算法思想
算法流程
算法步驟
算法實現
python
import timeit
from collections import deque
#==============================================================================
# 匈牙利算法
#==============================================================================
class HungarianAlgorithm(object):
def __init__(self,graph):
"""
@graph:圖的矩陣表示
"""
self.graph=graph
self.n=len(graph)
def find(self,x):
for i in range(self.n):
if self.graph[x][i]==1 and not self.used[i]:
self.used[i]=1#放入交替路
if self.match[i]==-1 or self.find(self.match[i])==1:
self.match[i]=x
self.match[x]=i
print(x+1,'->',i+1)
return 1
return 0
def hungarian1(self):
"""遞歸形式
"""
self.match=[-1]*self.n#記錄匹配情況
self.used=[False]*self.n#記錄是否訪問過
m=0
for i in range(self.n):
if self.match[i]==-1:
self.used=[False]*self.n
print('開始匹配:',i+1)
m+=self.find(i)
return m
def hungarian2(self):
"""循環形式
"""
match=[-1]*self.n#記錄匹配情況
used=[-1]*self.n#記錄是否訪問過
Q=deque() #設置隊列
ans=0
prev=[0]*self.n #代表上一節點
for i in range(self.n):
if match[i]==-1:
Q.clear()
Q.append(i)
prev[i]=-1#設i為出發點
flag=False #未找到增廣路
while len(Q)>0 and not flag:
u=Q.popleft()
for j in range(self.n):
if not flag and self.graph[u][j]==1 and used[j]!=i:
used[j]=i
if match[j]!=-1:
Q.append(match[j])
prev[match[j]]=u#記錄點的順序
else:
flag=True
d=u
e=j
while(d!=-1):#將原匹配的邊去掉加入原來不在匹配中的邊
t=match[d]
match[d]=e
match[e]=d
d=prev[d]
e=t
print('mathch:',match)
print('prev:',prev)
print('deque',Q)
if match[i]!=-1:#新增匹配邊
ans+=1
return ans
def do1():
graph=[(0,0,0,0,1,0,1,0),
(0,0,0,0,1,0,0,0),
(0,0,0,0,1,1,0,0),
(0,0,0,0,0,0,1,1),
(1,1,1,0,0,0,0,0),
(0,0,1,0,0,0,0,0),
(1,0,0,1,0,0,0,0),
(0,0,0,1,0,0,0,0)]
h=HungarianAlgorithm(graph)
print (h.hungarian1())
def do2():
graph=[(0,0,0,0,1,0,1,0),
(0,0,0,0,1,0,0,0),
(0,0,0,0,1,1,0,0),
(0,0,0,0,0,0,1,1),
(1,1,1,0,0,0,0,0),
(0,0,1,0,0,0,0,0),
(1,0,0,1,0,0,0,0),
(0,0,0,1,0,0,0,0)]
h=HungarianAlgorithm(graph)
print (h.hungarian2())
