結果
| 問題 |
No.798 コレクション
|
| コンテスト | |
| ユーザー |
 koyumeishi
|
| 提出日時 | 2019-03-15 22:37:38 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 10,708 bytes |
| コンパイル時間 | 1,506 ms |
| コンパイル使用メモリ | 123,472 KB |
| 実行使用メモリ | 186,812 KB |
| 最終ジャッジ日時 | 2024-07-01 21:15:41 |
| 合計ジャッジ時間 | 15,219 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 13 TLE * 3 -- * 7 |
ソースコード
#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;
namespace {
using Integer = long long; //__int128;
template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
template<class T> istream& operator , (istream& is, T& val){ return is >> val;}
template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
template<class T> ostream& operator , (ostream& os, const T& val){ return os << " " << val;}
template<class H> void print(const H& head){ cout << head; }
template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }
template<class H> void eprint(const H& head){ cerr << head; }
template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }
class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } };
inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }
inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed
mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());
template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }
inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;
// min cost flow
// https://min-25.hatenablog.com/entry/2017/09/08/182320
template <
typename CapType, typename TotalCapType,
typename CostType, typename TotalCostType
>
class CostScaling {
private:
static const int alpha = 8; // eps <- max(1, eps / alpha)
using cap_t = CapType;
using tcap_t = TotalCapType;
using cost_t = CostType; // > max{|C|} * (2 * |V|)
using tcost_t = TotalCostType;
static constexpr cost_t Inf = (tcap_t(1) << (sizeof(tcap_t) * 8 - 2)) - 1;
struct InputEdge { int from, to; cap_t b, c; cost_t cost; };
struct Edge { int to, rev; cap_t cap; cost_t cost; };
class Dinic {
public:
Dinic(int N, const vector<int>& ofs, vector<Edge>& edges,
vector<tcap_t>& capacity)
: N(N), ofs(ofs), edges(edges), capacity(capacity), last(N) {}
bool succeeded() {
// s -> u: capacity[u]
// u -> t: capacity[u + N]
tcap_t f = 0;
for (int u = 0; u < N; ++u) f += capacity[u];
vector<int> que(N);
while (f) {
dist.assign(N, -1);
int qh = 0, qt = 0, lv = N;
for (int u = 0; u < N; ++u) if (capacity[u] > 0) que[qt++] = u, dist[u] = 0;
for (; qh < qt; ) {
int u = que[qh++];
if (lv == N && capacity[u + N] > 0) lv = dist[u];
if (dist[u] > lv) break;
for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) {
int v = edges[ei].to;
if (edges[ei].cap > 0 && dist[v] == -1) {
que[qt++] = v, dist[v] = dist[u] + 1;
}
}
}
if (lv == N) break;
for (int u = 0; u < N; ++u) last[u] = ofs[u];
for (int u = 0; u < N; ++u) if (capacity[u] > 0) {
auto df = block_flow(u, capacity[u]);
f -= df, capacity[u] -= df;
}
}
return f == 0;
}
private:
tcap_t block_flow(int u, tcap_t f) {
tcap_t ret = 0;
if (capacity[u + N] > 0) {
tcap_t df = min(f, capacity[u + N]);
capacity[u + N] -= df;
return df;
}
for (auto& ei = last[u]; ei < ofs[u + 1]; ++ei) {
auto& e = edges[ei]; int v = e.to;
if (e.cap == 0 || dist[v] <= dist[u]) continue;
cap_t df = block_flow(v, min<cap_t>(e.cap, f));
if (df == 0) continue;
e.cap -= df, edges[e.rev].cap += df;
f -= df, ret += df;
if (f == 0) break;
}
return ret;
}
int N;
const vector<int>& ofs;
vector<Edge>& edges;
vector<tcap_t>& capacity;
vector<int> last, dist;
};
public:
CostScaling(int N, int M=0) : N(N), capacity(2 * N) {
if (M > 0) in.reserve(M);
}
void add_directed_edge(int u, int v, cap_t b, cap_t c, cost_t cost) {
if (b > 0) capacity[v] += b, capacity[u + N] += b;
else capacity[u] += -b, capacity[v + N] += -b;
in.push_back({u, v, b, c, cost});
}
pair<bool, tcost_t> minimum_cost_circulation() {
construct();
if (!has_feasible_circulation()) return {false, 0};
