結果
| 問題 | No.2320 Game World for PvP |
| ユーザー |
 iiljj
|
| 提出日時 | 2023-05-26 23:00:57 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 18,279 bytes |
| コンパイル時間 | 1,974 ms |
| コンパイル使用メモリ | 165,204 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-12-25 10:05:09 |
| 合計ジャッジ時間 | 2,956 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 30 |
ソースコード
/* #region Head */
// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath> // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;
#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))
#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define ISIZE(x) ((int)(x).size())
#define PERM(c) \
sort(ALL(c)); \
for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))
#define endl '\n'
constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
for (T &x : vec) is >> x;
return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
os << "{";
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
return os;
}
template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
REP(i, 0, SIZE(arr)) is >> arr[i];
return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
os << "{";
REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
is >> pair_var.first >> pair_var.second;
return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
os << "(" << pair_var.first << ", " << pair_var.second << ")";
return os;
}
// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
os << "{";
REPI(itr, map_var) {
os << *itr;
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
os << "{";
REPI(itr, map_var) {
auto [key, value] = *itr;
os << "(" << key << ", " << value << ")";
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
pq<T> pq_cp(pq_var);
os << "{";
if (!pq_cp.empty()) {
os << pq_cp.top(), pq_cp.pop();
while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
}
return os << "}";
}
// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
os << get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
os << ' ';
} else if constexpr (end_line) {
os << '\n';
}
return operator<< <N + 1, end_line>(os, a);
}
return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(cout, a); }
void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail) > 0) cout << ' ';
pprint(move(tail)...);
}
// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
DUMPOUT << head;
if (sizeof...(Tail) > 0) DUMPOUT << ", ";
dump_func(move(tail)...);
}
// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
if (comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
if (comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif
#ifndef MYLOCAL
#undef DEBUG_
#endif
#ifdef DEBUG_
#define DEB
#define dump(...) \
DUMPOUT << " " << string(#__VA_ARGS__) << ": " \
<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \
<< " ", \
dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif
#define VAR(type, ...) \
type __VA_ARGS__; \
assert((cin >> __VA_ARGS__));
template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }
struct AtCoderInitialize {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
AtCoderInitialize() {
ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }
template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i) v[i]--;
}
template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i) v[i]++;
}
/* #endregion */
// #include <atcoder/all>
// using namespace atcoder;
/* #region DINIC_SPARSE */
// using flow_type = int;
template <class flow_type> struct dinic_sparse {
struct edge {
int src, dst;
flow_type cap, flow;
int rev_idx;
bool is_rev;
};
int n, s, t;
std::vector<std::vector<edge>> g;
std::vector<int> level, prog, que;
std::vector<std::pair<std::pair<int, int>, flow_type>> edges;
dinic_sparse(int n_ = 0) : n(n_) {}
// Compute the maximum-flow from `s_` to `t_` by Dinic's algorithm.
flow_type maximum_flow(int s_, int t_) {
s = s_;
t = t_;
make_graph();
que.resize(n);
flow_type res = 0;
while (levelize()) {
prog.assign(n, 0);
res += augment(s, std::numeric_limits<flow_type>::max());
}
return res;
}
// Add an edge from `u` to `v` with capacity `c`. Note that it will be added
// to `g` when `make_graph` is called instead of just after calling this
// function.
void add_edge(int u, int v, flow_type c) {
if (u != v && c != 0) {
edges.emplace_back(std::make_pair(u, v), c);
}
}
void make_graph() {
g.assign(n, {});
if (true) {
std::sort(edges.begin(), edges.end());
for (auto it = edges.begin(); it != edges.end();) {
flow_type c = 0;
auto uv = it->first;
while (it != edges.end() && it->first == uv) {
c += it->second;
++it;
}
int u = uv.first, v = uv.second;
g[u].push_back({u, v, c, 0, (int)g[v].size(), false});
g[v].push_back({v, u, c, c, (int)g[u].size() - 1, true});
}
} else {
for (auto &e : edges) {
auto uv = e.first;
int u = uv.first, v = uv.second;
flow_type c = e.second;
g[u].push_back({u, v, c, 0, (int)g[v].size(), false});
g[v].push_back({v, u, c, c, (int)g[u].size() - 1, true});
}
}
}
bool levelize() {
int fst = 0, lst = 0;
que[lst++] = s;
level.assign(n, -1);
level[s] = 0;
while (fst != lst) {
int v = que[fst++];
if (v == t) break;
for (auto &e : g[v]) {
if (level[e.dst] == -1 && residue(e) != 0) {
level[e.dst] = level[v] + 1;
que[lst++] = e.dst;
}
}
}
return level[t] != -1;
}
flow_type augment(int v, flow_type lim) {
flow_type res = 0;
if (v == t) return lim;
for (int &i = prog[v]; i < (int)g[v].size(); ++i) {
if (lim == 0) break;
auto &e = g[v][i];
if (level[v] < level[e.dst] && residue(e) != 0) {
flow_type aug = augment(e.dst, std::min(lim, residue(e)));
if (aug == 0) continue;
e.flow += aug;
reverse(e).flow -= aug;
res += aug;
lim -= aug;
}
}
return res;
}
flow_type residue(const edge &e) { return e.cap - e.flow; }
edge &reverse(const edge &e) { return g[e.dst][e.rev_idx]; }
// Output current flow by graphviz dot language.
