結果
| 問題 | No.2604 Initial Motion |
| ユーザー |
 inksamurai
|
| 提出日時 | 2024-01-12 22:16:28 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 189 ms / 3,000 ms |
| コード長 | 10,025 bytes |
| コンパイル時間 | 2,893 ms |
| コンパイル使用メモリ | 220,004 KB |
| 最終ジャッジ日時 | 2025-02-18 18:28:49 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
ソースコード
#include <bits/stdc++.h>
// cut here
#include <utility>
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 atcoder
namespace atcoder {
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
} // namespace atcoder
namespace atcoder {
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) {
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());
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) {
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
// cut here
#define int ll
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define rng(i,c,n) for(int i=c;i<n;i++)
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)a.size()
#define vec(...) vector<__VA_ARGS__>
#define _4aNWZeC ios::sync_with_stdio(0),cin.tie(0)
using ll=long long;
using pii=pair<int,int>;
using vi=vector<int>;
void print(){cout<<'\n';}
template<class h,class...t>
void print(const h&v,const t&...u){cout<<v<<' ',print(u...);}
mt19937_64 qrand(chrono::steady_clock::now().time_since_epoch().count());
void slv(){
int n,k,m;
cin>>n>>k>>m;
swap(n,k);
// k=2000;
// n=2000;
// m=2000;
vi cnt_l(n);
rep(i,k){
int v;
// v=qrand()%n;
cin>>v;
v-=1;
cnt_l[v]++;
}
int s=0;
vi cnt_r(n);
rep(i,n){
int x;
// x=qrand()%n;
// s+=x;
cin>>x;
cnt_r[i]=x;
}
// if(s<k){
// cnt_r[0]+=k-s;
// }
vec(vec(pii)) adj(n);
rep(i,m){
int u,v,w;
// w=qrand()%(int)(1e12);
// while(1){
// u=qrand()%n;
// v=qrand()%n;
// if(u!=v) break;
// }
cin>>u>>v>>w;
u-=1,v-=1;
// print(u,v,w);
adj[u].pb({w,v}),adj[v].pb({w,u});
}
// const int inf=1e18;
// vec(vi) dist(n,vi(n,inf));
// rep(s,n){
// dist[s][s]=0;
// priority_queue<pii,vec(pii),greater<pii>> pq;
// pq.push({0,s});
// while(sz(pq)){
// auto [cosu,v]=pq.top();
// pq.pop();
// if(cosu!=dist[s][v]) continue;
// for(auto [w,u]:adj[v]){
// int ncosu=cosu+w;
// if(dist[s][u]>ncosu){
// dist[s][u]=ncosu;
// pq.push({ncosu,u});
// }
// }
// }
// }
atcoder::mcf_graph<int,int> g(2*n+2);
const int src=2*n;
const int tink=2*n+1;
rep(v,n){
g.add_edge(src,v,cnt_l[v],0);
g.add_edge(v+n,tink,cnt_r[v],0);
}
rep(v,n){
g.add_edge(v,v+n,n,0);
}
rep(v,n){
for(auto [w,u]:adj[v]){
g.add_edge(v,u,n,w);
}
}
auto res=g.flow(src,tink);
cout<<res.se<<"\n";
}
signed main(){
_4aNWZeC;
slv();
}