diff --git a/LibreOJ/115.cpp b/LibreOJ/115.cpp new file mode 100644 index 0000000..422f380 --- /dev/null +++ b/LibreOJ/115.cpp @@ -0,0 +1,117 @@ +/** + * @file 115.cpp + * @author Macesuted (i@macesuted.moe) + * @date 2024-09-18 + * + * @copyright Copyright (c) 2024 + * + */ + +#include +using namespace std; + +#ifndef LOCAL +#define endl '\n' +#endif + +#define maxm 15000 + +int ans[maxm]; + +class Dinic { + private: + struct Edge { + int to, rev; + int64_t cap; + int id; + }; + + vector> graph; + vector::iterator> cur; + vector dist, preF; + queue que; + int n, S, T; + + bool bfs(void) { + for (int i = 1; i <= n; i++) dist[i] = INT_MAX, cur[i] = graph[i].begin(); + que.push(S), dist[S] = 0; + while (!que.empty()) { + int p = que.front(); + que.pop(); + for (auto i : graph[p]) + if (i.cap && dist[i.to] > dist[p] + 1) dist[i.to] = dist[p] + 1, que.push(i.to); + } + return dist[T] != INT_MAX; + } + int64_t dfs(int p, int64_t rest) { + if (p == T) return rest; + int64_t use = 0, c; + for (auto i = cur[p]; i != graph[p].end() && rest; i++) { + cur[p] = i; + if (!i->cap || dist[i->to] != dist[p] + 1) continue; + if (!(c = dfs(i->to, min(rest, (int64_t)i->cap)))) dist[i->to] = -1; + i->cap -= c, graph[i->to][i->rev].cap += c, use += c, rest -= c; + } + return use; + } + + public: + void resize(int _n) { return graph.resize((n = _n + 2) + 1), cur.resize(n + 1), dist.resize(n + 1), preF.resize(n + 1); } + void addEdge(int from, int to, int64_t cap, int id, int lowf = 0) { + preF[from] -= lowf, preF[to] += lowf, cap -= lowf, ans[id] += lowf; + return graph[from].push_back(Edge{to, (int)graph[to].size(), cap, id}), + graph[to].push_back(Edge{from, (int)graph[from].size() - 1, 0, -id}); + } + bool preCheck(void) { + S = n - 1, T = n; + int64_t tot = 0; + for (int i = 1; i <= n; i++) { + if (preF[i] < 0) addEdge(i, T, -preF[i], -1); + if (preF[i] > 0) addEdge(S, i, preF[i], -1), tot += preF[i]; + } + int64_t ans = 0; + while (bfs()) ans += dfs(S, INT64_MAX); + for (int i = 1; i <= n; i++) + for (auto e : graph[i]) + if (e.id > 0) ::ans[e.id] += graph[e.to][e.rev].cap; + return ans == tot; + } + int64_t maxFlow(int _S, int _T) { + S = _S, T = _T; + int64_t ans = 0; + while (bfs()) ans += dfs(S, INT64_MAX); + return ans; + } +}; + +bool mem1; + +void solve(void) { + int n, m; + cin >> n >> m; + + Dinic dnc; + dnc.resize(n); + for (int i = 1, x, y, l, c; i <= m; i++) cin >> x >> y >> l >> c, dnc.addEdge(x, y, c, i, l); + if (!dnc.preCheck()) return cout << "NO" << endl, void(); + cout << "YES" << endl; + for (int i = 1; i <= m; i++) cout << ans[i] << endl; + return; +} + +bool mem2; + +int main() { + ios::sync_with_stdio(false), cin.tie(nullptr); +#ifdef LOCAL + cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl; +#endif + + int _ = 1; + while (_--) solve(); + +#ifdef LOCAL + cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl; +#endif + return 0; +} diff --git a/LibreOJ/116.cpp b/LibreOJ/116.cpp new file mode 100644 index 0000000..71a972c --- /dev/null +++ b/LibreOJ/116.cpp @@ -0,0 +1,108 @@ +/** + * @file 116.cpp + * @author Macesuted (i@macesuted.moe) + * @date 2024-09-18 + * + * @copyright Copyright (c) 2024 + * + */ + +#include +using namespace std; + +#ifndef LOCAL +#define endl '\n' +#endif + +class Dinic { + private: + struct Edge { + int to, rev; + int64_t cap; + }; + + vector> graph; + vector::iterator> cur; + vector dist, preF; + queue que; + int n, S, T; + + bool bfs(void) { + for (int i = 1; i <= n; i++) dist[i] = INT_MAX, cur[i] = graph[i].begin(); + que.push(S), dist[S] = 0; + while (!que.empty()) { + int p = que.front(); + que.pop(); + for (auto i : graph[p]) + if (i.cap && dist[i.to] > dist[p] + 1) dist[i.to] = dist[p] + 1, que.push(i.to); + } + return dist[T] != INT_MAX; + } + int64_t dfs(int p, int64_t rest) { + if (p == T) return rest; + int64_t used = 0, c; + for (auto i = cur[p]; i != graph[p].end() && rest; i++) { + cur[p] = i; + if (!i->cap || dist[i->to] != dist[p] + 1) continue; + if (!