結果
| 問題 |
No.3201 Corporate Synergy
|
| コンテスト | |
| ユーザー |
 noya2
|
| 提出日時 | 2025-07-12 01:08:23 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 18,755 bytes |
| コンパイル時間 | 3,866 ms |
| コンパイル使用メモリ | 296,432 KB |
| 実行使用メモリ | 7,844 KB |
| 最終ジャッジ日時 | 2025-07-12 01:08:28 |
| 合計ジャッジ時間 | 5,096 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 20 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/flow/project_selection.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/simple_queue.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/simple_queue.hpp"
namespace noya2::internal {
template <class T>
struct simple_queue {
std::vector<T> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const T& t) { payload.push_back(t); }
T& front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
} // namespace noya2::internal
#line 4 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"
#line 10 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"
namespace noya2 {
template <class Cap> struct mf_graph {
public:
mf_graph() : _n(0) {}
explicit mf_graph(int n) : _n(n), g(n) {}
int add_edge(int from, int to, Cap cap) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(0 <= cap);
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});
g[to].push_back(_edge{from, from_id, 0});
return m;
}
struct edge {
int from, to;
Cap cap, flow;
};
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};
}
std::vector<edge> edges() {
int m = int(pos.size());
std::vector<edge> result;
for (int i = 0; i < m; i++) {
result.push_back(get_edge(i));
}
return result;
}
void change_edge(int i, Cap new_cap, Cap new_flow) {
int m = int(pos.size());
assert(0 <= i && i < m);
assert(0 <= new_flow && new_flow <= new_cap);
auto& _e = g[pos[i].first][pos[i].second];
auto& _re = g[_e.to][_e.rev];
_e.cap = new_cap - new_flow;
_re.cap = new_flow;
}
Cap flow(int s, int t) {
return flow(s, t, std::numeric_limits<Cap>::max());
}
Cap flow(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
std::vector<int> level(_n), iter(_n);
internal::simple_queue<int> que;
auto bfs = [&]() {
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
que.clear();
que.push(s);
while (!que.empty()) {
int v = que.front();
que.pop();
for (auto e : g[v]) {
if (e.cap == 0 || level[e.to] >= 0) continue;
level[e.to] = level[v] + 1;
if (e.to == t) return;
que.push(e.to);
}
}
};
auto dfs = [&](auto self, int v, Cap up) {
if (v == s) return up;
Cap res = 0;
int level_v = level[v];
for (int& i = iter[v]; i < int(g[v].size()); i++) {
_edge& e = g[v][i];
if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
Cap d =
self(self, e.to, std::min(up - res, g[e.to][e.rev].cap));
if (d <= 0) continue;
g[v][i].cap += d;
g[e.to][e.rev].cap -= d;
res += d;
if (res == up) return res;
}
level[v] = _n;
return res;
};
Cap flow = 0;
while (flow < flow_limit) {
bfs();
if (level[t] == -1) break;
std::fill(iter.begin(), iter.end(), 0);
Cap f = dfs(dfs, t, flow_limit - flow);
if (!f) break;
flow += f;
}
return flow;
}
std::vector<bool> min_cut(int s) {
std::vector<bool> visited(_n);
internal::simple_queue<int> que;
que.push(s);
while (!que.empty()) {
int p = que.front();
que.pop();
visited[p] = true;
for (auto e : g[p]) {
if (e.cap && !visited[e.to]) {
visited[e.to] = true;
que.push(e.to);
}
}
}
return visited;
}
private:
int _n;
struct _edge {
int to, rev;
Cap cap;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
namespace noya2::internal {
template<class E>
struct csr {
csr () {}
csr (int _n) : n(_n) {}
csr (int _n, int m) : n(_n){
start.reserve(m);
elist.reserve(m);
}
// ACL style constructor (do not have to call build)
csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
for (auto &[i, e] : idx_elem){
start[i + 2]++;
}
for (int i = 1; i < n; i++){
start[i + 2] += start[i + 1];
}
for (auto &[i, e] : idx_elem){
