結果
| 問題 |
No.1288 yuki collection
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-09-11 01:10:34 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 484 ms / 5,000 ms |
| コード長 | 16,355 bytes |
| コンパイル時間 | 1,710 ms |
| コンパイル使用メモリ | 100,472 KB |
| 最終ジャッジ日時 | 2025-01-24 12:35:12 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 40 |
ソースコード
#line 1 "combinatorial_opt/test/mincostflow.yuki1288.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1288"
#line 2 "combinatorial_opt/mincostflow_nonegativeloop.hpp"
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
/*
// CUT begin
// Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed)
// Verified:
// - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702
// - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT
template <class Cap = long long, class Cost = long long, Cost INF_COST = std::numeric_limits<Cost>::max() / 2>
struct MinCostFlow {
struct _edge {
int to, rev;
Cap cap;
Cost cost;
template <class Ostream> friend Ostream &operator<<(Ostream &os, const _edge &e) {
return os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')';
}
};
bool _is_dual_infeasible;
int V;
std::vector<std::vector<_edge>> g;
std::vector<Cost> dist;
std::vector<int> prevv, preve;
std::vector<Cost> dual; // dual[V]: potential
std::vector<std::pair<int, int>> pos;
bool _initialize_dual_dag() {
std::vector<int> deg_in(V);
for (int i = 0; i < V; i++) {
for (const auto &e : g[i]) deg_in[e.to] += (e.cap > 0);
}
std::vector<int> st;
st.reserve(V);
for (int i = 0; i < V; i++) {
if (!deg_in[i]) st.push_back(i);
}
for (int n = 0; n < V; n++) {
if (int(st.size()) == n) return false; // Not DAG
int now = st[n];
for (const auto &e : g[now]) {
if (!e.cap) continue;
deg_in[e.to]--;
if (deg_in[e.to] == 0) st.push_back(e.to);
if (dual[e.to] >= dual[now] + e.cost) dual[e.to] = dual[now] + e.cost;
}
}
return true;
}
bool _initialize_dual_spfa() { // Find feasible dual's when negative cost edges exist
dual.assign(V, 0);
std::queue<int> q;
std::vector<int> in_queue(V);
std::vector<int> nvis(V);
for (int i = 0; i < V; i++) q.push(i), in_queue[i] = true;
while (q.size()) {
int now = q.front();
q.pop(), in_queue[now] = false;
if (nvis[now] > V) return false; // Negative cycle exists
nvis[now]++;
for (const auto &e : g[now]) {
if (!e.cap) continue;
if (dual[e.to] > dual[now] + e.cost) {
dual[e.to] = dual[now] + e.cost;
if (!in_queue[e.to]) in_queue[e.to] = true, q.push(e.to);
}
}
}
return true;
}
bool initialize_dual() {
return !_is_dual_infeasible or _initialize_dual_dag() or _initialize_dual_spfa();
}
template <class heap> void _dijkstra(int s) { // O(ElogV)
prevv.assign(V, -1);
preve.assign(V, -1);
dist.assign(V, INF_COST);
dist[s] = 0;
heap q;
q.emplace(0, s);
while (!q.empty()) {
auto p = q.top();
q.pop();
int v = p.second;
if (dist[v] < Cost(p.first)) continue;
for (int i = 0; i < (int)g[v].size(); i++) {
_edge &e = g[v][i];
auto c = dist[v] + e.cost + dual[v] - dual[e.to];
if (e.cap > 0 and dist[e.to] > c) {
dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i;
q.emplace(dist[e.to], e.to);
}
}
}
}
MinCostFlow(int V = 0) : _is_dual_infeasible(false), V(V), g(V), dual(V, 0) {
static_assert(INF_COST > 0, "INF_COST must be positive");
}
int add_edge(int from, int to, Cap cap, Cost cost) {
assert(0 <= from and from < V);
assert(0 <= to and to < V);
assert(cap >= 0);
if (cost < 0) _is_dual_infeasible = true;
pos.emplace_back(from, g[from].size());
g[from].push_back({to, (int)g[to].size() + (from == to), cap, cost});
g[to].push_back({from, (int)g[from].size() - 1, (Cap)0, -cost});
return int(pos.size()) - 1;
}
// Flush flow f from s to t. Graph must not have negative cycle.
