結果
| 問題 |
No.2320 Game World for PvP
|
| コンテスト | |
| ユーザー |
 maspy
|
| 提出日時 | 2023-05-26 21:37:17 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 4 ms / 2,000 ms |
| コード長 | 21,001 bytes |
| コンパイル時間 | 4,851 ms |
| コンパイル使用メモリ | 304,952 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-12-25 05:31:54 |
| 合計ジャッジ時間 | 5,977 ms |
|
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 * 4 |
| other | AC * 30 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sum = 0;
for (auto &&a: A) sum += a;
return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
assert(!que.empty());
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
assert(!que.empty());
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
template <class T>
static auto check(T &&x) -> decltype(x.write(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};
struct has_read_impl {
template <class T>
static auto check(T &&x) -> decltype(x.read(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};
struct Scanner {
FILE *fp;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) {
bool sep = false;
for (size_t i = st; i < ed; i++) {
if (isspace(line[i])) {
sep = true;
break;
}
}
if (!sep) reread();
}
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
if (neg) ref = -ref;
return true;
}
template <typename T,
typename enable_if<has_read<T>::value>::type * = nullptr>
inline bool read_single(T &x) {
x.read();
return true;
}
bool read_single(double &ref) {
string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
bool read_single(char &ref) {
string s;
if (!read_single(s) || s.size() != 1) return false;
ref = s[0];
return true;
}
template <class T>
bool read_single(vector<T> &ref) {
for (auto &d: ref) {
if (!read_single(d)) return false;
}
return true;
}
template <class T, class U>
bool read_single(pair<T, U> &p) {
return (read_single(p.first) && read_single(p.second));
}
template <size_t N = 0, typename T>
void read_single_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
read_single(x);
read_single_tuple<N + 1>(t);
}
}
template <class... T>
bool read_single(tuple<T...> &tpl) {
read_single_tuple(tpl);
return true;
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
Printer(FILE *_fp) : fp(_fp) {}
~Printer() { flush(); }
static constexpr size_t SIZE = 1 << 15;
FILE *fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write(const char val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write('0');
return;
}
if (val < 0) {
write('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char(0x30 | (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
pos += len;
}
void write(const string s) {
for (char c: s) write(c);
}
void write(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write(s[i]);
}
void write(const double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
void write(const long double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
template <typename T,
typename enable_if<has_write<T>::value>::type * = nullptr>
inline void write(T x) {
x.write();
}
template <class T>
void write(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
template <class T, class U>
void write(const pair<T, U> val) {
write(val.first);
write(' ');
write(val.second);
}
template <size_t N = 0, typename T>
void write_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { write(' '); }
const auto x = std::get<N>(t);
write(x);
write_tuple<N + 1>(t);
}
}
template <class... T>