elist[start[i + 1]++] = e;
}
prepared = true;
}
int add(int idx, E elem){
int eid = start.size();
start.emplace_back(idx);
elist.emplace_back(elem);
return eid;
}
void build(){
if (prepared) return ;
int m = start.size();
std::vector<E> nelist(m);
std::vector<int> nstart(n + 2, 0);
for (int i = 0; i < m; i++){
nstart[start[i] + 2]++;
}
for (int i = 1; i < n; i++){
nstart[i + 2] += nstart[i + 1];
}
for (int i = 0; i < m; i++){
nelist[nstart[start[i] + 1]++] = elist[i];
}
swap(elist,nelist);
swap(start,nstart);
prepared = true;
}
const auto operator[](int idx) const {
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
auto operator[](int idx){
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
const auto operator()(int idx, int l, int r) const {
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
auto operator()(int idx, int l, int r){
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
size_t size() const {
return n;
}
int n;
std::vector<int> start;
std::vector<E> elist;
bool prepared = false;
};
} // namespace noya2::internal
#line 151 "/Users/noya2/Desktop/Noya2_library/flow/maxflow.hpp"
namespace noya2 {
template<class Cap>
struct maxflow {
struct edge {
int from, to;
Cap cap, flow;
};
maxflow() : n(0) {}
explicit maxflow(int _n) : n(_n), g(n), degree(_n,0) {}
int add_edge(int from, int to, Cap cap){
assert(0 <= from && from < n);
assert(0 <= to && to < n);
assert(0 <= cap);
int eid = (int)(pos.size());
int from_id = degree[from];
int to_id = degree[to] + (from == to ? 1 : 0);
g.add(from, _edge{to, to_id, cap});
degree[from]++;
g.add(to, _edge{from, from_id, 0});
degree[to]++;
pos.emplace_back(from, from_id);
return eid;
}
edge get_edge(int i) {
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};
}
Cap flow(int s, int t){
return flow(s, t, std::numeric_limits<Cap>::max());
}
Cap flow(int s, int t, Cap flow_limit){
assert(0 <= s && s < n);
assert(0 <= t && t < n);
assert(s != t);
g.build();
std::vector<int> level(n), iter(n);
internal::simple_queue<int> que;
auto bfs = [&]() {
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
que.clear();
que.push(s);
while (!que.empty()){
int v = que.front(); que.pop();
for (auto e : g[v]){
if (e.cap == 0 || level[e.to] >= 0) continue;
level[e.to] = level[v] + 1;
if (e.to == t) return ;
que.push(e.to);
}
}
};
auto dfs = [&](auto sfs, int v, Cap up){
if (v == s) return up;
Cap res = 0;
int level_v = level[v];
for (int &i = iter[v]; i < degree[v]; i++){
_edge &e = g[v][i];
if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
Cap d = sfs(sfs, e.to, std::min(up - res, g[e.to][e.rev].cap));
if (d <= 0) continue;
g[v][i].cap += d;
g[e.to][e.rev].cap -= d;
res += d;
if (res == up) return res;
}
level[v] = n;
return res;
};
Cap flow = 0;
while (flow < flow_limit){
bfs();
if (level[t] == -1) break;
std::fill(iter.begin(), iter.end(), 0);
Cap f = dfs(dfs, t, flow_limit - flow);
if (!f) break;
flow += f;
}
return flow;
}
std::vector<bool> min_cut(int s){
std::vector<bool> visited(n);
internal::simple_queue<int> que;
que.push(s);
visited[s] = true;
while (!que.empty()){
int v = que.front(); que.pop();
for (auto e : g[v]){
if (e.cap && !visited[e.to]){
visited[e.to] = true;
que.push(e.to);
}
}
}
return visited;
}
private:
int n;
struct _edge {
int to, rev;
Cap cap;
};
std::vector<std::pair<int, int>> pos;
internal::csr<_edge> g;
std::vector<int> degree;
};
} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/flow/project_selection.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/flow/project_selection.hpp"
namespace noya2 {
/**
* @brief project selection problem (PSP) solver
* @cite https://en.wikipedia.org/wiki/Quadratic_pseudo-Boolean_optimization
* @cite https://theory-and-me.hatenablog.com/entry/2020/03/17/180157
*
* @tparam Cost is expected signed integer type such as `int`, `long long`.
