def process(g):
for i in range(len(capacities)):
nc = g(i)
ns = T.makeLeaf(nc, state)
if(isNewContents(ns)):
T.addSubtree(state, ns)
nss.append(ns)
def extendSolution(n):
nss = []
for i in D:
nc = i
st = T.makeLeaf(nc, n)
if(shouldBeAdded(st)):
T.addSubtree(n, st)
nss.append(st)
return nss
def extendSolution(n):
nss = []
for i in choices:
ncs = process(i)
for nc in ncs:
st = T.makeLeaf(nc, n)
if(shouldBeAdded(st)):
T.addSubtree(n, st)
nss.append(st)
return nss
def search(ic, extendSolution, isSolution):
initialState = T.makeLeaf(ic, None) # root state
queue = [initialState]
while(len(queue) is not 0):
s = queue.pop(0)
if(isSolution(s)):
strace = T.getTrace(s)
strace.pop(0)
return [T.getContents(s) for s in strace]
es = extendSolution(s)
queue.extend(es)
return None
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)
# Given a partial solution s, extend it by one step using each of the denominations available in D.
def extendSolution(n):
nss = []
for i in D:
nc = i
st = T.makeLeaf(nc, n)
if(shouldBeAdded(st)):
T.addSubtree(n, st)
nss.append(st)
return nss
def isSolution(n):
return getValue(n) == Q
## Helper functions - end ######################
## Main algorithm - begin ######################
initialContents = 0
queue = [T.makeLeaf(initialContents, None)]
while(len(queue) is not 0):
s = queue.pop(0)
if(isSolution(s)):
strace = T.getTrace(s)
strace.pop(0)
return [T.getContents(s) for s in strace]
es = extendSolution(s)
queue.extend(es)
return None
def fillJug(capacities, Q):
def isSolution(s):
def numOfNonEmptyJugs(c):
def f(x):
if(x == 0): return 0
return 1
ne = [f(i) for i in c]
return reduce(lambda x, y: x + y, ne, 0)
def totalQuantity(c):
return reduce(lambda x, y: x + y, c, 0)
c = T.getContents(s)
return (numOfNonEmptyJugs(c) == 1) and (totalQuantity(c) == Q)
##### extendSolution - Begin ##################
# Given an incomplete solution state, extend it by performing all the atomic operations:
# -- Create a new solution by emptying each jug one by one.
# -- Create a new solution by filling each jug to its capacity one by one.
# -- Create a new solution by transferring the contents of each jug to every other.
def extendSolution(state):
contents = T.getContents(state)
# empty the ith jug.
def empty(i):
newcontents = contents[:]
newcontents[i] = 0
return newcontents
# fill the ith jug to its capacity
def fill(i):
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):
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 isNewContents(n):
return not T.searchNode(n, T.getContents)
nss = []
def process(g):
for i in range(len(capacities)):
nc = g(i)
ns = T.makeLeaf(nc, state)
if(isNewContents(ns)):
T.addSubtree(state, ns)
nss.append(ns)
# Create new states by emptying jug i.
process(empty)
# Create new states by filling jug i.
process(fill)
# Create new states by transferring i's contents to each other j.
for i in range(len(capacities)):
process(lambda n: transfer(i, n))
return nss
##### extendSolution - End ##################
initialContents = [0] * len(capacities)
initialState = T.makeLeaf(initialContents, None) # root state
queue = [initialState]
while(len(queue) is not 0):
s = queue.pop(0)
if(isSolution(s)):
strace = T.getTrace(s)
strace.pop(0)
return [T.getContents(s) for s in strace]
es = extendSolution(s)
queue.extend(es)
return None