夫妻过河问题---图论算法的应用（Python实现）
class Graph(object):
"""docstring for Graph"""
def __init__(self, mat):
super(Graph, self).__init__()
self.n = len(mat[0])
self.edge = 0
self.mat = mat
self.vertex = []
self.visited = [0 for i in range(n)]
self.found = 0
self.path = []
self.solution = []
def DFS(self):
for i in range(self.n):
if not self.visited[i]:
self.dfs(i)
def dfs(self,i):
self.visited[i] = 1
print(i)
for j in range(self.n):
if not self.visited[j] and self.mat[i][j]:
self.dfs(j)
def CrossRiver(self):
self.vertex = []
for i in range(2):
for j in range(2):
for k in range(2):
for p in range(2):
for q in range(2):
for r in range(2):
self.vertex.append([i,j,k,p,q,r])
self.n = 64
self.mat = mat = [[0 for j in range(self.n)] for i in range(self.n)]
self.visited = [0 for i in range(self.n)]
self.initialize()
self.DFS_()
def DFS_(self):
for i in range(self.n):
if not self.visited[i] and not self.found:
self.dfs_(i)
def dfs_(self,i):
self.visited[i] = 1
#print(i,self.mat[i][63],self.vertex[i])
self.path.append(self.vertex[i])
if self.mat[i][63]:
#print(63,self.vertex[63])
print("found!")
self.path.append(self.vertex[63])
self.found = 1
for j in range(self.n):
if not self.visited[j] and self.mat[i][j] and self.isSafe(G.vertex[j]):
if not self.found:
self.dfs_(j)
def isSafe(self,state):
a1,a2,b1,b2,c1,c2 = state[0],state[1],state[2],state[3],state[4],state[5]
if [a1,a2,b1,b2,c1,c2] == [1,1,1,1,1,1]:
return True
if a2 != a1 and (a2 == b1 or a2 == c1):
return False
if b2 != b1 and (b2 == a1 or b2 == c1):
return False
if c2 != c1 and (c2 == a1 or c2 == b1):
return False
return True
def initialize(self):
for i in range(self.n):
for j in range(self.n):
if self.isConnected(self.vertex[i],self.vertex[j]):
self.mat[i][j] = 1
def isConnected(self,state1,state2):
changes = []
for i in range(len(state1)):
if state1[i] != state2[i]:
changes.append([state1[i],state2[i]])
if changes == []:
return False
if len(changes) == 1:
return True
if len(changes) == 2:
if changes[0][0] != changes[1][0]:
return False
else:
return True
else:
return False
def showMoves(self):
n = len(self.path)
solution = []
m1 = "Move man 1 to the other side; "
m2 = "Move lady 1 to the other side; "
m3 = "Move man 2 to the other side; "
m4 = "Move lady 2 to the other side; "
m5 = "Move man 3 to the other side; "
m6 = "Move lady 3 to the other side; "
n1 = "Move man 1 back from the other side; "
n2 = "Move lady 1 back from the other side; "
n3 = "Move man 2 back from the other side; "
n4 = "Move lady 2 back from the other side; "
n5 = "Move man 3 back from the other side; "
n6 = "Move lady 3 back from the other side; "
path = G.path
for i in range(n-1):
#This state
a1,a2,b1,b2,c1,c2 = path[i][0],path[i][1],path[i][2],\
path[i][3],path[i][4],path[i][5]
#Next state
a1n,a2n,b1n,b2n,c1n,c2n = path[i+1][0],path[i+1][1],path[i+1][2],\
path[i+1][3],path[i+1][4],path[i+1][5]
#Initialize move
move = ''
#Judge
#Couple one
if a1 == 0 and a1n == 1:
move += m1
if a1 == 1 and a1n == 0:
move += n1
if a2 == 0 and a2n == 1:
move += m2
if a2 == 1 and a2n == 0:
move += n2
#Copule two
if b1 == 0 and b1n == 1:
move += m3
if b1 == 1 and b1n == 0:
move += n3
if b2 == 0 and b2n == 1:
move += m4
if b2 == 1 and b2n == 0:
move += n4
#Couple three
if c1 == 0 and c1n == 1:
move += m5
if c1 == 1 and c1n == 0:
move += n5
if c2 == 0 and c2n == 1:
move += m6
if c2 == 1 and c2n == 0:
move += n6
self.solution.append('Step '+str(i+1)+': '+move)
for step in G.solution:
print(step)
n = 4
mat = [[0 for j in range(n)] for i in range(n)]
G = Graph(mat)
G.CrossRiver()
print("\n走法如下：")
for move in G.path:
print(move)
G.showMoves()