結果
| 問題 |
No.1288 yuki collection
|
| コンテスト | |
| ユーザー |
 kuhaku
|
| 提出日時 | 2025-05-30 19:22:17 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 44 ms / 5,000 ms |
| コード長 | 13,666 bytes |
| コンパイル時間 | 5,211 ms |
| コンパイル使用メモリ | 331,896 KB |
| 実行使用メモリ | 7,844 KB |
| 最終ジャッジ日時 | 2025-05-30 19:22:25 |
| 合計ジャッジ時間 | 6,728 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（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
// competitive-verifier: PROBLEM
#include <algorithm>
#include <cassert>
#include <limits>
#include <vector>
#include <iostream>
#include <utility>
namespace internal {
struct graph_csr {
private:
struct edge_list {
using const_iterator = std::vector<int>::const_iterator;
edge_list(const graph_csr &g, int v) : g(g), v(v) {}
const_iterator begin() const { return std::next(g.elist.begin(), g.start[v]); }
const_iterator end() const { return std::next(g.elist.begin(), g.start[v + 1]); }
private:
const graph_csr &g;
int v;
};
public:
graph_csr(int n) : _size(n), edges(), start(n + 1) {}
edge_list operator[](int i) const { return edge_list(*this, i); }
constexpr int size() const { return _size; }
void build() {
for (auto [u, v] : edges) ++start[u + 1];
for (int i = 0; i < _size; ++i) start[i + 1] += start[i];
auto counter = start;
elist = std::vector<int>(edges.size());
for (auto [u, v] : edges) elist[counter[u]++] = v;
}
void add_edge(int u, int v) { edges.emplace_back(u, v); }
void add_edges(int u, int v) {
edges.emplace_back(u, v);
edges.emplace_back(v, u);
}
void input_edge(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
std::cin >> from >> to;
add_edge(from - base, to - base);
}
build();
}
void input_edges(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
std::cin >> from >> to;
add_edges(from - base, to - base);
}
build();
}
int _size;
std::vector<std::pair<int, int>> edges;
std::vector<int> elist;
std::vector<int> start;
};
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
/// @brief 最小費用流
template <class Cap, class Cost>
struct mcf_graph {
mcf_graph() {}
explicit mcf_graph(int n) : _n(n) {}
int size() const { return _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.emplace_back(from, to, cap, 0, cost);
return m;
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
constexpr edge(int _from, int _to, Cap _cap, Cap _flow, Cost _cost)
: from(_from), to(_to), cap(_cap), flow(_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.emplace_back(e.from, _edge(e.to, -1, e.cap - e.flow, e.cost));
elist.emplace_back(e.to, _edge(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;
struct _edge {
int to, rev;
Cap cap;
Cost cost;
constexpr _edge() : to(), rev(), cap(), cost() {}
constexpr _edge(int _to, int _rev, Cap _cap, Cost _cost) : to(_to), rev(_rev), cap(_cap), cost(_cost) {}
};
std::vector<std::pair<Cap, Cost>> slope(internal::csr<_edge> &g, int s, int t, Cap flow_limit) {
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;
constexpr Q(Cost _key, int _to) : key(_key), to(_to) {}
constexpr 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();
size_t heap_r = 0;
dual_dist[s].second = 0;
que_min.emplace_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;
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;
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.emplace_back(e.to);
else que.emplace_back(dist_to, e.to);
}
}
}
if (!vis[t]) return false;
for (int v = 0; v < _n; ++v) {
if (!vis[v]) continue;
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.emplace_back(flow, cost);
prev_cost_per_flow = d;
}
return result;
}
};
#include <locale>
#include <string>
struct string_converter {
char type(const char &c) const {
return (std::islower(c) ? 'a' : std::isupper(c) ? 'A' : std::isdigit(c) ? '0' : 0);
}
int convert(const char &c) {
if (!start) start = type(c);
return c - start;
}
int convert(const char &c, const std::string &chars) { return chars.find(c); }
template <typename T>
auto convert(const T &v) {
std::vector<decltype(convert(v[0]))> res;
res.reserve(v.size());
for (auto &&e : v) res.emplace_back(convert(e));
return res;
}
template <typename T>
auto convert(const T &v, const std::string &chars) {
std::vector<decltype(convert(v[0], chars))> res;
res.reserve(v.size());
for (auto &&e : v) res.emplace_back(convert(e, chars));
return res;
}
int operator()(const char &v, char s = 0) {
start = s;
return convert(v);
}
int operator()(const char &v, const std::string &chars) { return convert(v, chars); }
template <typename T>
auto operator()(const T &v, char s = 0) {
start = s;
return convert(v);
}
template <typename T>
auto operator()(const T &v, const std::string &chars) {
return convert(v, chars);
}
private:
char start = 0;
} to_int;
#ifdef ATCODER
#pragma GCC target("sse4.2,avx512f,avx512dq,avx512ifma,avx512cd,avx512bw,avx512vl,bmi2")
#endif
#pragma GCC optimize("Ofast,fast-math,unroll-all-loops")
#include <bits/stdc++.h>
#ifndef ATCODER
#pragma GCC target("sse4.2,avx2,bmi2")
#endif
template <class T, class U>
constexpr bool chmax(T &a, const U &b) {
return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
constexpr bool chmin(T &a, const U &b) {
return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr double EPS = 1e-7;
constexpr double PI = 3.14159265358979323846;
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
struct Sonic {
Sonic() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(20);
}
constexpr void operator()() const {}
} sonic;
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &i : v) is >> i;
return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
for (auto it = v.begin(); it != v.end(); ++it) os << (it == v.begin() ? "" : " ") << *it;
return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
void Yes(bool is_correct = true) { std::cout << (is_correct ? "Yes\n" : "No\n"); }
void No(bool is_not_correct = true) { Yes(!is_not_correct); }
void YES(bool is_correct = true) { std::cout << (is_correct ? "YES\n" : "NO\n"); }
void NO(bool is_not_correct = true) { YES(!is_not_correct); }
void Takahashi(bool is_correct = true) { std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n'; }
void Aoki(bool is_not_correct = true) { Takahashi(!is_not_correct); }
int main(void) {
int n;
cin >> n;
string s;
cin >> s;
vector<int> a(n);
cin >> a;
auto v = to_int(s, "yuki");
vector u(4, vector<int>());
rep (i, n) {
u[v[i]].emplace_back(i);
}
mcf_graph<int, ll> mcf(n + 2);
int st = n, gl = n + 1;
if (u[0].empty()) {
co(0);
return 0;
}
mcf.add_edge(st, u[0][0], Inf, 0);
rep (i, 4) {
rep (j, u[i].size()) {
if (i < 3) {
auto it = lower_bound(all(u[i + 1]), u[i][j]);
if (it == u[i + 1].end())
continue;
mcf.add_edge(u[i][j], *it, 1, Inf - a[u[i][j]]);
} else {
mcf.add_edge(u[i][j], gl, 1, Inf - a[u[i][j]]);
}
if (j < (int)u[i].size() - 1) {
mcf.add_edge(u[i][j], u[i][j + 1], Inf, 0);
}
}
}
auto p = mcf.slope(st, gl);
ll ans = 0;
for (auto [l, r] : p) {
chmax(ans, (ll)l * 4 * Inf - r);
}
co(ans);
return 0;
}