Submission #217032

#TimeUsernameProblemLanguageResultExecution timeMemory
217032Blagojce새로운 문제 (COCI19_akvizna)C++11
65 / 130
1597 ms13040 KiB
#include <bits/stdc++.h> #define fr(i, n, m) for(int i = (n); i < (m); i ++) #define pb push_back #define st first #define nd second #define pq priority_queue #define all(x) begin(x),end(x) using namespace std; typedef long long ll; typedef long double ld; typedef pair<int,int> pii; ll const inf = 1e9; ll const mod = 1e9 + 7; ld const eps = 1e-9; struct line{ int K; ld m, b; bool isq; ld x; ld eval(ld X) const{ return X * m + b; } ld intersect(const line &l) const{ return 1.0 * (l.b - b) / (m - l.m); } bool operator < (const line &l) const{ if(l.isq) return x < l.x; else return m > l.m; } }; set<line> hull; typedef set<line>::iterator iter; bool cPrev(iter it){ return it != hull.begin(); } bool cNext(iter it){ return it != hull.end() && next(it) != hull.end(); } bool bad(const line &l1, const line &l2, const line &l3){ return l1.intersect(l3) <= l1.intersect(l2); } bool bad(iter it){ return cPrev(it) && cNext(it) && bad(*prev(it), *it, *next(it)); } iter update(iter it){ if(!cPrev(it)) return it; ld x = prev(it)->intersect(*it); line l = *it; l.x = x; it = hull.erase(it); return hull.insert(it, l); } void addLine(ld m, ld b, int K){ line l; l.K = K; l.m = m, l.b = b, l.isq = false; l.x = -inf; iter it = hull.lower_bound(l); it = hull.insert(it, l); if(bad(it)){ hull.erase(it); return; } while(cPrev(it) && bad(prev(it))) hull.erase(prev(it)); while(cNext(it) && bad(next(it))) hull.erase(next(it)); it = update(it); if(cPrev(it)) update(prev(it)); if(cNext(it)) update(next(it)); } pair<int,ld> query(ld x){ line q; q.x = x; q.isq = true; iter it = --hull.lower_bound(q); int K = it->K; ld ret = it->eval(x); it ++; if(it != hull.end()){ ld ret2 = it->eval(x); if(abs(ret - ret2) < eps){ K = min(K, it->K); } } return {K, ret}; } ld ANS; int calculate(ld lambda, int N){ hull.clear(); addLine(0, 0, 0); fr(i, 1, N){ pair<int, ld> best = query(-1.0/i); ld currans = -best.nd + 1 - lambda; addLine(-i, -currans, best.st + 1); } pair<int, ld> best = query(-1.0/N); ANS = -best.nd + 1 - lambda; return best.st + 1; } ld solve(int N, int K){ ld l = 0, r = 1; ld best = 0; fr(j, 0, 30){ ld mid = (l + r) / 2; int i = calculate(mid, N); if(i <= K){ best = mid; r = mid-eps; } else{ l = mid + eps; } } calculate(best, N); return ANS + K*best; } int main() { int N, K; cin >> N >> K; cout << fixed<<setprecision(9) <<solve(N, K)<<endl; return 0; }
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