From e9eb5f8437f234f817aff8d9fdb0be074efcd66c Mon Sep 17 00:00:00 2001
From: Vishnunair585 <vishnumnair595@gmail.com>
Date: Fri, 24 Apr 2026 18:54:24 +0530
Subject: [PATCH 1/2] Optimize BFS and fix min-cut detection

---
 networking_flow/minimum_cut.py | 56 ++++++++++++++++++++++------------
 1 file changed, 37 insertions(+), 19 deletions(-)

diff --git a/networking_flow/minimum_cut.py b/networking_flow/minimum_cut.py
index 164b45f1012a..b5a8f6807d31 100644
--- a/networking_flow/minimum_cut.py
+++ b/networking_flow/minimum_cut.py
@@ -1,5 +1,7 @@
 # Minimum cut on Ford_Fulkerson algorithm.
 
+from collections import deque
+
 test_graph = [
     [0, 16, 13, 0, 0, 0],
     [0, 0, 10, 12, 0, 0],
@@ -11,56 +13,72 @@
 
 
 def bfs(graph, s, t, parent):
-    # Return True if there is node that has not iterated.
     visited = [False] * len(graph)
-    queue = [s]
+    queue = deque([s])
     visited[s] = True
 
     while queue:
-        u = queue.pop(0)
+        u = queue.popleft()
+
         for ind in range(len(graph[u])):
-            if visited[ind] is False and graph[u][ind] > 0:
+            if not visited[ind] and graph[u][ind] > 0:
                 queue.append(ind)
                 visited[ind] = True
                 parent[ind] = u
 
+                # Early exit if sink is found
+                if ind == t:
+                    return True
+
     return visited[t]
 
 
+def dfs(graph, s, visited):
+    visited[s] = True
+    for i in range(len(graph)):
+        if graph[s][i] > 0 and not visited[i]:
+            dfs(graph, i, visited)
+
+
 def mincut(graph, source, sink):
-    """This array is filled by BFS and to store path
+    """
+    Returns max_flow and minimum cut edges.
+
     >>> mincut(test_graph, source=0, sink=5)
-    [(1, 3), (4, 3), (4, 5)]
+    (23, [(1, 3), (4, 3), (4, 5)])
     """
-    parent = [-1] * (len(graph))
+    residual = [i[:] for i in graph]
+    parent = [-1] * len(graph)
     max_flow = 0
-    res = []
-    temp = [i[:] for i in graph]  # Record original cut, copy.
-    while bfs(graph, source, sink, parent):
+
+    while bfs(residual, 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])
+            path_flow = min(path_flow, residual[parent[s]][s])
             s = parent[s]
 
         max_flow += path_flow
-        v = sink
 
+        v = sink
         while v != source:
             u = parent[v]
-            graph[u][v] -= path_flow
-            graph[v][u] += path_flow
+            residual[u][v] -= path_flow
+            residual[v][u] += path_flow
             v = parent[v]
 
+    visited = [False] * len(graph)
+    dfs(residual, source, visited)
+
+    res = []
     for i in range(len(graph)):
-        for j in range(len(graph[0])):
-            if graph[i][j] == 0 and temp[i][j] > 0:
+        for j in range(len(graph)):
+            if visited[i] and not visited[j] and graph[i][j] > 0:
                 res.append((i, j))
 
-    return res
+    return max_flow, res
 
 
 if __name__ == "__main__":
-    print(mincut(test_graph, source=0, sink=5))
+    print(mincut(test_graph, source=0, sink=5))
\ No newline at end of file

From cf993135940a74628813528aaec2eedc296e0ae9 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 24 Apr 2026 13:25:21 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 networking_flow/minimum_cut.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/networking_flow/minimum_cut.py b/networking_flow/minimum_cut.py
index b5a8f6807d31..1124ad2be21c 100644
--- a/networking_flow/minimum_cut.py
+++ b/networking_flow/minimum_cut.py
@@ -81,4 +81,4 @@ def mincut(graph, source, sink):
 
 
 if __name__ == "__main__":
-    print(mincut(test_graph, source=0, sink=5))
\ No newline at end of file
+    print(mincut(test_graph, source=0, sink=5))