a) {for (auto p = a.rbegin(); p != a.rend(); p++) {if (y.fi == p->fi) break;if (p->fi % y.fi == 0) p->se -= y.se;}}}// 以下、倍数変換template <typename T>void mul_zeta_trans(vector<T> &a) {int n = sz(a)-1;fore(p, primes) {if (p > n) break;for (int i = n / p; i > 0; --i) a[i] += a[i * p];}}template <typename T>void mul_mobius_trans(vector<T> &a) {int n = sz(a)-1;fore(p, primes) {if (p > n) break;for (int i = 1; i * p <= n; ++i) a[i] -= a[i * p];}}template <typename I, typename T>void mul_zeta_trans(map<I, T> &a) {fore(y, a) {for (auto p = a.rbegin(); p != a.rend(); p++) {if (y.fi == p->fi) break;if (p->fi % y.fi == 0) y.se += p.se;}}}template <typename I, typename T>void mul_mobius_trans(map<I, T> &a) {for (auto p1 = a.rbegin(); p1 != a.rend(); p1++) {for (auto p2 = a.rbegin(); p2 != p1; p2++) {if (p2->fi % p1->fi == 0) p1->se += p2.se;}}}} sieve(1e6);// エラストテネスの篩// .primes : n以下の素数を小さい順で格納しているベクトル。// .isPrime(int x) : xの素数判定。boolで返す// .factorList(int x) : xの素因数分解。xの素因数を小さいものから個数分列挙。vector<int>で返す。// .factor(int x) : 素因数分解その２、xの素因数を小さいものからpair<int int>{素因数、個数}の形で列挙。vector<pii>で返す。xはllでもok。// 宣言方法 : n=1e6(デフォルト)で初期化している。// 注意点 : factorList、factorは呼び出し毎に約数個分の計算時間がかかってしまうため、何度も呼び出すときは予め別の配列に格納しておくこと。// 約数/倍数 ゼータ・メビウス変換// f = Σg : g → f をゼータ変換、f → g をメビウス変換// map<I,T>はI が idx T が 関数値void solve(){ll n,k; cin>>n>>k;ld l = 0,u = n+2;ll cnt = 0;rep1(i,n+1) cnt += sieve.totient(i);cnt--;if (2*cnt+1<k) dame1;if (cnt+1==k){cout << "1/1" << endl;return;}ll temp = k;if (k>cnt) k = 2*cnt+2-k;auto check = [&](ld mid)->bool{ll cnt = 0;vl g(n+1);auto f = [&](int a,int b)->bool{assert(b>0);ld p = (ld)b/a;return (p<=mid);};repx(i,2,n+1){int l=1,u=i-1;if (f(i,u)){g[i] = u;continue;}if (!f(i,l)) continue;while(u-l>1){int mi = (l+u)/2;if (f(i,mi)) l = mi;else u = mi;}g[i] = l;}sieve.div_mobius_trans(g);cnt = sumv(g);return (cnt>=k);};while(u-l>1e-13){ld mid = (u+l) / 2;if (check(mid)) u = mid;else l = mid;}pii ans;ld mn = 1e9;rep1(i,n+1){auto f = [&](int a,int b)->bool{assert(b>0);ld p = (ld)b/a;return (p<=u);};auto upd = [&](int x)->void{if (x>n) return;ld p = (ld)x/i;p = abs(p-u);if (chmin(mn,p)){ans = {i,x};}return;};int li=1,ui=n;if (!f(i,li)){upd(li);continue;}while(ui-li>1){int mid = (li+ui)/2;if (f(i,mid)) li = mid;else ui = mid;}upd(li);upd(li+1);}ll d = gcd(ans.fi,ans.se);ans.fi /= d;ans.se /= d;if (temp>cnt) swap(ans.fi,ans.se);string s;s += to_string(ans.se);s += '/';s += to_string(ans.fi);cout << s << endl;return;}int main(){ios::sync_with_stdio(false);cin.tie(0);int t = 1;cin>>t;rep(i,t){solve();}return 0;}