using Pque = std::priority_queue<std::pair<Cost, int>, std::vector<std::pair<Cost, int>>, std::greater<std::pair<Cost, int>>>;
template <class heap = Pque> std::pair<Cap, Cost> flow(int s, int t, const Cap &flow_limit) {
// You can also use radix_heap<typename std::make_unsigned<Cost>::type, int> as prique
if (!initialize_dual()) throw; // Fail to find feasible dual
Cost cost = 0;
Cap flow_rem = flow_limit;
while (flow_rem > 0) {
_dijkstra<heap>(s);
if (dist[t] == INF_COST) break;
for (int v = 0; v < V; v++) dual[v] = std::min(dual[v] + dist[v], INF_COST);
Cap d = flow_rem;
for (int v = t; v != s; v = prevv[v]) d = std::min(d, g[prevv[v]][preve[v]].cap);
flow_rem -= d;
cost += d * (dual[t] - dual[s]);
for (int v = t; v != s; v = prevv[v]) {
_edge &e = g[prevv[v]][preve[v]];
e.cap -= d;
g[v][e.rev].cap += d;
}
}
return std::make_pair(flow_limit - flow_rem, cost);
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
template <class Ostream> friend Ostream &operator<<(Ostream &os, const edge &e) {
return os << '(' << e.from << "->" << e.to << ',' << e.flow << '/' << e.cap << ",$" << e.cost << ')';
}
};
edge get_edge(int edge_id) const {
int m = int(pos.size());
assert(0 <= edge_id and edge_id < m);
auto _e = g[pos[edge_id].first][pos[edge_id].second];
auto _re = g[_e.to][_e.rev];
return {pos[edge_id].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost};
}
std::vector<edge> edges() const {
std::vector<edge> ret(pos.size());
for (int i = 0; i < int(pos.size()); i++) ret[i] = get_edge(i);
return ret;
}
template <class Ostream> friend Ostream &operator<<(Ostream &os, const MinCostFlow &mcf) {
os << "[MinCostFlow]V=" << mcf.V << ":";
for (int i = 0; i < mcf.V; i++) {
for (auto &e : mcf.g[i]) os << "\n" << i << "->" << e.to << ":cap" << e.cap << ",$" << e.cost;
}
return os;
}
};
*/
template <class Cap, class Cost, Cost INF_COST = std::numeric_limits<Cost>::max() / 2> struct MinCostFlow {
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; }
}
};
public:
MinCostFlow() {}
explicit MinCostFlow(int n) : is_dual_infeasible(false), _n(n) {
static_assert(std::numeric_limits<Cap>::max() > 0, "max() must be greater than 0");
}
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);
if (cost < 0) is_dual_infeasible = true;
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 = 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:
bool is_dual_infeasible;
int _n;
std::vector<edge> _edges;
// inside edge
struct _edge {
int to, rev;
Cap cap;
Cost cost;
};
std::vector<std::pair<Cap, Cost>> slope(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);
if (is_dual_infeasible) {
auto check_dag = [&]() {
std::vector<int> deg_in(_n);
for (int v = 0; v < _n; v++) {
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
deg_in[g.elist[i].to] += g.elist[i].cap > 0;
}
}
std::vector<int> st;
st.reserve(_n);
for (int i = 0; i < _n; i++) {
if (!deg_in[i]) st.push_back(i);
}
for (int n = 0; n < _n; n++) {
if (int(st.size()) == n) return false; // Not DAG
int now = st[n];
for (int i = g.start[now]; i < g.start[now + 1]; i++) {
const auto &e = g.elist[i];
if (!e.cap) continue;
deg_in[e.to]--;
if (deg_in[e.to] == 0) st.push_back(e.to);
if (dual_dist[e.to].first >= dual_dist[now].first + e.cost)
dual_dist[e.to].first = dual_dist[now].first + e.cost;
}
}
return true;
}();
if (!check_dag) throw;
}
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
unsigned 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;
}
};
#line 3 "combinatorial_opt/test/mincostflow.yuki1288.test.cpp"
#include <iostream>
#include <numeric>
#include <string>
#line 7 "combinatorial_opt/test/mincostflow.yuki1288.test.cpp"
using namespace std;
int main() {
int N;
string S;
cin >> N >> S;
vector<long long> V(N);
for (auto &x : V) cin >> x;
const int s = N * 5, t = s + 1;
MinCostFlow<int, long long> graph(t + 1);
for (int d = 0; d < 5; d++) {
for (int i = 0; i < N - 1; i++) graph.add_edge(d * N + i, d * N + i + 1, N / 4, 0);
}
graph.add_edge(s - 1, 0, N / 4, 0);
for (int i = 0; i < N; i++) {
int b = 0;
if (S[i] == 'u') b = N * 1;
if (S[i] == 'k') b = N * 2;
if (S[i] == 'i') b = N * 3;
int fr = b + i + N, to = b + i;
graph.add_edge(s, fr, 1, 0);
graph.add_edge(fr, to, 1, V[i]);
graph.add_edge(to, t, 1, 0);
}
auto cost = graph.flow(s, t, N).second;
cout << accumulate(V.begin(), V.end(), 0LL) - cost << '\n';
}