Created
April 28, 2020 20:05
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Ford Fulkerson algorithm
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import java.util.ArrayDeque; | |
import java.util.Queue; | |
public class Ford { | |
private static boolean bfs(int[][] residual, int s, int t, int[] path) { | |
Queue<Integer> queue = new ArrayDeque<>(); | |
boolean[] visited = new boolean[residual.length]; | |
queue.add(s); | |
visited[s] = true; | |
while (!queue.isEmpty()) { | |
int current = queue.poll(); | |
for (int i = 0; i < residual.length; ++i) { | |
if (visited[i]) continue; | |
if (residual[current][i] > 0) { | |
queue.add(i); | |
visited[i] = true; | |
path[i] = current; | |
if (i == t) | |
return true; | |
} | |
} | |
} | |
return false; | |
} | |
private static int ford(int[][] graph, int source, int sink) { | |
int maxFlow = 0; | |
int[][] residual = new int[graph.length][graph.length]; | |
for (int i = 0; i < graph.length; ++i) | |
System.arraycopy(graph[i], 0, residual[i], 0, graph.length); | |
int[] path = new int[graph.length]; | |
while (bfs(residual, source, sink, path)) { | |
int pathFlow = Integer.MAX_VALUE; | |
int current = sink; | |
while (current != source) { | |
int parent = path[current]; | |
pathFlow = Math.min(pathFlow, residual[parent][current]); | |
current = parent; | |
} | |
maxFlow += pathFlow; | |
current = sink; | |
while (current != source) { | |
int parent = path[current]; | |
residual[parent][current] -= pathFlow; | |
residual[current][parent] += pathFlow; | |
current = parent; | |
} | |
} | |
return maxFlow; | |
} | |
public static void main(String[] args) { | |
int[][] graph = new int[][]{ | |
//0 1 2 3 4 5 6 7 8 9 | |
{0, 8, 0, 0, 0, 1, 0, 0, 0, 0}, // 0 | |
{0, 0, 7, 0, 0, 0, 0, 0, 0, 0}, // 1 | |
{0, 0, 0, 7, 0, 0, 0, 0, 0, 0}, // 2 | |
{0, 0, 0, 0, 3, 0, 0, 0, 0, 0}, // 3 | |
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, // 4 | |
{0, 6, 2, 0, 0, 0, 2, 1, 10, 0}, // 5 | |
{0, 0, 0, 2, 0, 0, 0, 0, 1, 9}, // 6 | |
{0, 0, 0, 0, 0, 0, 0, 0, 4, 0}, // 7 | |
{0, 0, 0, 0, 0, 0, 0, 0, 0, 8}, // 8 | |
{0, 0, 0, 0, 10, 0, 0, 0, 0, 0}, // 9 | |
}; | |
System.out.print(ford(graph, 0, 4)); | |
} | |
} |
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