# Hopcroft–Karp algorithm in Python

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Published on 2011-01-15T00:11:09Z
Indexed on
2011/01/15
4:53 UTC

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I am trying to implement the Hopcroft Karp algorithm in Python using networkx as graph representation.

Currently I am as far as this:

```
#Algorithms for bipartite graphs
import networkx as nx
import collections
class HopcroftKarp(object):
INFINITY = -1
def __init__(self, G):
self.G = G
def match(self):
self.N1, self.N2 = self.partition()
self.pair = {}
self.dist = {}
self.q = collections.deque()
#init
for v in self.G:
self.pair[v] = None
self.dist[v] = HopcroftKarp.INFINITY
matching = 0
while self.bfs():
for v in self.N1:
if self.pair[v] and self.dfs(v):
matching = matching + 1
return matching
def dfs(self, v):
if v != None:
for u in self.G.neighbors_iter(v):
if self.dist[ self.pair[u] ] == self.dist[v] + 1 and self.dfs(self.pair[u]):
self.pair[u] = v
self.pair[v] = u
return True
self.dist[v] = HopcroftKarp.INFINITY
return False
return True
def bfs(self):
for v in self.N1:
if self.pair[v] == None:
self.dist[v] = 0
self.q.append(v)
else:
self.dist[v] = HopcroftKarp.INFINITY
self.dist[None] = HopcroftKarp.INFINITY
while len(self.q) > 0:
v = self.q.pop()
if v != None:
for u in self.G.neighbors_iter(v):
if self.dist[ self.pair[u] ] == HopcroftKarp.INFINITY:
self.dist[ self.pair[u] ] = self.dist[v] + 1
self.q.append(self.pair[u])
return self.dist[None] != HopcroftKarp.INFINITY
def partition(self):
return nx.bipartite_sets(self.G)
```

The algorithm is taken from http://en.wikipedia.org/wiki/Hopcroft%E2%80%93Karp_algorithm However it does not work. I use the following test code

```
G = nx.Graph([
(1,"a"), (1,"c"),
(2,"a"), (2,"b"),
(3,"a"), (3,"c"),
(4,"d"), (4,"e"),(4,"f"),(4,"g"),
(5,"b"), (5,"c"),
(6,"c"), (6,"d")
])
matching = HopcroftKarp(G).match()
print matching
```

Unfortunately this does not work, I end up in an endless loop :(. Can someone spot the error, I am out of ideas and I must admit that I have not yet fully understand the algorithm, so it is mostly an implementation of the pseudo code on wikipedia

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