//codeforces.com/problemset/problem/573/E //kod oparty jest na rozwiazaniu http://codeforces.com/contest/573/submission/12767462 autora ww. zadania #include <bits/stdc++.h> using namespace std; #define e1 first #define e2 second #define x first #define y second #define pb push_back #define mp make_pair #define boost ios_base::sync_with_stdio(false) #define eb emplace_back #define OUT(x) {cout << x; exit(0); } #define FOR(i,a,b) for(int i=(a);i<=(b);++i) #define scanf(...) scanf(__VA_ARGS__)?:0 typedef long long int ll; typedef unsigned long long ull; typedef pair <int, int> PII; typedef pair <ll, ll> PLL; typedef pair <PLL, int> PLLI; typedef pair <PLL, PLL> PP; typedef pair <PII, int> PPI; typedef pair <ll, int> PLI; typedef unsigned int ui; const int inf = 1e9+9; const ll MOD = 1e9+696969; const long long INF = 1e18+3; #define maxn 1000100 PLL t[maxn]; inline ll readLL() { char zn; ll x = 0; while (1) { zn = getchar_unlocked(); if (zn >= '0' && zn <= '9') break; } while (1) { x = (x << 1) + (x << 3) + zn - '0'; zn = getchar_unlocked(); if (isspace(zn)) return x; } } struct line { int a, id; ll b; line(int aa, ll bb, int idd) : a(aa), id(idd), b(bb) {} // does (this,B) intersect before (B,C) bool before(const line & B, const line & C) { // a*x + b = B.a*x + B.b // x * (a-B.a) = B.b-b // x * q1 = p1 ll p1 = B.b - b, p2 = C.b - b; int q1 = a - B.a, q2 = a - C.a; if(q1 < 0) { p1 *= -1; q1 *= -1; } if(q2 < 0) { p2 *= -1; q2 *= -1; } // x1 = p1/q1, x2 = p2/q2 return p1*q2 <= p2*q1; } ll f(int x) { return (ll) a * x + b; } }; vector <PLL> wektor; bool porownaj(int aa, int bb) { return wektor[aa].first < wektor[bb].first; } struct hull { vector<PLL> a; // numbers from input vector<bool> taken; vector<line> w; // hull vector<int> order; int n; int pointer; int count; // number of taken elements ll sum; // sum of taken elements hull(){} hull(vector<PLL> aa) : a(aa) { count = sum = 0; n = (int) a.size(); taken.resize(n, false); for(int i = 0; i < n; ++i) order.push_back(i); // we find order only once, in constructor wektor = a; sort(order.begin(), order.end(), porownaj); build(); } void build() { // build hull pointer = 0; vector<ll> val(n); ll suf = sum; int cnt = 0; for(int i = 0; i < n; ++i) { if(taken[i]) { suf -= a[i].first; ++cnt; } else val[i] = suf + a[i].second + (ll)a[i].first * (cnt + 1); } vector<line> sorted; // linear sort using vector<int> order for(int u=0; u<(int)order.size(); ++u) { int i = order[u]; if(!taken[i]) sorted.push_back(line(a[i].first, val[i], i)); } w.clear(); for(int i=0; i<(int)sorted.size(); ++i) { if(!w.empty() && w.back().a == sorted[i].a) { if(sorted[i].b <= w.back().b) continue; else w.pop_back(); } while((int) w.size() >= 2) { line & A = w[(int)w.size()-2]; line & B = w[(int)w.size()-1]; if(A.before(B, sorted[i])) break; w.pop_back(); } w.push_back(sorted[i]); } } pair<ll, int> best(int before) { // find the best candidate, move pointer if(w.empty()) return make_pair(42LL, -1); while(pointer <= (int) w.size()-2 && w[pointer].f(before) < w[pointer+1].f(before)) ++pointer; assert(pointer < (int) w.size()); return make_pair(w[pointer].f(before), w[pointer].id); } void remove(int i) { // mark as taken assert(!taken[i]); taken[i] = true; sum += a[i].first; ++count; build(); } } h[1005]; int a[1005*1005]; int bucket[1051005]; int main() { int n; n=readLL(); for(int i = 0; i < n; ++i) t[i].first = readLL(), t[i].second = readLL(); //n = 300000; //for (int i=0; i<n; ++i) t[i].first = i + 1, t[i].second = n - i - 1; sort(t, t + n); for(int i = 0; i < n; ++i) a[i] = t[i].first; // divide into Parts with size sqrt(n) int s = max(1, int(sqrt(n))); for(int i = 0; i < n; i++) bucket[i] = i / s; for(int i = 0; i < n; i += s) { vector<PLL> w; for(int j = i; j < min(n, i+s); ++j) w.push_back(make_pair(a[j], t[j].second)); h[bucket[i]] = hull(w); } ll output = 0; // max(score) ll score = 0; // score for current set/subsequence while(true) { pair<ll,int> m = make_pair(42LL, -1); ll suf = 0; // sum of elements on the right int cnt = -1; // how many on the left for(int i = 0; i < n; i += s) suf += h[bucket[i]].sum; for(int i = 0; i < n; i += s) { suf -= h[bucket[i]].sum; // we ask this Part about max(ax+b) where x = cnt pair<ll, int> p = h[bucket[i]].best(cnt); p.first += suf; // extra constant if(p.second != -1) if(m.second == -1 || p.first > m.first) m = make_pair(p.first, i+p.second); cnt += h[bucket[i]].count; } if(m.second == -1) break; score += m.first; output = max(output, score); printf("%lld\n", output); int i = m.second; h[bucket[i]].remove(i-i/s*s); } return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 | //codeforces.com/problemset/problem/573/E //kod oparty jest na rozwiazaniu http://codeforces.com/contest/573/submission/12767462 autora ww. zadania #include <bits/stdc++.h> using namespace std; #define e1 first #define e2 second #define x first #define y second #define pb push_back #define mp make_pair #define boost ios_base::sync_with_stdio(false) #define eb emplace_back #define OUT(x) {cout << x; exit(0); } #define FOR(i,a,b) for(int i=(a);i<=(b);++i) #define scanf(...) scanf(__VA_ARGS__)?:0 typedef long long int ll; typedef unsigned long long ull; typedef pair <int, int> PII; typedef pair <ll, ll> PLL; typedef pair <PLL, int> PLLI; typedef pair <PLL, PLL> PP; typedef pair <PII, int> PPI; typedef pair <ll, int> PLI; typedef unsigned int ui; const int inf = 1e9+9; const ll MOD = 1e9+696969; const long long INF = 1e18+3; #define maxn 1000100 PLL t[maxn]; inline ll readLL() { char zn; ll x = 0; while (1) { zn = getchar_unlocked(); if (zn >= '0' && zn <= '9') break; } while (1) { x = (x << 1) + (x << 3) + zn - '0'; zn = getchar_unlocked(); if (isspace(zn)) return x; } } struct line { int a, id; ll b; line(int aa, ll bb, int idd) : a(aa), id(idd), b(bb) {} // does (this,B) intersect before (B,C) bool before(const line & B, const line & C) { // a*x + b = B.a*x + B.b // x * (a-B.a) = B.b-b // x * q1 = p1 ll p1 = B.b - b, p2 = C.b - b; int q1 = a - B.a, q2 = a - C.a; if(q1 < 0) { p1 *= -1; q1 *= -1; } if(q2 < 0) { p2 *= -1; q2 *= -1; } // x1 = p1/q1, x2 = p2/q2 return p1*q2 <= p2*q1; } ll f(int x) { return (ll) a * x + b; } }; vector <PLL> wektor; bool porownaj(int aa, int bb) { return wektor[aa].first < wektor[bb].first; } struct hull { vector<PLL> a; // numbers from input vector<bool> taken; vector<line> w; // hull vector<int> order; int n; int pointer; int count; // number of taken elements ll sum; // sum of taken elements hull(){} hull(vector<PLL> aa) : a(aa) { count = sum = 0; n = (int) a.size(); taken.resize(n, false); for(int i = 0; i < n; ++i) order.push_back(i); // we find order only once, in constructor wektor = a; sort(order.begin(), order.end(), porownaj); build(); } void build() { // build hull pointer = 0; vector<ll> val(n); ll suf = sum; int cnt = 0; for(int i = 0; i < n; ++i) { if(taken[i]) { suf -= a[i].first; ++cnt; } else val[i] = suf + a[i].second + (ll)a[i].first * (cnt + 1); } vector<line> sorted; // linear sort using vector<int> order for(int u=0; u<(int)order.size(); ++u) { int i = order[u]; if(!taken[i]) sorted.push_back(line(a[i].first, val[i], i)); } w.clear(); for(int i=0; i<(int)sorted.size(); ++i) { if(!w.empty() && w.back().a == sorted[i].a) { if(sorted[i].b <= w.back().b) continue; else w.pop_back(); } while((int) w.size() >= 2) { line & A = w[(int)w.size()-2]; line & B = w[(int)w.size()-1]; if(A.before(B, sorted[i])) break; w.pop_back(); } w.push_back(sorted[i]); } } pair<ll, int> best(int before) { // find the best candidate, move pointer if(w.empty()) return make_pair(42LL, -1); while(pointer <= (int) w.size()-2 && w[pointer].f(before) < w[pointer+1].f(before)) ++pointer; assert(pointer < (int) w.size()); return make_pair(w[pointer].f(before), w[pointer].id); } void remove(int i) { // mark as taken assert(!taken[i]); taken[i] = true; sum += a[i].first; ++count; build(); } } h[1005]; int a[1005*1005]; int bucket[1051005]; int main() { int n; n=readLL(); for(int i = 0; i < n; ++i) t[i].first = readLL(), t[i].second = readLL(); //n = 300000; //for (int i=0; i<n; ++i) t[i].first = i + 1, t[i].second = n - i - 1; sort(t, t + n); for(int i = 0; i < n; ++i) a[i] = t[i].first; // divide into Parts with size sqrt(n) int s = max(1, int(sqrt(n))); for(int i = 0; i < n; i++) bucket[i] = i / s; for(int i = 0; i < n; i += s) { vector<PLL> w; for(int j = i; j < min(n, i+s); ++j) w.push_back(make_pair(a[j], t[j].second)); h[bucket[i]] = hull(w); } ll output = 0; // max(score) ll score = 0; // score for current set/subsequence while(true) { pair<ll,int> m = make_pair(42LL, -1); ll suf = 0; // sum of elements on the right int cnt = -1; // how many on the left for(int i = 0; i < n; i += s) suf += h[bucket[i]].sum; for(int i = 0; i < n; i += s) { suf -= h[bucket[i]].sum; // we ask this Part about max(ax+b) where x = cnt pair<ll, int> p = h[bucket[i]].best(cnt); p.first += suf; // extra constant if(p.second != -1) if(m.second == -1 || p.first > m.first) m = make_pair(p.first, i+p.second); cnt += h[bucket[i]].count; } if(m.second == -1) break; score += m.first; output = max(output, score); printf("%lld\n", output); int i = m.second; h[bucket[i]].remove(i-i/s*s); } return 0; } |