Initial commit

python/Algorithms/maxflow_fordfulkerson_simple.py

@@ -0,0 +1,28 @@
+# https://en.wikipedia.org/wiki/Ford–Fulkerson_algorithm in O(V^2 * flow)
+
+
+def max_flow(cap, s, t):
+    def augment_path(cap, visited, i, t):
+        if i == t:
+            return True
+        visited[i] = True
+        for j in range(len(cap)):
+            if not visited[j] and cap[i][j] > 0 and augment_path(cap, visited, j, t):
+                cap[i][j] -= 1
+                cap[j][i] += 1
+                return True
+        return False
+
+    flow = 0
+    while True:
+        if not augment_path(cap, [False] * len(cap), s, t):
+            return flow
+        flow += 1
+
+
+def test():
+    capacity = [[0, 1, 1, 0], [1, 0, 1, 1], [1, 1, 0, 1], [0, 1, 1, 0]]
+    assert max_flow(capacity, 0, 3) == 2
+
+
+test()