const int cost_multiplier = 2 << __lg(N); // should be > |V|
cost_t eps = 0;
for (auto& e : edges) e.cost *= cost_multiplier, eps = max(eps, e.cost);
while (eps > 1) refine(eps = max<cost_t>(1, eps / alpha));
tcost_t ret = initial_cost;
for (auto& e : edges) ret -= (e.cost / cost_multiplier) * e.cap;
return {true, ret / 2};
}
private:
void refine(const cost_t eps) {
auto cost_p = [&] (int u, const Edge& e) {
return e.cost + potential[u] - potential[e.to];
};
for (int u = 0; u < N; ++u) for (int i = ofs[u]; i < ofs[u + 1]; ++i) {
auto& e = edges[i];
if (cost_p(u, e) < 0) edges[e.rev].cap += e.cap, e.cap = 0;
}
vector<tcap_t> excess(initial_excess);
for (auto& e : edges) excess[e.to] -= e.cap;
vector<int> stack; stack.reserve(N);
for (int u = 0; u < N; ++u) if (excess[u] > 0) stack.push_back(u);
auto residue = [&] (const Edge& e) -> cap_t { return e.cap; };
auto push = [&] (int u, Edge& e, cap_t df) {
e.cap -= df; edges[e.rev].cap += df;
excess[e.to] += df; excess[u] -= df;
if (excess[e.to] > 0 && excess[e.to] <= df) {
stack.push_back(e.to);
}
};
auto relabel = [&] (int u, cost_t delta) {
potential[u] -= delta + eps;
};
auto relabel_in_advance = [&] (int u) {
if (excess[u] != 0) return false;
auto delta = Inf;
for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) {
auto& e = edges[ei];
if (residue(e) == 0) continue;
if (cost_p(u, e) < 0) return false;
else delta = min<tcost_t>(delta, cost_p(u, e));
}
relabel(u, delta);
return true;
};
auto discharge = [&] (int u) {
auto delta = Inf;
for (int ei = ofs[u]; ei < ofs[u + 1]; ++ei) {
auto& e = edges[ei];
if (residue(e) == 0) continue;
if (cost_p(u, e) < 0) {
if (relabel_in_advance(e.to)) {
--ei; continue; // modify ei (!)
}
cap_t df = min<tcap_t>(excess[u], residue(e));
push(u, e, df);
if (!excess[u]) return;
} else delta = min<tcost_t>(delta, cost_p(u, e));
}
relabel(u, delta);
stack.push_back(u);
};
while (!stack.empty()) {
auto u = stack.back(); stack.pop_back();
discharge(u);
}
}
void construct() {
ofs.assign(N + 1, 0);
edges.resize(2 * in.size());
initial_excess.assign(N, 0);
initial_cost = 0;
potential.assign(N, 0);
for (auto& e : in) ofs[e.from + 1]++, ofs[e.to + 1]++;
for (int i = 1; i <= N; ++i) ofs[i] += ofs[i - 1];
for (auto& e : in) {
initial_excess[e.to] += e.c;
initial_excess[e.from] += -e.b;
initial_cost += tcost_t(e.cost) * (e.c + e.b);
edges[ofs[e.from]++] = {e.to, ofs[e.to], e.c - e.b, e.cost};
edges[ofs[e.to]++] = {e.from, ofs[e.from] - 1, 0, -e.cost};
}
for (int i = N; i > 0; --i) ofs[i] = ofs[i - 1];
ofs[0] = 0;
}
bool has_feasible_circulation() {
return Dinic(N, ofs, edges, capacity).succeeded();
}
private:
int N;
vector<InputEdge> in;
vector<tcap_t> capacity;
vector<int> ofs;
vector<Edge> edges;
tcost_t initial_cost;
vector<tcap_t> initial_excess;
vector<tcost_t> potential;
};
// cap, total_cap, cost * (2 * |V|), total_cost
using MCC = CostScaling<int, int64_t, int64_t, int64_t>;
// using MCC = CostScaling<int, int, int, int>;
int main(){
int n;
cin >> n;
vector<pair<int,int>> v(n);
cin >> v;
// Min_Cost_Flow<long long> f(n + n + 1 + 2, 1000000000);
MCC f(n+n+3);
int source = n+n+1;
int sink = source+1;
int odd = n+n;
// f.add_edge(odd, sink, n/3, 0);
f.add_directed_edge(odd, sink, n/3, n/3, 0);
for(int i=0; i<n; i++){
// f.add_edge(source, i, 1, v[i].first);
f.add_directed_edge(source, i, 0, 1, v[i].first);
for(int j=0; j<n-n/3; j++){
// f.add_edge(i, n+j, 1, v[i].second * j);
f.add_directed_edge(i, n+j, 0, 1, v[i].second * j);
}
// f.add_edge(i, odd, 1, -v[i].first);
f.add_directed_edge(i, odd, 0, 1, -v[i].first);
}
for(int i=0; i<n-n/3; i++){
// f.add_edge(n+i, sink, 1, 0);
f.add_directed_edge(n+i, sink, 1, 1, 0);
}
f.add_directed_edge(sink, source, n, n, 0);
// long long cost = f.min_cost_flow(source, sink, n);
long long cost = f.minimum_cost_circulation().second;
println(cost);
return 0;
}