bool write(tuple<T...> tpl) {
write_tuple(tpl);
return true;
}
template <class T, size_t S>
void write(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
void write(i128 val) {
string s;
bool negative = 0;
if (val < 0) {
negative = 1;
val = -val;
}
while (val) {
s += '0' + int(val % 10);
val /= 10;
}
if (negative) s += "-";
reverse(all(s));
if (len(s) == 0) s = "0";
write(s);
}
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
printer.write(head);
if (sizeof...(Tail)) printer.write(' ');
print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
scanner.read(head);
read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 1 "/home/maspy/compro/library/flow/maxflow.hpp"
template <typename Cap>
struct MaxFlowGraph {
struct Edge {
int to, rev;
Cap cap;
Cap flow = 0;
};
int N;
vc<tuple<int, int, Cap, Cap>> dat;
vc<int> prog, level;
vc<int> que;
vc<Edge> edges;
vc<int> indptr;
Cap flow_ans;
bool calculated;
bool is_prepared;
MaxFlowGraph(int N) : N(N), calculated(0), is_prepared(0) {}
void add(int frm, int to, Cap cap, Cap rev_cap = 0) {
assert(0 <= frm && frm < N);
assert(0 <= to && to < N);
assert(Cap(0) <= cap);
if (frm == to) return;
dat.eb(frm, to, cap, rev_cap);
}
void build() {
assert(!is_prepared);
int M = len(dat);
is_prepared = 1;
indptr.assign(N, 0);
for (auto&& [a, b, c, d]: dat) indptr[a]++, indptr[b]++;
indptr = cumsum<int>(indptr);
vc<int> nxt_idx = indptr;
edges.resize(2 * M);
for (auto&& [a, b, c, d]: dat) {
int p = nxt_idx[a]++;
int q = nxt_idx[b]++;
edges[p] = Edge{b, q, c};
edges[q] = Edge{a, p, d};
}
}
vc<tuple<int, int, Cap>> get_flow_edges() {
vc<tuple<int, int, Cap>> res;
FOR(frm, N) {
FOR(k, indptr[frm], indptr[frm + 1]) {
auto& e = edges[k];
if (e.flow <= 0) continue;
res.eb(frm, e.to, e.flow);
}
}
return res;
}
Cap flow(int source, int sink) {
assert(is_prepared);
if (calculated) return flow_ans;
calculated = true;
flow_ans = 0;
while (set_level(source, sink)) {
prog = indptr;
while (1) {
Cap x = flow_dfs(source, sink, infty<Cap>);
if (x == 0) break;
flow_ans += x;
chmin(flow_ans, infty<Cap>);
if (flow_ans == infty<Cap>) return flow_ans;
}
}
return flow_ans;
}
// 最小カットの値および、カットを表す 01 列を返す
pair<Cap, vc<int>> cut(int source, int sink) {
Cap f = flow(source, sink);
vc<int> res(N);
FOR(v, N) res[v] = (level[v] >= 0 ? 0 : 1);
return {f, res};
}
private:
bool set_level(int source, int sink) {
que.resize(N);
level.assign(N, -1);
level[source] = 0;
int l = 0, r = 0;
que[r++] = source;
while (l < r) {
int v = que[l++];
FOR(k, indptr[v], indptr[v + 1]) {
auto& e = edges[k];
if (e.cap > 0 && level[e.to] == -1) {
level[e.to] = level[v] + 1;
if (e.to == sink) return true;
que[r++] = e.to;
}
}
}
return false;
}
Cap flow_dfs(int v, int sink, Cap lim) {
if (v == sink) return lim;
Cap res = 0;
for (int& i = prog[v]; i < indptr[v + 1]; ++i) {
auto& e = edges[i];
if (e.cap > 0 && level[e.to] == level[v] + 1) {
Cap a = flow_dfs(e.to, sink, min(lim, e.cap));
if (a > 0) {
e.cap -= a, e.flow += a;
edges[e.rev].cap += a, edges[e.rev].flow -= a;
res += a;
lim -= a;
if (lim == 0) break;
}
}
}
return res;
}
};
#line 2 "/home/maspy/compro/library/flow/binary_optimization.hpp"
template <typename T, bool MINIMIZE>
struct Binary_Optimization {
int n;
int nxt;
int source, sink;
T base_cost;
map<pair<int, int>, T> edges;
Binary_Optimization(int n) : n(n), base_cost(0) {
source = n;
sink = n + 1;
nxt = n + 2;
}
