結果
| 問題 | No.1301 Strange Graph Shortest Path |
| ユーザー |
 theory_and_me
|
| 提出日時 | 2020-11-28 00:28:01 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 202 ms / 3,000 ms |
| コード長 | 7,791 bytes |
| コンパイル時間 | 2,535 ms |
| コンパイル使用メモリ | 223,468 KB |
| 実行使用メモリ | 39,532 KB |
| 最終ジャッジ日時 | 2024-07-26 21:24:20 |
| 合計ジャッジ時間 | 9,048 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 142 ms
39,004 KB |
| testcase_03 | AC | 117 ms
34,872 KB |
| testcase_04 | AC | 181 ms
37,828 KB |
| testcase_05 | AC | 125 ms
38,480 KB |
| testcase_06 | AC | 162 ms
35,240 KB |
| testcase_07 | AC | 149 ms
37,200 KB |
| testcase_08 | AC | 121 ms
35,276 KB |
| testcase_09 | AC | 130 ms
33,572 KB |
| testcase_10 | AC | 118 ms
34,724 KB |
| testcase_11 | AC | 148 ms
36,288 KB |
| testcase_12 | AC | 155 ms
36,316 KB |
| testcase_13 | AC | 131 ms
38,588 KB |
| testcase_14 | AC | 157 ms
33,732 KB |
| testcase_15 | AC | 129 ms
34,520 KB |
| testcase_16 | AC | 177 ms
37,848 KB |
| testcase_17 | AC | 154 ms
39,532 KB |
| testcase_18 | AC | 141 ms
35,980 KB |
| testcase_19 | AC | 138 ms
35,620 KB |
| testcase_20 | AC | 157 ms
34,236 KB |
| testcase_21 | AC | 151 ms
37,992 KB |
| testcase_22 | AC | 181 ms
35,148 KB |
| testcase_23 | AC | 136 ms
38,948 KB |
| testcase_24 | AC | 174 ms
35,012 KB |
| testcase_25 | AC | 168 ms
37,940 KB |
| testcase_26 | AC | 149 ms
36,424 KB |
| testcase_27 | AC | 136 ms
36,336 KB |
| testcase_28 | AC | 126 ms
37,992 KB |
| testcase_29 | AC | 202 ms
36,996 KB |
| testcase_30 | AC | 147 ms
37,544 KB |
| testcase_31 | AC | 162 ms
37,392 KB |
| testcase_32 | AC | 2 ms
5,376 KB |
| testcase_33 | AC | 99 ms
32,708 KB |
| testcase_34 | AC | 143 ms
39,408 KB |
ソースコード
#include <bits/stdc++.h>
#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
namespace atcoder {
template <class Cap, class Cost> struct mcf_graph {
public:
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);
int m = int(pos.size());
pos.push_back({from, int(g[from].size())});
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});
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<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
std::vector<Cost> dual(_n, 0), dist(_n);
std::vector<int> pv(_n), pe(_n);
std::vector<bool> vis(_n);
auto dual_ref = [&]() {
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;
};
Cap flow = 0;
Cost cost = 0, prev_cost = -1;
std::vector<std::pair<Cap, Cost>> result;
result.push_back({flow, cost});
while (flow < flow_limit) {
if (!dual_ref()) 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 == d) {
result.pop_back();
}
result.push_back({flow, cost});
prev_cost = cost;
}
return result;
}
private:
int _n;
struct _edge {
int to, rev;
Cap cap;
Cost cost;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
} // namespace atcoder
using namespace std;
using namespace atcoder;
#define REP(i,n) for(ll i=0;i<(ll)n;i++)
#define dump(x) cerr << "Line " << __LINE__ << ": " << #x << " = " << (x) << "\n";
#define spa << " " <<
#define fi first
#define se second
#define ALL(a) (a).begin(),(a).end()
#define ALLR(a) (a).rbegin(),(a).rend()
using ld = long double;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
template<typename T> using V = vector<T>;
template<typename T> using P = pair<T, T>;
template<typename T> vector<T> make_vec(size_t n, T a) { return vector<T>(n, a); }
template<typename... Ts> auto make_vec(size_t n, Ts... ts) { return vector<decltype(make_vec(ts...))>(n, make_vec(ts...)); }
template<class S, class T> ostream& operator << (ostream& os, const pair<S, T> v){os << "(" << v.first << ", " << v.second << ")"; return os;}
template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
template<class T> ostream& operator<<(ostream& os, const vector<vector<T>> &v){ for(auto &e : v){os << e << "\n";} return os;}
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
template <class T> void UNIQUE(vector<T> &x) {sort(ALL(x));x.erase(unique(ALL(x)), x.end());}
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
void fail() { cout << -1 << '\n'; exit(0); }
inline int popcount(const int x) { return __builtin_popcount(x); }
inline int popcount(const ll x) { return __builtin_popcountll(x); }
template<typename T> void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++)
{cerr<<v[i][0];for(ll j=1;j<w;j++)cerr spa v[i][j];cerr<<"\n";}};
template<typename T> void debug(vector<T>&v,ll n){if(n!=0)cerr<<v[0];
for(ll i=1;i<n;i++)cerr spa v[i];
cerr<<"\n";};
const ll INF = (1ll<<62);
// const ld EPS = 1e-10;
// const ld PI = acos(-1.0);
const ll mod = (int)1e9 + 7;
//const ll mod = 998244353;
int main(){
ll N, M;
cin >> N >> M;
V<ll> u(M), v(M), c(M), d(M);
REP(i, M) cin >> u[i] >> v[i] >> c[i] >> d[i];
REP(i, M) u[i]--, v[i]--;
mcf_graph<ll, ll> G(N);
REP(i, M){
G.add_edge(u[i], v[i], 1, c[i]);
G.add_edge(u[i], v[i], 1, d[i]);
G.add_edge(v[i], u[i], 1, c[i]);
G.add_edge(v[i], u[i], 1, d[i]);
}
cout << G.flow(0, N-1, 2).second << endl;
return 0;
}