81 lines
2.0 KiB
Java
81 lines
2.0 KiB
Java
import java.util.*;
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import java.util.stream.Stream;
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// https://en.wikipedia.org/wiki/Dinic%27s_algorithm in O(V^2 * E)
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public class MaxFlowDinic {
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static class Edge {
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int t, rev, cap, f;
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public Edge(int t, int rev, int cap) {
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this.t = t;
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this.rev = rev;
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this.cap = cap;
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}
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}
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public static void addEdge(List<Edge>[] graph, int s, int t, int cap) {
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graph[s].add(new Edge(t, graph[t].size(), cap));
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graph[t].add(new Edge(s, graph[s].size() - 1, 0));
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}
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static boolean dinicBfs(List<Edge>[] graph, int src, int dest, int[] dist) {
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Arrays.fill(dist, -1);
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dist[src] = 0;
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int[] Q = new int[graph.length];
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int sizeQ = 0;
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Q[sizeQ++] = src;
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for (int i = 0; i < sizeQ; i++) {
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int u = Q[i];
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for (Edge e : graph[u]) {
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if (dist[e.t] < 0 && e.f < e.cap) {
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dist[e.t] = dist[u] + 1;
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Q[sizeQ++] = e.t;
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}
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}
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}
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return dist[dest] >= 0;
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}
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static int dinicDfs(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
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if (u == dest)
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return f;
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for (; ptr[u] < graph[u].size(); ++ptr[u]) {
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Edge e = graph[u].get(ptr[u]);
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if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
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int df = dinicDfs(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
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if (df > 0) {
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e.f += df;
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graph[e.t].get(e.rev).f -= df;
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return df;
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}
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}
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}
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return 0;
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}
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public static int maxFlow(List<Edge>[] graph, int src, int dest) {
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int flow = 0;
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int[] dist = new int[graph.length];
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while (dinicBfs(graph, src, dest, dist)) {
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int[] ptr = new int[graph.length];
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while (true) {
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int df = dinicDfs(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
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if (df == 0)
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break;
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flow += df;
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}
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}
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return flow;
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}
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// Usage example
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public static void main(String[] args) {
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List<Edge>[] graph = Stream.generate(ArrayList::new).limit(3).toArray(List[]::new);
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addEdge(graph, 0, 1, 3);
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addEdge(graph, 0, 2, 2);
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addEdge(graph, 1, 2, 2);
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System.out.println(4 == maxFlow(graph, 0, 2));
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}
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}
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