def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
board_size = range(n)
queens = ["queen%d" % i for i in range(1, n + 1)]
for var in queens:
csp.add_variable(var, board_size)
for id1 in range(n):
for id2 in range(id1 + 1, n):
csp.add_binary_factor(queens[id1], queens[id2],
lambda rcolv1, rcolv2: rcolv1 != rcolv2)
csp.add_binary_factor(
queens[id1], queens[id2],
lambda rcolv1, rcolv2: abs(rcolv1 - rcolv2) != abs(id1 - id2))
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem b
# TODO: BEGIN_YOUR_CODE
for i in range(n):
csp.add_variable(i, range(n))
for var1 in range(n):
for var2 in range(n):
if var1 != var2:
csp.add_binary_factor(
var1, var2,
lambda x, y: x != y and abs(x - y) != abs(var1 - var2))
# raise NotImplementedError
# TODO: END_YOUR_CODE
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem b
# TODO: BEGIN_YOUR_CODE
# Queens is a list of variables, which denote the position of the queen in each row
# Queens is defined as 'Qi', where i is the row of a queen
Queens = ['Q' + str(i+1) for i in range(n)]
value_list = [i+1 for i in range(n)]
for queen in Queens:
csp.add_variable(queen, value_list)
# binary_factor: two queens can't in the same column, and duijiaoxian
for queen1 in Queens:
for queen2 in Queens:
if queen1 != queen2:
# Using the define 'Qi', to get i
row1 = int(queen1.split('Q')[1])
row2 = int(queen2.split('Q')[1])
delta = abs(row1 - row2)
csp.add_binary_factor(queen1, queen2, lambda x, y: x != y and abs(x-y) != delta)
# TODO: END_YOUR_CODE
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem a
# TODO: BEGIN_YOUR_CODE
domin = []
for i in range(1, n + 1):
domin.append(i)
for i in range(1, n + 1):
csp.add_variable(i, domin)
# print(csp.values)
for i in range(1, n + 1):
for j in range(1, n + 1):
if i != j:
k = abs(i - j)
csp.add_binary_factor(
i, j, lambda x, y: x + k != y and x - k != y and x != y)
# print((csp.binary_factors[1][4][3]))
# raise NotImplementedError
# TODO: END_YOUR_CODE
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem b
# TODO: BEGIN_YOUR_CODE
variables = []
for i in range(n):
# name variables from y1 to yn
var = 'y{}'.format(i + 1)
# assign values to variables
csp.add_variable(var, range(1, n + 1))
variables.append(var)
for i in range(len(variables)):
for j in range(len(variables)):
if variables[i] != variables[j]:
distance = abs(i - j)
# Generate binary constraints between queens
csp.add_binary_factor(
variables[i], variables[j],
lambda y1, y2: y1 != y2 and distance != abs(y1 - y2))
#raise NotImplementedError
# TODO: END_YOUR_CODE
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem b
# TODO: BEGIN_YOUR_CODE
# refer the formulation 2
# there n variables in TOTAL, each one represents the Position of queen in row Qi
for i in range(n): # add all the variables to CSP
csp.add_variable(var=i, domain=list(range(n)))
# 添加一元约束
csp.add_unary_factor(
var=i,
factor_function=lambda x: 1) # factor_function作用在变量var的每个值value上
# def binaryConstraints(value1,value2):
# return abs(value1-value2)
# 添加二元约束
for i in range(n):
for j in range(n):
if i == j:
continue
# factor_function分别作用在变量var1和var2的每个值value1,value2上
csp.add_binary_factor(var1=i,
var2=j,
factor_function=lambda x, y: abs(x - y) !=
abs(i - j)) # 两个皇后不在对角线上
csp.add_binary_factor(
var1=i, var2=j,
factor_function=lambda x, y: x != y) # 两个皇后不在同一列上
# raise NotImplementedError
# TODO: END_YOUR_CODE
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem a
# TODO: BEGIN_YOUR_CODE
for i in range(n):
csp.add_variable('Q' + str(i), list(range(n))) # the position of a queen in each row (from 0 to n-1)
for i in range(n-1):
for j in range(i+1, n):
csp.add_binary_factor('Q' + str(i), 'Q' + str(j), lambda x, y: x != y)
csp.add_binary_factor('Q' + str(i), 'Q' + str(j), lambda x, y: abs(x-y) != abs(j-i))
# TODO: END_YOUR_CODE
return csp
def create_n_queens_csp(n=8):
"""Create an N-Queen problem on the board of size n * n.
You should call csp.add_variable() and csp.add_binary_factor().
Args:
n: int, number of queens, or the size of one dimension of the board.
Returns
csp: A CSP problem with correctly configured factor tables
such that it can be solved by a weighted CSP solver
"""
csp = CSP()
# TODO: Problem a
# TODO: BEGIN_YOUR_CODE
vars = []
for i in range(1, n + 1):
# we suppose that on a board, we put in queens with order.
# In other words, Xi is fixed for each queen,
# we only have to consider Yi for each queen
varName = 'Y' + str(i)
csp.add_variable(varName, range(1, n + 1))
vars.append(varName)
rule1 = lambda x, y: x != y
for var in vars:
for anotherVar in vars:
if var != anotherVar:
# csp.add_binary_factor(var, anotherVar, lambda y1, y2: y1 != y2)
dist = abs(vars.index(anotherVar) - vars.index(var))
csp.add_binary_factor(
var, anotherVar,
lambda y1, y2: y1 != y2 and abs(y1 - y2) != dist)
# raise NotImplementedError
# TODO: END_YOUR_CODE
return csp
