diff --git a/algorithms/graph/dinic.cpp b/algorithms/graph/dinic.cpp
index 1403b4436df2d07a64b98e3730598bf8739467ee..fb65287d7ff7d164b87f978ee293830d9047dd3b 100644
--- a/algorithms/graph/dinic.cpp
+++ b/algorithms/graph/dinic.cpp
@@ -15,11 +15,11 @@ struct Dinic {
Dinic(int N) :
N(N), depth(N), start(N), graph(N) {}
- void add_edge(int s, int t, int c) {
- Edge forw = { t, 0, c, (int) graph[t].size() };
- Edge back = { s, 0, 0, (int) graph[s].size() };
- graph[s].pb(forw);
- graph[t].pb(back);
+ void add_edge(int u, int v, int c) {
+ Edge forw = { v, 0, c, (int) graph[v].size() };
+ Edge back = { u, 0, 0, (int) graph[u].size() };
+ graph[u].pb(forw);
+ graph[v].pb(back);
}
bool bfs(int s, int t) {
diff --git a/algorithms/graph/min_cost_max_flow.cpp b/algorithms/graph/min_cost_max_flow.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..ff37950aedc271abe87842c3cfa663bb76371ef4
--- /dev/null
+++ b/algorithms/graph/min_cost_max_flow.cpp
@@ -0,0 +1,79 @@
+/// Minimum Cost Maximum Flow
+///
+/// Time: O(V^2 * E)
+/// Space: O(V + E)
+
+struct MinCostMaxFlow {
+ struct Edge { int u, v, cap, cost; };
+
+ int N;
+ vector<Edge> edges;
+ vector<vector<int>> adj;
+ vector<int> vis, dist, par, ind;
+
+ MinCostMaxFlow(int N) :
+ N(N), vis(N), dist(N), par(N), ind(N), adj(N) {}
+
+ void add_edge(int u, int v, int cap, int cost) {
+ adj[u].pb(edges.size());
+ edges.pb({ u, v, cap, cost });
+
+ adj[v].pb(edges.size());
+ edges.pb({ v, u, 0, -cost });
+ }
+
+ // Shortest Path Faster Algorithm (slower than
+ // Dijkstra but works with negative edges).
+ bool spfa(int s, int t) {
+ fill(all(dist), inf);
+ dist[s] = 0;
+
+ queue<int> Q;
+ Q.push(s);
+
+ while (!Q.empty()) {
+ int u = Q.front(); Q.pop();
+ vis[u] = 0;
+
+ for (auto i : adj[u]) {
+ Edge &e = edges[i];
+ int v = e.v;
+
+ if (e.cap > 0 && dist[v] > dist[u] + e.cost) {
+ dist[v] = dist[u] + e.cost;
+ par[v] = u;
+ ind[v] = i;
+
+ if (!vis[v]) {
+ Q.push(v);
+ vis[v] = 1;
+ }
+ }
+ }
+ }
+
+ return dist[t] < inf;
+ }
+
+ // Returns pair (min_cost, max_flow).
+ ii run(int s, int t) {
+ int min_cost = 0;
+ int max_flow = 0;
+
+ while (spfa(s, t)) {
+ int flow = inf;
+ for (int i = t; i != s; i = par[i])
+ flow = min(flow, edges[ind[i]].cap);
+
+ for (int i = t; i != s; i = par[i]) {
+ edges[ind[i] ].cap -= flow;
+ edges[ind[i]^1].cap += flow;
+ }
+
+ min_cost += flow * dist[t];
+ max_flow += flow;
+ }
+
+ return ii(min_cost, max_flow);
+ }
+};
diff --git a/caderno.pdf b/caderno.pdf
index 05adf703638921726f8fe8b69b23750388d1f202..3ae532569df79b62bfa711e4c399d821fab6ba0d 100644
Binary files a/caderno.pdf and b/caderno.pdf differ
diff --git a/contests/Cadernaveis/UVA10594.cpp b/contests/Cadernaveis/UVA10594.cpp
index 8a5b115e381cc538ffaf056ff7edee7eb68d4cd9..c0794ea984ade55b6a9fd3af58ad0232ada97027 100644
--- a/contests/Cadernaveis/UVA10594.cpp
+++ b/contests/Cadernaveis/UVA10594.cpp
@@ -1,5 +1,7 @@
#include <bits/stdc++.h>
+#define MAXN 110
+#define MAXM 20010
#define EPS 1e-6
#define MOD 1000000007
#define inf 0x3f3f3f3f
@@ -16,63 +18,82 @@
using namespace std;
-typedef long long ll;
-typedef pair<int,int> ii;
+using ll = long long;
+using ii = pair<int,int>;
-int N;
-int par[MAX];
