八數碼問題也稱為九宮問題。在3×3的棋盤，擺有八個棋子，每個棋子上標有1至8的某一數字，不同棋子上標的數字不相同。棋盤上還有一個空格，與空格相鄰的棋子可以移到空格中。要求解決的問題是：給出一個初始狀態和一個目標狀態，找出一種從初始狀態轉變成目標狀態的移動棋子步數最少的移動步驟。
import numpy as np
class State:
def __init__(self, state, directionFlag=None, parent=None):
self.state = state
self.direction = ['up', 'down', 'right', 'left']
if directionFlag:
self.direction.remove(directionFlag)
self.parent = parent
self.symbol = ' '
def getDirection(self):
return self.direction
def showInfo(self):
for i in range(3):
for j in range(3):
print(self.state[i, j], end=' ')
print("\n")
print('->\n')
return
def getEmptyPos(self):
postion = np.where(self.state == self.symbol)
return postion
def generateSubStates(self):
if not self.direction:
return []
subStates = []
boarder = len(self.state) - 1
row, col = self.getEmptyPos()
if 'left' in self.direction and col > 0:
s = self.state.copy()
temp = s.copy()
s[row, col] = s[row, col-1]
s[row, col-1] = temp[row, col]
news = State(s, directionFlag='right', parent=self)
subStates.append(news)
if 'up' in self.direction and row > 0:
s = self.state.copy()
temp = s.copy()
s[row, col] = s[row-1, col]
s[row-1, col] = temp[row, col]
news = State(s, directionFlag='down', parent=self)
subStates.append(news)
if 'down' in self.direction and row boarder:
s = self.state.copy()
temp = s.copy()
s[row, col] = s[row+1, col]
s[row+1, col] = temp[row, col]
news = State(s, directionFlag='up', parent=self)
subStates.append(news)
if self.direction.count('right') and col boarder:
s = self.state.copy()
temp = s.copy()
s[row, col] = s[row, col+1]
s[row, col+1] = temp[row, col]
news = State(s, directionFlag='left', parent=self)
subStates.append(news)
return subStates
def solve(self):
openTable = []
closeTable = []
openTable.append(self)
steps = 1
while len(openTable) > 0:
n = openTable.pop(0)
closeTable.append(n)
subStates = n.generateSubStates()
path = []
for s in subStates:
if (s.state == s.answer).all():
while s.parent and s.parent != originState:
path.append(s.parent)
s = s.parent
path.reverse()
return path, steps+1
openTable.extend(subStates)
steps += 1
else:
return None, None
if __name__ == '__main__':
symbolOfEmpty = ' '
State.symbol = symbolOfEmpty
originState = State(np.array([[2, 8, 3], [1, 6 , 4], [7, symbolOfEmpty, 5]]))
State.answer = np.array([[1, 2, 3], [8, State.symbol, 4], [7, 6, 5]])
s1 = State(state=originState.state)
path, steps = s1.solve()
if path:
for node in path:
node.showInfo()
print(State.answer)
print("Total steps is %d" % steps)