*/
template<class Cost>
struct project_selection {
int n;
// It costs c0 without any constraints.
Cost c0;
// It costs c1[ 2*i + x_i ].
std::vector<Cost> c1;
maxflow<Cost> mfg;
project_selection () {}
project_selection (int _n) : n(_n), c0(0), c1(_n*2, 0), mfg(n+2) {}
void cost_total(Cost cost){
c0 += cost;
}
void profit_total(Cost profit){
cost_total(-profit);
}
void cost_x0(int x, Cost cost){
c1[2*x + 0] += cost;
}
void cost_x1(int x, Cost cost){
c1[2*x + 1] += cost;
}
void cost_xp(int x, int p, Cost cost){
assert(p == 0 || p == 1);
c1[2*x + p] += cost;
}
void cost_xf(int x, std::array<Cost,2> cost){
cost_x0(x, cost[0]);
cost_x1(x, cost[1]);
}
void profit_x0(int x, Cost profit){
cost_x0(x, -profit);
}
void profit_x1(int x, Cost profit){
cost_x1(x, -profit);
}
void profit_xp(int x, int p, Cost profit){
cost_xp(x, p, -profit);
}
void profit_xf(int x, std::array<Cost,2> profit){
cost_xf(x, {-profit[0],-profit[1]});
}
void ensure_x0(int x){
// todo
assert(false);
}
void cost_x0y1(int x, int y, Cost c){
assert(c >= 0);
mfg.add_edge(x, y, c);
}
void cost_x1y0(int x, int y, Cost c){
cost_x0y1(y, x, c);
}
void cost_xfyg(int x, int y, std::array<std::array<Cost,2>,2> cost){
cost_total(cost[0][0]);
cost_x1(x, cost[1][0] - cost[0][0]);
cost_x1(y, cost[1][1] - cost[1][0]);
cost_x0y1(x, y, cost[1][0] + cost[0][1] - cost[0][0] - cost[1][1]);
}
void profit_x0y0(int x, int y, Cost profit){
profit_total(profit);
cost_x1(x, profit);
cost_x0y1(x, y, profit);
}
void profit_x1y1(int x, int y, Cost profit){
profit_x1(y, profit);
cost_x0y1(x, y, profit);
}
// Only once call is permitted.
Cost min_cost(){
int s = n, t = n+1;
for (int x = 0; x < n; x++){
Cost x0 = c1[2*x + 0];
Cost x1 = c1[2*x + 1];
c0 += std::min(x0, x1);
if (x0 < x1){
mfg.add_edge(s, x, x1 - x0);
}
if (x0 > x1){
mfg.add_edge(x, t, x0 - x1);
}
}
Cost ans = c0 + mfg.flow(s, t);
return ans;
}
Cost max_profit(){
return -min_cost();
}
// Ensure : call after min_cost()
std::vector<bool> answer(){
auto ans = mfg.min_cut(n);
ans.pop_back(); // pop s
ans.pop_back(); // pop t
for (int i = 0; i < n; i++){
ans[i] = !ans[i];
}
return ans;
}
};
} // namespace noya2
#line 4 "c.cpp"
void solve(){
int n; in(n);
vector<ll> p(n); in(p);
project_selection<ll> ps(n+200);
rep(i,n){
ps.profit_x1(i,p[i]);
}
int m; in(m);
rep(i,m){
int u, v; in(u,v); u--, v--;
ps.cost_x0y1(u,v,linf);
}
int k; in(k);
rep(i,k){
int u, v; in(u,v); u--, v--;
ll s; in(s);
ps.profit_x1(n+i,s);
ps.cost_x0y1(u,n+i,linf);
ps.cost_x0y1(v,n+i,linf);
}
out(ps.max_profit());
}
int main(){
int t = 1; //in(t);
while (t--) { solve(); }
}