def makeChange(Q, D):
## Helper functions - begin ######################
def getValue(n):
p = T.parent(n)
if(p == None):
return T.getContents(n)
else:
return T.getContents(n) + getValue(p)
def shouldBeAdded(n):
return (not getValue(n) > Q)
# This function returns the list of new partial solutions that can be created with a value x.
# It just returns a list with only one element indicating increment of sum by x.
def process(x): return [x]
# Given a partial solution s, extend it by one step using each of the denominations available in D.
extendSolution = bfs.makeExtendSolution(D, process, shouldBeAdded)
def isSolution(n):
return getValue(n) == Q
## Helper functions - end ######################
## Main algorithm - begin ######################
return bfs.search(0, extendSolution, isSolution)
def fillJug(capacities, Q):
INITACTION = 0
EMPTYACTION = 1
FILLACTION = 2
TRANSFERACTION = 3
# Given a list of incremental contents, this function computes the actual contents at every step.
# Example: if contents = [(FILLACTION, 1), (FILLACTION, 2), (TRANSFERACTION, (2, 0)] the output
# for capacities=[3, 4, 5] is [[0, 4, 0], [0, 4, 5], [3, 4, 5]]
# The last element of this output list is the final actual contents of the jugs.
def getValueFromContents(contents):
values = []
value = [0] * len(capacities)
for content in contents:
if(content[0] == EMPTYACTION):
value = empty(content[1], value)
elif(content[0] == FILLACTION):
value = fill(content[1], value)
elif(content[0] == TRANSFERACTION):
value = transfer(content[1][0], content[1][1], value)
else:
pass
values.append(value)
return values
# This calls the getValueFromContents function to obtain the sequence of actual contents, and
# returns the last element of this list, which is the current actual contents.
def getValue(n):
ntrace = T.getTrace(n)
contents = [T.getContents(n1) for n1 in ntrace]
return getValueFromContents(contents)[-1]
def isSolution(s):
def numOfNonEmptyJugs(c):
def g(x, y):
if(y == 0): return x
return x + 1
return reduce(g, c, 0)
def totalQuantity(c):
return reduce(lambda x, y: x + y, c, 0)
v = getValue(s)
return (numOfNonEmptyJugs(v) == 1) and (totalQuantity(v) == Q)
# empty the ith jug.
def empty(i, contents):
newcontents = contents[:]
newcontents[i] = 0
return newcontents
# fill the ith jug to its capacity
def fill(i, contents):
newcontents = contents[:]
newcontents[i] = capacities[i]
return newcontents
# transfer the contents of jug i to jug j. Do it only if:
# -- i is not empty
# -- j is not full
# Transfer only so much as j can hold (in case i holds more fluid than j can take)
def transfer(i, j, contents):
def min(x, y):
if(x < y): return x
return y
def isEmpty(i): return contents[i] == 0
def isFull(i): return contents[i] == capacities[i]
newcontents = contents[:]
if(not (isEmpty(i) or isFull(j))):
q = min(contents[i], capacities[j] - contents[j])
newcontents[i] -= q
newcontents[j] += q
return newcontents
def process(i):
nss = []
nss.append((EMPTYACTION, i))
nss.append((FILLACTION, i))
for j in range(len(capacities)):
if(i != j):
nss.append((TRANSFERACTION, (i, j)))
return nss
# Determine whether a node with the same contents as node n already exists.
def isNewContents(n): return not T.searchNode(n, getValue)
# Criterion for adding a particular configuration into the BFS queue: The set of jug-contents should never
# have happened so far.
def shouldBeAdded(n): return isNewContents(n)
# The first argument is the range of jug indexes.
extendSolution = bfs.makeExtendSolution(range(len(capacities)), process, shouldBeAdded)
result = bfs.search((INITACTION, None), extendSolution, isSolution)
return getValueFromContents(result)
def fillJug(capacities, Q):
INITACTION = 0
EMPTYACTION = 1
FILLACTION = 2
TRANSFERACTION = 3
def getValueFromContents(contents):
values = []
value = [0] * len(capacities)
for content in contents:
if(content[0] == EMPTYACTION):
value = empty(content[1], value)
elif(content[0] == FILLACTION):
value = fill(content[1], value)
elif(content[0] == TRANSFERACTION):
value = transfer(content[1][0], content[1][1], value)
else:
pass
values.append(value)
return values
#
def getValue(n):
ntrace = T.getTrace(n)
contents = [T.getContents(n1) for n1 in ntrace]
return getValueFromContents(contents)[-1]
def isSolution(s):
def numOfNonEmptyJugs(c):
def g(x, y):
if(y == 0): return x
return x + 1
return reduce(g, c, 0)
def totalQuantity(c):
return reduce(lambda x, y: x + y, c, 0)
v = getValue(s)
return (numOfNonEmptyJugs(v) == 1) and (totalQuantity(v) == Q)
# empty the ith jug.
def empty(i, contents):
newcontents = contents[:]
newcontents[i] = 0
return newcontents
# fill the ith jug to its capacity
def fill(i, contents):
newcontents = contents[:]
newcontents[i] = capacities[i]
return newcontents
# transfer the contents of jug i to jug j. Do it only if:
# -- i is not empty
# -- j is not full
# Transfer only so much as j can hold (in case i holds more fluid than j can take)
def transfer(i, j, contents):
def min(x, y):
if(x < y): return x
return y
def isEmpty(i): return contents[i] == 0
def isFull(i): return contents[i] == capacities[i]
newcontents = contents[:]
if(not (isEmpty(i) or isFull(j))):
q = min(contents[i], capacities[j] - contents[j])
newcontents[i] -= q
newcontents[j] += q
return newcontents
def process(i):
nss = []
ns = (EMPTYACTION, i)
nss.append(ns)
ns = (FILLACTION, i)
nss.append(ns)
for j in range(len(capacities)):
if(i != j):
ns = (TRANSFERACTION, (i, j))
nss.append(ns)
return nss
# Determine whether a node with the same contents as node n already exists.
def isNewContents(n): return not T.searchNode(n, getValue)
# Criterion for adding a particular configuration into the BFS queue: The set of jug-contents should never
# have happened so far.
def shouldBeAdded(n): return isNewContents(n)
extendSolution = bfs.makeExtendSolution(range(len(capacities)), process, shouldBeAdded)
##### extendSolution - End ##################
result = bfs.search((INITACTION, None), extendSolution, isSolution)
return getValueFromContents(result)