// Run `dot $filename -o out.png -T png` on shell.
void show(const std::string &filename = "out.dot") {
int fst = 0, lst = 0;
que[lst++] = s;
level.assign(n, -1);
level[s] = 0;
while (fst != lst) {
int v = que[fst++];
for (auto &e : g[v]) {
if (!e.is_rev && level[e.dst] == -1 && e.flow) {
level[e.dst] = level[v] + 1;
que[lst++] = e.dst;
}
}
}
std::map<int, std::vector<int>> rank_to_vertices;
for (int i = 0; i < n; ++i) {
rank_to_vertices[level[i]].push_back(i);
}
std::ostringstream oss;
oss << "digraph {" << '\n';
for (int i = 0; i < n; ++i) {
oss << "\t" << i;
if (i == s || i == t) {
oss << " [ peripheries = 2 ]";
}
oss << ";\n";
for (auto &e : g[i]) {
if (!e.is_rev) {
const char *color = e.flow ? "black" : "gray";
oss << "\t" << e.src << " -> " << e.dst << "\t[ "
<< "label = \"" << e.flow << "/" << e.cap << "\", "
<< "color = \"" << color << "\", "
<< "fontcolor = \"" << color << "\"];\n";
}
}
}
for (auto &p : rank_to_vertices) {
const char *rank = p.first != -1 ? "same" : "sink";
oss << "\t{ rank = " << rank << "; ";
for (int v : p.second) {
if (v != s && v != t) {
oss << v << "; ";
}
}
oss << "}\n";
}
oss << "\t{ rank = same; " << s << "; }\n";
oss << "\t{ rank = same; " << t << "; }\n";
oss << "}\n";
std::ofstream ofs(filename);
ofs << oss.str();
}
};
/* #endregion */
/* #region ProjectSelectionProblem */
template <typename Flow = ll> struct ProjectSelectionProblem {
int n;
int S, T;
dinic_sparse<Flow> dn;
vc<Flow> costs0, costs1;
Flow offset;
ProjectSelectionProblem(int n) : n(n), S(n), T(n + 1), dn(n + 2), costs0(n, 0), costs1(n, 0), offset(0) {}
// i番目の2択問題に関する選択肢ごとのコストを登録する
void register_costs_of_choice(int i, Flow cost0, Flow cost1) {
assert(i < n);
costs0[i] += cost0; // 選択肢 0
costs1[i] += cost1; // 選択肢 1
}
// i番目の2択問題に関する選択肢ごとの報酬を登録する
void register_rewards_of_choice(int i, Flow reward0, Flow reward1) {
Flow cost0 = -reward0;
Flow cost1 = -reward1;
register_costs_of_choice(i, cost0, cost1);
}
// choice0_idx 番目の2択問題で選択肢 0, choide1_idx 番目の2択問題で選択肢 1, が
// 同時に生起したときのコストを登録する
void register_cost_of_comb01(int choice0_idx, int choide1_idx, Flow cost) {
assert(choice0_idx < n);
assert(choide1_idx < n);
assert(cost >= 0);
dn.add_edge(choide1_idx, choice0_idx, cost);
}
// choide1_idx 番目の2択問題で選択肢 1, choice0_idx 番目の2択問題で選択肢 0, が
// 同時に生起したときのコストを登録する
void register_cost_of_comb10(int choice1_idx, int choide0_idx, Flow cost) {
register_cost_of_comb01(choide0_idx, choice1_idx, cost);
}
// 選択肢 0 が共起したときの報酬 (>=0) を登録する
void register_reward_of_comb00(int i, int j, Flow reward) {
assert(reward >= 0);
register_cost_of_comb01(i, j, reward);
costs1[i] += reward;
offset -= reward;
}
// 選択肢 1 が共起したときの報酬 (>=0) を登録する
void register_reward_of_comb11(int i, int j, Flow reward) {
assert(reward >= 0);
register_cost_of_comb01(j, i, reward);
costs0[i] += reward;
offset -= reward;
}
Flow exec_mincost() {
// offset = 0;
REP(i, 0, n) {
Flow mi = min(costs0[i], costs1[i]);
dn.add_edge(S, i, costs0[i] - mi); // 選択肢 0
dn.add_edge(i, T, costs1[i] - mi); // 選択肢 1
offset += mi;
}
Flow f = dn.maximum_flow(S, T);
return f + offset;
}
Flow exec_maxreward() { return -exec_mincost(); }
};
/* #endregion */
// Problem
void solve() {
VAR(ll, n, s, t);
vll e(s), r(t);
cin >> e, r;
e--, r--;
vvll c(n, vll(n));
cin >> c;
vll team(n, -1); // -1: 未定，0/1: 各チーム
for (const auto &ei : e) team[ei] = 0;
for (const auto &ri : r) team[ri] = 1;
ProjectSelectionProblem<> ps(n); //
// 連携力ごとに，確定 or 未確定 で分けていく
ll sum = 0;
REP(i, 0, n - 1) REP(j, i + 1, n) {
if (team[i] != -1 && team[j] != -1) {
if (team[i] == team[j]) {
// 同じチームであることが確定している
sum += c[i][j];
}
// else 同じチームでないことが確定している
} else if (team[i] != -1) {
// i はチーム確定，j は未確定
if (team[i] == 0) {
ps.register_rewards_of_choice(j, c[i][j], 0);
} else {
ps.register_rewards_of_choice(j, 0, c[i][j]);
}
} else if (team[j] != -1) {
// j はチーム確定，i は未確定
if (team[j] == 0) {
ps.register_rewards_of_choice(i, c[i][j], 0);
} else {
ps.register_rewards_of_choice(i, 0, c[i][j]);
}
} else {
// i も j もチーム未確定
ps.register_reward_of_comb00(i, j, c[i][j]);
ps.register_reward_of_comb11(i, j, c[i][j]);
}
}
ll ma = ps.exec_maxreward();
ll ans = sum + ma;
// dump(sum, ma);
pprint(ans);
}
// entry point
int main() {
solve();
return 0;
}