Submission #994547
Source Code Expand
#include<bits/stdc++.h> using namespace std; #define int __int128 class ConvexHullDynamic { typedef long long coef_t; typedef long long coord_t; typedef long long val_t; /* * Line 'y=a*x+b' represented by 2 coefficients 'a' and 'b' * and 'xLeft' which is intersection with previous line in hull(first line has -INF) */ private: struct Line { coef_t a, b; double xLeft; enum Type { line, maxQuery, minQuery } type; coord_t val; explicit Line(coef_t aa = 0, coef_t bb = 0) : a(aa), b(bb), xLeft(-INFINITY), type(Type::line), val(0) {} val_t valueAt(coord_t x) const { return a * x + b; } friend bool areParallel(const Line &l1, const Line &l2) { return l1.a == l2.a; } friend double intersectX(const Line &l1, const Line &l2) { return areParallel(l1, l2) ? INFINITY : 1.0 * (l2.b - l1.b) / (l1.a - l2.a); } bool operator<(const Line &l2) const { if(l2.type == line) return this->a < l2.a; if(l2.type == maxQuery) return this->xLeft < l2.val; if(l2.type == minQuery) return this->xLeft > l2.val; } }; private: bool isMax; //whether or not saved envelope is top(search of max value) std::set< Line > hull; //envelope itself private: /* * INFO: Check position in hull by iterator * COMPLEXITY: O(1) */ bool hasPrev(std::set< Line >::iterator it) { return it != hull.begin(); } bool hasNext(std::set< Line >::iterator it) { return it != hull.end() && std::next(it) != hull.end(); } /* * INFO: Check whether line l2 is irrelevant * NOTE: Following positioning in hull must be true * l1 is next left to l2 * l2 is right between l1 and l3 * l3 is next right to l2 * COMPLEXITY: O(1) */ bool irrelevant(const Line &l1, const Line &l2, const Line &l3) { return intersectX(l1, l3) <= intersectX(l1, l2); } bool irrelevant(std::set< Line >::iterator it) { return hasPrev(it) && hasNext(it) && (isMax && irrelevant(*std::prev(it), *it, *std::next(it)) || !isMax && irrelevant(*std::next(it), *it, *std::prev(it))); } /* * INFO: Updates 'xValue' of line pointed by iterator 'it' * COMPLEXITY: O(1) */ std::set< Line >::iterator updateLeftBorder(std::set< Line >::iterator it) { if(isMax && !hasPrev(it) || !isMax && !hasNext(it)) return it; double val = intersectX(*it, isMax ? *std::prev(it) : *std::next(it)); Line buf(*it); it = hull.erase(it); buf.xLeft = val; it = hull.insert(it, buf); return it; } public: explicit ConvexHullDynamic(bool isMax) : isMax(isMax) {} /* * INFO: Adding line to the envelope * Line is of type 'y=a*x+b' represented by 2 coefficients 'a' and 'b' * COMPLEXITY: Adding N lines(N calls of function) takes O(N*log N) time */ void addLine(coef_t a, coef_t b) { //find the place where line will be inserted in set Line l3 = Line(a, b); auto it = hull.lower_bound(l3); //if parallel line is already in set, one of them becomes irrelevant if(it != hull.end() && areParallel(*it, l3)) { if(isMax && it->b < b || !isMax && it->b > b) it = hull.erase(it); else return; } //try to insert it = hull.insert(it, l3); if(irrelevant(it)) { hull.erase(it); return; } //remove lines which became irrelevant after inserting line while(hasPrev(it) && irrelevant(std::prev(it))) hull.erase(std::prev(it)); while(hasNext(it) && irrelevant(std::next(it))) hull.erase(std::next(it)); //refresh 'xLine' it = updateLeftBorder(it); if(hasPrev(it)) updateLeftBorder(std::prev(it)); if(hasNext(it)) updateLeftBorder(std::next(it)); } /* * INFO: Query, which returns max/min(depends on hull type - see more info above) value in point with abscissa 'x' * COMPLEXITY: O(log N), N-amount of lines in hull */ val_t getBest(coord_t x) const { Line q; q.val = x; q.type = isMax ? Line::Type::maxQuery : Line::Type::minQuery; auto bestLine = hull.lower_bound(q); if(isMax) --bestLine; return bestLine->valueAt(x); } }; signed main() { long long N, A; cin >> N >> A; if(N == 1) { cout << 1 << endl; return (0); } if(N <= A) { cout << N << endl; return (0); } ConvexHullDynamic cht(1); cht.addLine(1, 0); for(long long j = A; true; j++) { if(cht.getBest(j) >= N) { cout << j << endl; return (0); } long long val = cht.getBest(j - A); cht.addLine(val, -val * j); } }