-int graph[MAX][MAX], rg[MAX][MAX];
+struct MinCostMaxFlow {
+ struct Edge {
+ int u, v, cap, cost;
+ };
-bool cont[MAX];
+ int N;
+ vector<Edge> edges;
+ vector<vector<int>> adj;
+ vector<int> vis, dist, par, ind;
+ MinCostMaxFlow(int N) :
+ N(N), vis(N), dist(N), par(N), ind(N), adj(N) {}
-bool bfs(int s, int t) {
- queue<int> Q;
- Q.push(s);
- cont[s] = true;
+ void add_edge(int u, int v, int cap, int cost) {
+ adj[u].pb(edges.size());
+ edges.pb({ u, v, cap, cost });
- while (!Q.empty()) {
- int u = Q.front(); Q.pop();
-
- // Sink was found, there is a path
- if (u == t)
- return true;
-
- for (int i = 0; i < N; ++i)
- if (!cont[i] && rg[u][i]) {
- cont[i] = true;
- par[i] = u;
- Q.push(i);
- }
+ adj[v].pb(edges.size());
+ edges.pb({ v, u, 0, -cost });
}
- return false;
-}
+ bool spfa(int s, int t) {
+ fill(all(dist), inf);
+ dist[s] = 0;
-int edmonds_karp(int s, int t) {
- int ans = 0;
- par[s] = -1;
+ queue<int> Q;
+ Q.push(s);
- mset(cont, 0);
- memcpy(rg, graph, sizeof(graph));
+ while (!Q.empty()) {
+ int u = Q.front(); Q.pop();
+ vis[u] = 0;
- while (bfs(s, t)) {
- int flow = inf;
+ for (auto i : adj[u]) {
+ Edge &e = edges[i];
+ int v = e.v;
- for (int i = t; par[i] != -1; i = par[i])
- flow = min(flow, rg[par[i]][i]);
+ if (e.cap > 0 && dist[v] > dist[u] + e.cost) {
+ dist[v] = dist[u] + e.cost;
+ par[v] = u;
+ ind[v] = i;
- for (int i = t; par[i] != -1; i = par[i]) {
- rg[par[i]][i] -= flow;
- rg[i][par[i]] += flow;
+ if (!vis[v]) {
+ Q.push(v);
+ vis[v] = 1;
+ }
+ }
+ }
}
- ans += flow;
- mset(cont, 0);
+ return dist[t] < inf;
}
- return ans;
-}
+ pair<ll,int> run(int s, int t) {
+ ll mincost = 0;
+ int maxflow = 0;
+
+ while (spfa(s, t)) {
+ ll flow = inf;
+ for (int i = t; i != s; i = par[i])
+ flow = min(flow, (ll) edges[ind[i]].cap);
+
+ for (int i = t; i != s; i = par[i]) {
+ edges[ind[i] ].cap -= flow;
+ edges[ind[i]^1].cap += flow;
+ }
+
+ mincost += flow * dist[t];
+ maxflow += flow;
+ }
+
+ return make_pair(mincost, maxflow);
+ }
+};
int main() {
ios::sync_with_stdio(0);
@@ -80,10 +101,23 @@ int main() {
int n, m;
while (cin >> n >> m) {
+ MinCostMaxFlow mcmf(110);
+
+ vector<pair<ii,int>> aux(m);
+ for (int i = 0; i < m; ++i)
+ cin >> aux[i].fi.fi >> aux[i].fi.se >> aux[i].se;
+
+ int d, k; cin >> d >> k;
+ mcmf.add_edge(0, 1, d, 0);
for (int i = 0; i < m; ++i) {
- int a, b, c; cin >> a >> b >> c;
-
+ mcmf.add_edge(aux[i].fi.fi, aux[i].fi.se, k, aux[i].se);
+ mcmf.add_edge(aux[i].fi.se, aux[i].fi.fi, k, aux[i].se);
}
+
+ pair<ll,int> ans = mcmf.run(0, n);
+
+ if (ans.se != d) cout << "Impossible." << ende;
+ else cout << ans.fi << ende;
}
return 0;
diff --git a/contests/Cadernaveis/in b/contests/Cadernaveis/in
deleted file mode 100644
index 7fe77f6847af1c61e722fd515fb19ab9b3007682..0000000000000000000000000000000000000000
--- a/contests/Cadernaveis/in
+++ /dev/null
@@ -1,20 +0,0 @@
-2
-0 0 0 0 6 9 8 3 0
-9 8 0 0 0 0 0 7 6
-6 0 0 0 3 8 0 5 1
-2 0 5 0 8 1 0 9 0
-0 6 0 0 0 0 0 8 0
-0 9 0 3 7 0 6 0 2
-3 4 0 8 5 0 0 0 9
-7 2 0 0 0 0 0 6 8
-0 5 6 9 2 0 0 0 0
-
-0 0 0 0 6 9 8 3 0
-9 8 0 0 0 0 0 7 6
-6 0 0 0 3 8 0 5 1
-2 0 5 4 8 1 0 9 0
-0 6 0 0 0 0 0 8 0
-0 9 0 3 7 0 6 0 2
-3 4 0 8 5 0 0 0 9
-7 2 0 0 0 0 0 6 8
-0 5 6 9 2 0 0 0 0