結果
| 問題 |
No.1678 Coin Trade (Multiple)
|
| コンテスト | |
| ユーザー |
👑  potato167
|
| 提出日時 | 2021-09-10 22:22:23 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 258 ms / 5,000 ms |
| コード長 | 9,530 bytes |
| コンパイル時間 | 3,050 ms |
| コンパイル使用メモリ | 219,316 KB |
| 最終ジャッジ日時 | 2025-01-24 11:25:52 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 56 |
ソースコード
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#define _GLIBCXX_DEBUG
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=1167167167167167167;
const int INF=2100000000;
ll mod=1e9+7;
#define rep(i,a) for (ll i=0;i<a;i++)
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";}
namespace atcoder {
namespace internal {
template <class E> struct csr {
std::vector<int> start;
std::vector<E> elist;
explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
: start(n + 1), elist(edges.size()) {
for (auto e : edges) {
start[e.first + 1]++;
}
for (int i = 1; i <= n; i++) {
start[i] += start[i - 1];
}
auto counter = start;
for (auto e : edges) {
elist[counter[e.first]++] = e.second;
}
}
};
} // namespace internal
namespace internal {
template <class T> struct simple_queue {
std::vector<T> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const T& t) { payload.push_back(t); }
T& front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
} // namespace internal
template <class Cap, class Cost> struct mcf_graph {
public:
mcf_graph() {}
explicit mcf_graph(int n) : _n(n) {}
int add_edge(int from, int to, Cap cap, Cost cost) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(0 <= cap);
assert(0 <= cost);
int m = int(_edges.size());
_edges.push_back({from, to, cap, 0, cost});
return m;
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
};
edge get_edge(int i) {
int m = int(_edges.size());
assert(0 <= i && i < m);
return _edges[i];
}
std::vector<edge> edges() { return _edges; }
std::pair<Cap, Cost> flow(int s, int t) {
return flow(s, t, std::numeric_limits<Cap>::max());
}
std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
return slope(s, t, flow_limit).back();
}
std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
return slope(s, t, std::numeric_limits<Cap>::max());
}
std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
int m = int(_edges.size());
std::vector<int> edge_idx(m);
auto g = [&]() {
std::vector<int> degree(_n), redge_idx(m);
std::vector<std::pair<int, _edge>> elist;
elist.reserve(2 * m);
for (int i = 0; i < m; i++) {
auto e = _edges[i];
edge_idx[i] = degree[e.from]++;
redge_idx[i] = degree[e.to]++;
elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}});
elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}});
}
auto _g = internal::csr<_edge>(_n, elist);
for (int i = 0; i < m; i++) {
auto e = _edges[i];
edge_idx[i] += _g.start[e.from];
redge_idx[i] += _g.start[e.to];
_g.elist[edge_idx[i]].rev = redge_idx[i];
_g.elist[redge_idx[i]].rev = edge_idx[i];
}
return _g;
}();
auto result = slope(g, s, t, flow_limit);
for (int i = 0; i < m; i++) {
auto e = g.elist[edge_idx[i]];
_edges[i].flow = _edges[i].cap - e.cap;
}
return result;
}
private:
int _n;
std::vector<edge> _edges;
// inside edge
struct _edge {
int to, rev;
Cap cap;
Cost cost;
};
std::vector<std::pair<Cap, Cost>> slope(internal::csr<_edge>& g,
int s,
int t,
Cap flow_limit) {
// variants (C = maxcost):
// -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
// reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
// dual_dist[i] = (dual[i], dist[i])
std::vector<std::pair<Cost, Cost>> dual_dist(_n);
std::vector<int> prev_e(_n);
std::vector<bool> vis(_n);
struct Q {
Cost key;
int to;
bool operator<(Q r) const { return key > r.key; }
};
std::vector<int> que_min;
std::vector<Q> que;
auto dual_ref = [&]() {
for (int i = 0; i < _n; i++) {
dual_dist[i].second = std::numeric_limits<Cost>::max();
}
std::fill(vis.begin(), vis.end(), false);
que_min.clear();
que.clear();
// que[0..heap_r) was heapified
size_t heap_r = 0;
dual_dist[s].second = 0;
que_min.push_back(s);
while (!que_min.empty() || !que.empty()) {
int v;
if (!que_min.empty()) {
v = que_min.back();
que_min.pop_back();
} else {
while (heap_r < que.size()) {
heap_r++;
std::push_heap(que.begin(), que.begin() + heap_r);
}
v = que.front().to;
std::pop_heap(que.begin(), que.end());
que.pop_back();
heap_r--;
}
if (vis[v]) continue;
vis[v] = true;
if (v == t) break;
// dist[v] = shortest(s, v) + dual[s] - dual[v]
// dist[v] >= 0 (all reduced cost are positive)
// dist[v] <= (n-1)C
Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
auto e = g.elist[i];
if (!e.cap) continue;
// |-dual[e.to] + dual[v]| <= (n-1)C
// cost <= C - -(n-1)C + 0 = nC
Cost cost = e.cost - dual_dist[e.to].first + dual_v;
if (dual_dist[e.to].second - dist_v > cost) {
Cost dist_to = dist_v + cost;
dual_dist[e.to].second = dist_to;
prev_e[e.to] = e.rev;
if (dist_to == dist_v) {
que_min.push_back(e.to);
} else {
que.push_back(Q{dist_to, e.to});
}
}
}
}
if (!vis[t]) {
return false;
}
for (int v = 0; v < _n; v++) {
if (!vis[v]) continue;
// dual[v] = dual[v] - dist[t] + dist[v]
// = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
// (shortest(s, v) + dual[s] - dual[v]) = - shortest(s,
// t) + dual[t] + shortest(s, v) = shortest(s, v) -
// shortest(s, t) >= 0 - (n-1)C
dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
}
return true;
};
Cap flow = 0;
Cost cost = 0, prev_cost_per_flow = -1;
std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
while (flow < flow_limit) {
if (!dual_ref()) break;
Cap c = flow_limit - flow;
for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
}
for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
auto& e = g.elist[prev_e[v]];
e.cap += c;
g.elist[e.rev].cap -= c;
}
Cost d = -dual_dist[s].first;
flow += c;
cost += c * d;
if (prev_cost_per_flow == d) {
result.pop_back();
}
result.push_back({flow, cost});
prev_cost_per_flow = d;
}
return result;
}
};
} // namespace atcoder
using namespace atcoder;
// rainy ~ 雨に打たれて ~
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N,K;
cin>>N>>K;
mcf_graph<ll,ll> G(N+2);
rep(i,N+1) G.add_edge(i,i+1,K,INF);
vector<ll> A(N+1);
rep(i,N){
int M;
cin>>A[i+1]>>M;
rep(j,M){
ll b;
cin>>b;
G.add_edge(b,i+1,1,(i+1-b)*(ll)INF-A[i+1]+A[b]);
}
}
ll ans=G.flow(0,N+1).second;
cout<<(ll)K*(ll)INF*(ll)(N+1)-ans<<"\n";
}