Submission Info
Submission Time | |
---|---|
Task | E - Cookies |
User | ei13333 |
Language | C++14 (GCC 5.4.1) |
Score | 500 |
Code Size | 4849 Byte |
Status | TLE |
Exec Time | 2107 ms |
Memory | 89216 KB |
Judge Result
Set Name | sample | dataset1 | dataset2 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Score / Max Score | 0 / 0 | 500 / 500 | 0 / 500 | ||||||||
Status |
|
|
|
Set Name | Test Cases |
---|---|
sample | sample-01.txt, sample-02.txt, sample-03.txt |
dataset1 | sample-01.txt, 01-01.txt, 01-02.txt, 01-03.txt, 01-04.txt, 01-05.txt, 01-06.txt, 01-07.txt, 01-08.txt, 01-09.txt, 01-10.txt, 01-11.txt, 01-12.txt, 01-13.txt, 01-14.txt, 01-15.txt, 01-16.txt, 01-17.txt, 01-18.txt, 01-19.txt, 01-20.txt, 01-21.txt, 01-22.txt, 01-23.txt, 01-24.txt, 01-25.txt, 01-26.txt |
dataset2 | sample-01.txt, sample-02.txt, sample-03.txt, 01-01.txt, 01-02.txt, 01-03.txt, 01-04.txt, 01-05.txt, 01-06.txt, 01-07.txt, 01-08.txt, 01-09.txt, 01-10.txt, 01-11.txt, 01-12.txt, 01-13.txt, 01-14.txt, 01-15.txt, 01-16.txt, 01-17.txt, 01-18.txt, 01-19.txt, 01-20.txt, 01-21.txt, 01-22.txt, 01-23.txt, 01-24.txt, 01-25.txt, 01-26.txt, 02-01.txt, 02-02.txt, 02-03.txt, 02-04.txt, 02-05.txt, 02-06.txt, 02-07.txt, 02-08.txt, 02-09.txt, 02-10.txt, 02-11.txt, 02-12.txt, 02-13.txt, 02-14.txt, 02-15.txt, 02-16.txt, 02-17.txt, 02-18.txt, 02-19.txt, 02-20.txt, 02-21.txt, 02-22.txt, 02-23.txt, 02-24.txt, 02-25.txt, 02-26.txt, 02-27.txt, 02-28.txt, 02-29.txt, 02-30.txt, 02-31.txt, 02-32.txt, 02-33.txt, 02-34.txt, 02-35.txt, 02-36.txt, 02-37.txt, 02-38.txt, 02-39.txt, 02-40.txt |
Case Name | Status | Exec Time | Memory |
---|---|---|---|
01-01.txt | AC | 3 ms | 256 KB |
01-02.txt | AC | 3 ms | 256 KB |
01-03.txt | AC | 3 ms | 256 KB |
01-04.txt | AC | 3 ms | 256 KB |
01-05.txt | AC | 3 ms | 256 KB |
01-06.txt | AC | 3 ms | 256 KB |
01-07.txt | AC | 3 ms | 256 KB |
01-08.txt | AC | 3 ms | 256 KB |
01-09.txt | AC | 3 ms | 256 KB |
01-10.txt | AC | 3 ms | 256 KB |
01-11.txt | AC | 3 ms | 256 KB |
01-12.txt | AC | 3 ms | 256 KB |
01-13.txt | AC | 3 ms | 256 KB |
01-14.txt | AC | 3 ms | 256 KB |
01-15.txt | AC | 3 ms | 256 KB |
01-16.txt | AC | 3 ms | 256 KB |
01-17.txt | AC | 3 ms | 256 KB |
01-18.txt | AC | 3 ms | 256 KB |
01-19.txt | AC | 3 ms | 256 KB |
01-20.txt | AC | 3 ms | 256 KB |
01-21.txt | AC | 3 ms | 256 KB |
01-22.txt | AC | 3 ms | 256 KB |
01-23.txt | AC | 3 ms | 256 KB |
01-24.txt | AC | 3 ms | 256 KB |
01-25.txt | AC | 3 ms | 256 KB |
01-26.txt | AC | 3 ms | 256 KB |
02-01.txt | AC | 3 ms | 256 KB |
02-02.txt | AC | 3 ms | 256 KB |
02-03.txt | AC | 3 ms | 384 KB |
02-04.txt | AC | 3 ms | 256 KB |
02-05.txt | AC | 3 ms | 256 KB |
02-06.txt | AC | 3 ms | 256 KB |
02-07.txt | AC | 3 ms | 256 KB |
02-08.txt | AC | 3 ms | 256 KB |
02-09.txt | AC | 3 ms | 256 KB |
02-10.txt | AC | 3 ms | 256 KB |
02-11.txt | AC | 3 ms | 256 KB |
02-12.txt | AC | 3 ms | 256 KB |
02-13.txt | AC | 3 ms | 256 KB |
02-14.txt | AC | 3 ms | 256 KB |
02-15.txt | AC | 3 ms | 256 KB |
02-16.txt | AC | 3 ms | 256 KB |
02-17.txt | AC | 3 ms | 256 KB |
02-18.txt | AC | 3 ms | 384 KB |
02-19.txt | AC | 4 ms | 384 KB |
02-20.txt | AC | 7 ms | 768 KB |
02-21.txt | AC | 40 ms | 3328 KB |
02-22.txt | TLE | 2107 ms | 85248 KB |
02-23.txt | AC | 1945 ms | 78336 KB |
02-24.txt | AC | 1926 ms | 78336 KB |
02-25.txt | AC | 3 ms | 256 KB |
02-26.txt | AC | 3 ms | 256 KB |
02-27.txt | AC | 3 ms | 256 KB |
02-28.txt | AC | 3 ms | 256 KB |
02-29.txt | AC | 3 ms | 256 KB |
02-30.txt | AC | 3 ms | 256 KB |
02-31.txt | AC | 3 ms | 256 KB |
02-32.txt | AC | 3 ms | 256 KB |
02-33.txt | AC | 3 ms | 256 KB |
02-34.txt | AC | 3 ms | 256 KB |
02-35.txt | AC | 3 ms | 256 KB |
02-36.txt | AC | 3 ms | 256 KB |
02-37.txt | AC | 4 ms | 384 KB |
02-38.txt | AC | 9 ms | 1024 KB |
02-39.txt | AC | 1696 ms | 66176 KB |
02-40.txt | TLE | 2107 ms | 89216 KB |
sample-01.txt | AC | 3 ms | 256 KB |
sample-02.txt | AC | 3 ms | 256 KB |
sample-03.txt | AC | 3 ms | 256 KB |