Merge pull request #263 from pl04351820/master

Networking flow add

networking_flow/Ford_Fulkerson.py

@@ -0,0 +1,56 @@
+# Ford-Fulkerson Algorithm for Maximum Flow Problem
+"""
+Description:
+    (1) Start with initial flow as 0;
+    (2) Choose augmenting path from source to sink and add path to flow;
+"""
+    
+def BFS(graph, s, t, parent):
+    # Return True if there is node that has not iterated.
+    visited = [False]*len(graph)
+    queue=[]
+    queue.append(s)
+    visited[s] = True
+    
+    while queue:
+        u = queue.pop(0)
+        for ind in range(len(graph[u])):
+            if visited[ind] == False and graph[u][ind] > 0:
+                queue.append(ind)
+                visited[ind] = True
+                parent[ind] = u
+
+    return True if visited[t] else False
+     
+def FordFulkerson(graph, source, sink):
+    # This array is filled by BFS and to store path
+    parent = [-1]*(len(graph))
+    max_flow = 0 
+    while BFS(graph, source, sink, parent) :
+        path_flow = float("Inf")
+        s = sink
+
+        while(s !=  source):
+            # Find the minimum value in select path
+            path_flow = min (path_flow, graph[parent[s]][s])
+            s = parent[s]
+
+        max_flow +=  path_flow
+        v = sink
+
+        while(v !=  source):
+            u = parent[v]
+            graph[u][v] -= path_flow
+            graph[v][u] += path_flow
+            v = parent[v]
+    return max_flow
+
+graph = [[0, 16, 13, 0, 0, 0],
+         [0, 0, 10 ,12, 0, 0],
+         [0, 4, 0, 0, 14, 0],
+         [0, 0, 9, 0, 0, 20],
+         [0, 0, 0, 7, 0, 4],
+         [0, 0, 0, 0, 0, 0]]
+
+source, sink = 0, 5
+print(FordFulkerson(graph, source, sink))

networking_flow/Minimum_cut.py

@@ -0,0 +1,59 @@
+# Minimum cut on Ford_Fulkerson algorithm.
+    
+def BFS(graph, s, t, parent):
+    # Return True if there is node that has not iterated.
+    visited = [False]*len(graph)
+    queue=[]
+    queue.append(s)
+    visited[s] = True
+    
+    while queue:
+        u = queue.pop(0)
+        for ind in range(len(graph[u])):
+            if visited[ind] == False and graph[u][ind] > 0:
+                queue.append(ind)
+                visited[ind] = True
+                parent[ind] = u
+
+    return True if visited[t] else False
+ 
+def mincut(graph, source, sink):
+    # This array is filled by BFS and to store path
+    parent = [-1]*(len(graph))
+    max_flow = 0 
+    res = []
+    temp = [i[:] for i in graph]   # Record orignial cut, copy.
+    while BFS(graph, source, sink, parent) :
+        path_flow = float("Inf")
+        s = sink
+
+        while(s !=  source):
+            # Find the minimum value in select path
+            path_flow = min (path_flow, graph[parent[s]][s])
+            s = parent[s]
+
+        max_flow +=  path_flow
+        v = sink
+        
+        while(v !=  source):
+            u = parent[v]
+            graph[u][v] -= path_flow
+            graph[v][u] += path_flow
+            v = parent[v]
+
+    for i in range(len(graph)):
+        for j in range(len(graph[0])):
+            if graph[i][j] == 0 and temp[i][j] > 0:
+                res.append((i,j))
+
+    return res
+
+graph = [[0, 16, 13, 0, 0, 0],
+         [0, 0, 10 ,12, 0, 0],
+         [0, 4, 0, 0, 14, 0],
+         [0, 0, 9, 0, 0, 20],
+         [0, 0, 0, 7, 0, 4],
+         [0, 0, 0, 0, 0, 0]]
+
+source, sink = 0, 5
+print(mincut(graph, source, sink))