Add Ford Fulkerson Algorithm

pydatastructs/graphs/algorithms.py

@@ -1143,6 +1143,50 @@ def _breadth_first_search_max_flow(graph: Graph, source_node, sink_node, flow_pa
     return (0, parent)
 
 
+def _copy_graph_with_residual_edges(graph: Graph) -> Graph:
+    vertices = [graph.__getattribute__(v) for v in graph.vertices]
+    new_graph = type(graph)(*vertices)
+    for key, edge in graph.edge_weights.items():
+        new_graph.add_edge(edge.source.name, edge.target.name, edge.value)
+    for key, edge in list(new_graph.edge_weights.items()):
+        src = edge.source.name
+        tgt = edge.target.name
+        if new_graph.get_edge(tgt, src) is None:
+            new_graph.add_edge(tgt, src, 0)
+    return new_graph
+
+
+def _dfs_max_flow(graph: Graph, node, sink, flow_passed, visited, flow):
+    if node == sink:
+        return flow
+    visited[node] = True
+    for next_node in graph.neighbors(node):
+        capacity = graph.get_edge(node, next_node.name).value
+        fp = flow_passed.get((node, next_node.name), 0)
+        residual_capacity = capacity - fp
+        if residual_capacity > 0 and next_node.name not in visited:
+            bottleneck_flow = _dfs_max_flow(
+                graph, next_node.name, sink, flow_passed, visited, min(flow, residual_capacity)
+            )
+            if bottleneck_flow > 0:
+                flow_passed[(node, next_node.name)] = fp + bottleneck_flow
+                flow_passed[(next_node.name, node)] = flow_passed.get((next_node.name, node), 0) - bottleneck_flow
+                return bottleneck_flow
+    return 0
+
+def _max_flow_ford_fulkerson_(graph: Graph, source, sink):
+    graph_copy = _copy_graph_with_residual_edges(graph)
+    m_flow = 0
+    flow_passed = {}
+    while True:
+        visited = {}
+        new_flow = _dfs_max_flow(graph_copy, source, sink, flow_passed, visited, float('inf'))
+        if new_flow == 0:
+            break
+        m_flow += new_flow
+    return m_flow
+
+
 def _max_flow_edmonds_karp_(graph: Graph, source, sink):
     m_flow = 0
     flow_passed = {}

pydatastructs/graphs/tests/test_algorithms.py

@@ -448,3 +448,5 @@ def _test_max_flow(ds, algorithm):
     _test_max_flow("Matrix", "edmonds_karp")
     _test_max_flow("List", "dinic")
     _test_max_flow("Matrix", "dinic")
+    _test_max_flow("List", "ford_fulkerson")
+    _test_max_flow("Matrix", "ford_fulkerson")