def get_sum_variable(csp, name, variables, maxSum):
"""
Given a list of |variables| each with non-negative integer domains,
returns the name of a new variable with domain range(0, maxSum+1), such that
it's consistent with the value |n| iff the assignments for |variables|
sums to |n|.
@param name: Prefix of all the variables that are going to be added.
Can be any hashable objects. For every variable |var| added in this
function, it's recommended to use a naming strategy such as
('sum', |name|, |var|) to avoid conflicts with other variable names.
@param variables: A list of variables that are already in the CSP that
have non-negative integer values as its domain.
@param maxSum: An integer indicating the maximum sum value allowed. You
can use it to get the auxiliary variables' domain
@return result: The name of a newly created variable with domain range
[0, maxSum] such that it's consistent with an assignment of |n|
iff the assignment of |variables| sums to |n|.
"""
# BEGIN_YOUR_CODE (around 20 lines of code expected)
result = ('sum', name, 'aggregated')
csp.add_variable(result, range(maxSum+1))
if len(variables) == 0:
csp.add_unary_factor(result, lambda val: not val)
return result
prev_domain = [(0,0)]
# for i in range(maxSum+1):
# for j in range():
# domain.append(i, j)
for i, X_i in enumerate(variables):
domain_i = csp.values[X_i]
curr_domain = list(set([(x1[1], x1[1]+x2) for x1 in prev_domain for x2 in domain_i if x1[1]+x2<=maxSum]))
A_i = ('sum', name, i)
csp.add_variable(A_i, curr_domain)
prev_domain = curr_domain
if i == 0:
csp.add_unary_factor(A_i, lambda b: b[0] == 0)
else:
csp.add_binary_factor(('sum', name, i-1), A_i, lambda a,b: a[1] == b[0])
csp.add_binary_factor(X_i, A_i, lambda a,b: b[1] == b[0] + a)
csp.add_binary_factor(A_i, result, lambda a, b: a[1] == b)
return result
def get_or_variable(csp, name, variables, value):
"""
Create a new variable with domain [True, False] that can only be assigned to
True iff at least one of the |variables| is assigned to |value|. You should
add any necessary intermediate variables, unary factors, and binary
factors to achieve this. Then, return the name of this variable.
@param name: Prefix of all the variables that are going to be added.
Can be any hashable objects. For every variable |var| added in this
function, it's recommended to use a naming strategy such as
('or', |name|, |var|) to avoid conflicts with other variable names.
@param variables: A list of variables in the CSP that are participating
in this OR function. Note that if this list is empty, then the returned
variable created should never be assigned to True.
@param value: For the returned OR variable being created to be assigned to
True, at least one of these variables must have this value.
@return result: The OR variable's name. This variable should have domain
[True, False] and constraints s.t. it's assigned to True iff at least
one of the |variables| is assigned to |value|.
"""
result = ('or', name, 'aggregated')
csp.add_variable(result, [True, False])
# no input variable, result should be False
if len(variables) == 0:
csp.add_unary_factor(result, lambda val: not val)
return result
# Let the input be n variables X0, X1, ..., Xn.
# After adding auxiliary variables, the factor graph will look like this:
#
# ^--A0 --*-- A1 --*-- ... --*-- An --*-- result--^^
# | | |
# * * *
# | | |
# X0 X1 Xn
#
# where each "--*--" is a binary constraint and "--^" and "--^^" are unary
# constraints. The "--^^" constraint will be added by the caller.
for i, X_i in enumerate(variables):
# create auxiliary variable for variable i
# use systematic naming to avoid naming collision
A_i = ('or', name, i)
# domain values:
# - [ prev ]: condition satisfied by some previous X_j
# - [equals]: condition satisfied by X_i
# - [ no ]: condition not satisfied yet
csp.add_variable(A_i, ['prev', 'equals', 'no'])
# incorporate information from X_i
def factor(val, b):
if (val == value): return b == 'equals'
return b != 'equals'
csp.add_binary_factor(X_i, A_i, factor)
if i == 0:
# the first auxiliary variable, its value should never
# be 'prev' because there's no X_j before it
csp.add_unary_factor(A_i, lambda b: b != 'prev')
else:
# consistency between A_{i-1} and A_i
def factor(b1, b2):
if b1 in ['equals', 'prev']: return b2 != 'no'
return b2 != 'prev'
csp.add_binary_factor(('or', name, i - 1), A_i, factor)
# consistency between A_n and result
# hacky: reuse A_i because of python's loose scope
csp.add_binary_factor(A_i, result, lambda val, res: res == (val != 'no'))
return result