(c = dfs(i->to, min(rest, (int64_t)i->cap)))) dist[i->to] = -1; + i->cap -= c, graph[i->to][i->rev].cap += c, used += c, rest -= c; + } + return used; + } + + public: + void resize(int _n) { return graph.resize((n = _n + 2) + 1), cur.resize(n + 1), dist.resize(n + 1), preF.resize(n + 1); } + void addEdge(int from, int to, int64_t cap, int64_t lowf = 0) { + preF[from] -= lowf, preF[to] += lowf, cap -= lowf; + return graph[from].push_back(Edge{to, (int)graph[to].size(), cap}), + graph[to].push_back(Edge{from, (int)graph[from].size() - 1, 0}); + } + int64_t maxFlow(int _S, int _T) { + addEdge(_T, _S, INT64_MAX, 0); + + S = n - 1, T = n; + int64_t tot = 0, ans = 0; + for (int i = 1; i <= n; i++) { + if (preF[i] < 0) addEdge(i, T, -preF[i]); + if (preF[i] > 0) addEdge(S, i, preF[i]), tot += preF[i]; + } + while (bfs()) ans += dfs(S, INT64_MAX); + if (ans != tot) return -1; + + ans = 0, S = _S, T = _T; + while (bfs()) ans += dfs(S, INT64_MAX); + return ans; + } +}; + +bool mem1; + +void solve(void) { + int n, m, S, T; + cin >> n >> m >> S >> T; + + Dinic dnc; + dnc.resize(n); + for (int i = 1, x, y, l, c; i <= m; i++) cin >> x >> y >> l >> c, dnc.addEdge(x, y, c, l); + int64_t ans = dnc.maxFlow(S, T); + if (ans == -1) return cout << "please go home to sleep" << endl, void(); + cout << ans << endl; + return; +} + +bool mem2; + +int main() { + ios::sync_with_stdio(false), cin.tie(nullptr); +#ifdef LOCAL + cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl; +#endif + + int _ = 1; + while (_--) solve(); + +#ifdef LOCAL + cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl; +#endif + return 0; +} diff --git a/LibreOJ/117.cpp b/LibreOJ/117.cpp new file mode 100644 index 0000000..51b0a8d --- /dev/null +++ b/LibreOJ/117.cpp @@ -0,0 +1,124 @@ +/** + * @file 117.cpp + * @author Macesuted (i@macesuted.moe) + * @date 2024-09-18 + * + * @copyright Copyright (c) 2024 + * + */ + +#include +using namespace std; + +#ifndef LOCAL +#define endl '\n' +#endif + +class Dinic { + private: + struct Edge { + int to, rev; + int64_t cap; + }; + + vector> graph; + vector::iterator> cur; + vector dist, preF; + queue que; + int n, S, T; + + bool bfs(void) { + for (int i = 1; i <= n; i++) dist[i] = INT_MAX, cur[i] = graph[i].begin(); + que.push(S), dist[S] = 0; + while (!que.empty()) { + int p = que.front(); + que.pop(); + for (auto i : graph[p]) + if (i.cap && dist[i.to] > dist[p] + 1) dist[i.to] = dist[p] + 1, que.push(i.to); + } + return dist[T] != INT_MAX; + } + int64_t dfs(int p, int64_t rest) { + if (p == T) return rest; + int64_t used = 0, c; + for (auto i = cur[p]; i != graph[p].end() && rest; i++) { + cur[p] = i; + if (!i->cap || dist[i->to] != dist[p] + 1) continue; + if (!(c = dfs(i->to, min(rest, (int64_t)i->cap)))) dist[i->to] = -1; + i->cap -= c, graph[i->to][i->rev].cap += c, used += c, rest -= c; + } + return used; + } + + public: + void resize(int _n) { return graph.resize((n = _n + 2) + 1), cur.resize(n + 1), dist.resize(n + 1), preF.resize(n + 1); } + void addEdge(int from, int to, int64_t cap, int64_t lowf = 0) { + preF[from] -= lowf, preF[to] += lowf, cap -= lowf; + return graph[from].push_back(Edge{to, (int)graph[to].size(), cap}), + graph[to].push_back(Edge{from, (int)graph[from].size() - 1, 0}); + } + int64_t maxFlow(int _S, int _T) { + addEdge(_T, _S, INT64_MAX, 0); + + S = n - 1, T = n; + int64_t tot = 0, ans = 0; + for (int i = 1; i <= n; i++) { + if (preF[i] < 0) addEdge(i, T, -preF[i]); + if (preF[i] > 0) addEdge(S, i, preF[i]), tot += preF[i]; + } + while (bfs()) ans += dfs(S, INT64_MAX); + if (ans != tot) return -1; + + ans = 0, S = _S, T = _T; + while (bfs()) ans += dfs(S, INT64_MAX); + return ans; + } + int64_t minFlow(int _S, int _T) { + addEdge(_T, _S, INT64_MAX, 0); + + S = n - 1, T = n; + int64_t tot = 0, ans = 0; + for (int i = 1; i <= n; i++) { + if (preF[i] < 0) addEdge(i, T, -preF[i]); + if (preF[i] > 0) addEdge(S, i, preF[i]), tot += preF[i]; + } + while (bfs()) ans += dfs(S, INT64_MAX); + if (ans != tot) return -1; + + ans = INT64_MAX, S = _T, T = _S; + while (bfs()) ans -= dfs(S, INT64_MAX); + return ans; + } +}; + +bool mem1; + +void solve(void) { + int n, m, S, T; + cin >> n >> m >> S >> T; + + Dinic dnc; + dnc.resize(n); + for (int i = 1, x, y, l, c; i <= m; i++) cin >> x >> y >> l >> c, dnc.addEdge(x, y, c, l); + int64_t ans = dnc.minFlow(S, T); + if (ans == -1) return cout << "please go home to sleep" << endl, void(); + cout << ans << endl; + return; +} + +bool mem2; + +int main() { + ios::sync_with_stdio(false), cin.tie(nullptr); +#ifdef LOCAL + cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl; +#endif + + int _ = 1; + while (_--) solve(); + +#ifdef LOCAL + cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl; +#endif + return 0; +} diff --git a/templates/Graph.md b/templates/Graph.md index 46d79a4..c2a2f67 100644 --- a/templates/Graph.md +++ b/templates/Graph.md @@ -118,3 +118,87 @@ class DinicWithCost { } }; ``` + +## Dinic with Lowerbound + +```cpp +class DinicWithLowerbound { + private: + struct Edge { + int to, rev; + int64_t cap; + }; + + vector> graph; + vector::iterator> cur; + vector dist, preF; + queue que; + int n, S, T; + + bool bfs(void) { + for (int i = 1; i <= n; i++) dist[i] = INT_MAX, cur[i] = graph[i].begin(); + que.push(S), dist[S] = 0; + while (!que.empty()) { + int p = que.front(); + que.pop(); + for (auto i : graph[p]) + if (i.cap && dist[i.to] > dist[p] + 1) dist[i.to] = dist[p] + 1, que.push(i.to); + } + return dist[T] != INT_MAX; + } + int64_t dfs(int p, int64_t rest) { + if (p == T) return rest; + int64_t used = 0, c; + for (auto i = cur[p]; i != graph[p].end() && rest; i++) { + cur[p] = i; + if (!i->cap || dist[i->to] != dist[p] + 1) continue; + if (!(c = dfs(i->to, min(rest, (int64_t)i->cap)))) dist[i->to] = -1; + i->cap -= c, graph[i->to][i->rev].cap += c, used += c, rest -= c; + } + return used; + } + + public: + void resize(int _n) { + return graph.resize((n = _n + 2) + 1), cur.resize(n + 1), + dist.resize(n + 1), preF.resize(n + 1); + } + void addEdge(int from, int to, int64_t cap, int64_t lowf = 0) { + preF[from] -= lowf, preF[to] += lowf, cap -= lowf; + return graph[from].push_back(Edge{to, (int)graph[to].size(), cap}), + graph[to].push_back(Edge{from, (int)graph[from].size() - 1, 0}); + } + int64_t maxFlow(int _S, int _T) { + addEdge(_T, _S, INT64_MAX, 0); + + S = n - 1, T = n; + int64_t tot = 0, ans = 0; + for (int i = 1; i <= n; i++) { + if (preF[i] < 0) addEdge(i, T, -preF[i]); + if (preF[i] > 0) addEdge(S, i, preF[i]), tot += preF[i]; + } + while (bfs()) ans += dfs(S, INT64_MAX); + if (ans != tot) return -1; + + ans = 0, S = _S, T = _T; + while (bfs()) ans += dfs(S, INT64_MAX); + return ans; + } + int64_t minFlow(int _S, int _T) { + addEdge(_T, _S, INT64_MAX, 0); + + S = n - 1, T = n; + int64_t tot = 0, ans = 0; + for (int i = 1; i <= n; i++) { + if (preF[i] < 0) addEdge(i, T, -preF[i]); + if (preF[i] > 0) addEdge(S, i, preF[i]), tot += preF[i]; + } + while (bfs()) ans += dfs(S, INT64_MAX); + if (ans != tot) return -1; + + ans = INT64_MAX, S = _T, T = _S; + while (bfs()) ans -= dfs(S, INT64_MAX); + return ans; + } +}; +``` \ No newline at end of file