// xi を 0, 1 にするときにかかるコストを追加する。
void add_1(int i, T x0, T x1) {
assert(0 <= i && i < n);
if (!MINIMIZE) { x0 = -x0, x1 = -x1; }
_add_1(i, x0, x1);
}
// (xi,xj) = (00,01,10,11) とするときにかかるコストを追加する。
// コストが劣モ x00 + x11 <= x10 + x10 になっている必要がある。
// 特に、対角成分に利得を与えることができる。
void add_2(int i, int j, T x00, T x01, T x10, T x11) {
assert(i != j);
assert(0 <= i && i < n);
assert(0 <= j && j < n);
if (!MINIMIZE) {
x00 = -x00, x01 = -x01;
x10 = -x10, x11 = -x11;
}
_add_2(i, j, x00, x01, x10, x11);
}
// (xi,xj,xk) = (000,001,010,011,100,101,110,111)
// とするときにかかるコストを追加する。劣モになっている必要がある。
// 特に、000 や 111 に利得を与えることができる。
void add_3(int i, int j, int k, T x000, T x001, T x010, T x011, T x100,
T x101, T x110, T x111) {
assert(i != j && i != k && j != k);
assert(0 <= i && i < n);
assert(0 <= j && j < n);
assert(0 <= k && k < n);
if (!MINIMIZE) {
x000 = -x000, x001 = -x001;
x010 = -x010, x011 = -x011;
x100 = -x100, x101 = -x101;
x110 = -x110, x111 = -x111;
}
_add_3(i, j, k, x000, x001, x010, x011, x100, x101, x110, x111);
}
// 最小値および、01 列を返す
pair<T, vc<int>> calc() {
MaxFlowGraph<T> G(nxt);
for (auto&& [key, cap]: edges) {
auto [frm, to] = key;
G.add(frm, to, cap);
}
G.build();
auto [val, cut] = G.cut(source, sink);
val += base_cost;
chmin(val, infty<T>);
cut.resize(n);
if (!MINIMIZE) val = -val;
return {val, cut};
}
void debug() {
print("base_cost", base_cost);
print("source=", source, "sink=", sink);
for (auto&& [key, cap]: edges) print(key, cap);
}
private:
void add_edge(int i, int j, T t) {
assert(t >= 0);
if (t == 0) return;
pair<int, int> key = mp(i, j);
edges[key] += t;
chmin(edges[key], infty<T>);
}
void _add_1(int i, T x0, T x1) {
if (x0 <= x1) {
base_cost += x0;
add_edge(source, i, x1 - x0);
} else {
base_cost += x1;
add_edge(i, sink, x0 - x1);
}
}
void _add_2(int i, int j, T x00, T x01, T x10, T x11) {
assert(x00 + x11 <= x01 + x10);
_add_1(i, x00, x10);
_add_1(j, 0, x11 - x10);
add_edge(i, j, x01 + x10 - x00 - x11);
}
void _add_3(int i, int j, int k, T x000, T x001, T x010, T x011, T x100,
T x101, T x110, T x111) {
T p = x000 - x100 - x010 - x001 + x110 + x101 + x011 - x111;
if (p > 0) {
base_cost += x000;
_add_1(i, 0, x100 - x000);
_add_1(j, 0, x010 - x000);
_add_1(k, 0, x001 - x000);
_add_2(i, j, 0, 0, 0, x000 + x110 - x100 - x010);
_add_2(i, k, 0, 0, 0, x000 + x101 - x100 - x001);
_add_2(j, k, 0, 0, 0, x000 + x011 - x010 - x001);
// あとは、111 のときに利得 p を追加する
base_cost -= p;
// 111 以外だとコスト p
add_edge(i, nxt, p);
add_edge(j, nxt, p);
add_edge(k, nxt, p);
add_edge(nxt, sink, p);
++nxt;
} else {
p = -p;
base_cost += x111;
_add_1(i, x011 - x111, 0);
_add_1(i, x101 - x111, 0);
_add_1(i, x110 - x111, 0);
_add_2(i, j, x111 + x001 - x011 - x101, 0, 0, 0);
_add_2(i, k, x111 + x010 - x011 - x110, 0, 0, 0);
_add_2(j, k, x111 + x100 - x101 - x110, 0, 0, 0);
// 000 のときに利得 p を追加する
base_cost -= p;
// 000 以外だとコスト p
add_edge(nxt, i, p);
add_edge(nxt, j, p);
add_edge(nxt, k, p);
add_edge(source, nxt, p);
++nxt;
}
}
};
#line 5 "main.cpp"
void solve() {
LL(N, S, T);
vc<int> state(N, -1);
FOR(S) {
INT(x);
--x;
state[x] = 0;
}
FOR(T) {
INT(x);
--x;
state[x] = 1;
}
Binary_Optimization<i128, false> X(N);
FOR(i, N) {
if (state[i] == 0) X.add_1(i, 0, -infty<ll>);
if (state[i] == 1) X.add_1(i, -infty<ll>, 0);
}
FOR(i, N) FOR(j, N) {
INT(x);
if (i >= j) continue;
X.add_2(i, j, x, 0, 0, x);
}
auto [val, x] = X.calc();
print(val);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}