結果
| 問題 |
No.1288 yuki collection
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2020-11-13 22:51:26 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2,526 ms / 5,000 ms |
| コード長 | 12,815 bytes |
| コンパイル時間 | 2,790 ms |
| コンパイル使用メモリ | 214,936 KB |
| 最終ジャッジ日時 | 2025-01-15 23:47:35 |
|
ジャッジサーバーID （参考情報） |
judge4 / 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
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x) {}
#endif
// MinCostFlow based on AtCoder Library, no namespace, no private variables, compatible with C++11
// Reference: <https://atcoder.github.io/ac-library/production/document_ja/mincostflow.html>
// **NO NEGATIVE COST EDGES**
template <class Cap, class Cost>
struct mcf_graph {
mcf_graph() {}
mcf_graph(int n) : _n(n), g(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(pos.size());
pos.push_back({from, int(g[from].size())});
int from_id = int(g[from].size());
int to_id = int(g[to].size());
if (from == to) to_id++;
g[from].push_back(_edge{to, to_id, cap, cost});
g[to].push_back(_edge{from, from_id, 0, -cost});
return m;
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
};
edge get_edge(int i) {
int m = int(pos.size());
assert(0 <= i && i < m);
auto _e = g[pos[i].first][pos[i].second];
auto _re = g[_e.to][_e.rev];
return edge{
pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,
};
}
std::vector<edge> edges() {
int m = int(pos.size());
std::vector<edge> result(m);
for (int i = 0; i < m; i++) {
result[i] = get_edge(i);
}
return result;
}
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<Cost> dual, dist;
std::vector<int> pv, pe;
std::vector<bool> vis;
bool _dual_ref(int s, int t) {
std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
std::fill(pv.begin(), pv.end(), -1);
std::fill(pe.begin(), pe.end(), -1);
std::fill(vis.begin(), vis.end(), false);
struct Q {
Cost key;
int to;
bool operator<(Q r) const { return key > r.key; }
};
std::priority_queue<Q> que;
dist[s] = 0;
que.push(Q{0, s});
while (!que.empty()) {
int v = que.top().to;
que.pop();
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
for (int i = 0; i < int(g[v].size()); i++) {
auto e = g[v][i];
if (vis[e.to] || !e.cap) continue;
// |-dual[e.to] + dual[v]| <= (n-1)C
// cost <= C - -(n-1)C + 0 = nC
Cost cost = e.cost - dual[e.to] + dual[v];
if (dist[e.to] - dist[v] > cost) {
dist[e.to] = dist[v] + cost;
pv[e.to] = v;
pe[e.to] = i;
que.push(Q{dist[e.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[v] -= dist[t] - dist[v];
}
return true;
}
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);
// 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.assign(_n, 0), dist.assign(_n, 0);
pv.assign(_n, 0), pe.assign(_n, 0);
vis.assign(_n, false);
Cap flow = 0;
Cost cost = 0, prev_cost_per_flow = -1;
std::vector<std::pair<Cap, Cost>> result;
result.push_back({flow, cost});
while (flow < flow_limit) {
if (!_dual_ref(s, t)) break;
Cap c = flow_limit - flow;
for (int v = t; v != s; v = pv[v]) {
c = std::min(c, g[pv[v]][pe[v]].cap);
}
for (int v = t; v != s; v = pv[v]) {
auto& e = g[pv[v]][pe[v]];
e.cap -= c;
g[v][e.rev].cap += c;
}
Cost d = -dual[s];
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;
}
struct _edge {
int to, rev;
Cap cap;
Cost cost;
};
int _n;
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
// <https://kopricky.github.io/code/NetworkFlow/min_cost_flow_DAG.html>
template<typename CapType, typename CostType> class MinCostFlowDAG {
public:
using Cat = CapType;
using Cot = CostType;
using pti = pair<Cot, int>;
struct edge {
int to, rev;
Cat cap;
Cot cost;
};
const int V;
const Cot inf;
vector<vector<edge> > G;
vector<Cot> h, dist;
vector<int> deg, ord, prevv, preve;
MinCostFlowDAG(const int node_size) : V(node_size), inf(numeric_limits<Cot>::max()),
G(V), h(V, inf), dist(V), deg(V, 0), prevv(V), preve(V){}
void add_edge(const int from, const int to, const Cat cap, const Cot cost){
if(cap == 0) return;
G[from].push_back((edge){to, (int)G[to].size(), cap, cost});
G[to].push_back((edge){from, (int)G[from].size() - 1, 0, -cost});
++deg[to];
}
bool tsort(){
queue<int> que;
for(int i = 0; i < V; ++i){
if(deg[i] == 0) que.push(i);
}
while(!que.empty()){
const int p = que.front();
que.pop();
ord.push_back(p);
for(auto& e : G[p]){
if(e.cap > 0 && --deg[e.to] == 0) que.push(e.to);
}
}
return (*max_element(deg.begin(), deg.end()) == 0);
}
void calc_potential(const int s){
h[s] = 0;
for(const int v : ord){
if(h[v] == inf) continue;
for(const edge& e : G[v]){
if(e.cap > 0) h[e.to] = min(h[e.to], h[v] + e.cost);
}
}
}
void Dijkstra(const int s){
priority_queue<pti,vector<pti>,greater<pti> > que;
fill(dist.begin(), dist.end(), inf);
dist[s] = 0;
que.push(pti(0, s));
while(!que.empty()){
pti p = que.top();
que.pop();
const int v = p.second;
if(dist[v] < p.first) continue;
for(int i = 0; i < (int)G[v].size(); ++i){
edge& e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]){
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v, preve[e.to] = i;
que.push(pti(dist[e.to], e.to));
}
}
}
}
void update(const int s, const int t, Cat& f, Cot& res){
for(int i = 0; i < V; i++){
if(dist[i] != inf) h[i] += dist[i];
}
Cat d = f;
for(int v = t; v != s; v = prevv[v]){
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += h[t] * d;
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;
}
}
Cot solve(const int s, const int t, Cat f){
if(!tsort()) assert(false); // not DAG
calc_potential(s);
Cot res = 0;
while(f > 0){
Dijkstra(s);
if(dist[t] == inf) return -inf;
update(s, t, f, res);
}
return res;
}
};
constexpr int B = 501;
int main()
{
int N;
string S;
cin >> N >> S;
vector<lint> V(N);
cin >> V;
const int s = N * 5, t = s + 1;
MinCostFlowDAG<int, lint> graph(t + 1);
REP(d, 5) {
REP(i, N - 1) {
graph.add_edge(d * N + i, d * N + i + 1, N / 4, 0);
}
}
graph.add_edge(s - 1, 0, N / 4, 0);
REP(i, N)
{
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.solve(s, t, N);
cout << accumulate(ALL(V), 0LL) - cost << '\n';
}