My approach to question "Regular Bracket Sequences" codeforces

bracket-pattern-generator-faster.py

def incrementNextRightSlotAlgorithm(n): 
    if n == 1:
        yield [1]
    elif n == 0:
        yield []
    else:
        for x in range(n,0,-1):
            for y in incrementNextRightSlotAlgorithm(n-x):
                yield([x]+y)

def toBracket(n):
    if n == 1:
        yield '()'
    else:
        for x in bracketPatternMaker(n-1):
            yield('('+ x +')')

def slotObjects(array):
    objK = [toBracket(n) for n in array]
    #the reason we dont iterate the first slotObject is
    #because the slotIterator method will do the 
    #iteration to the object at the first index
    valK = [objK[0]] + [next(a) for a in objK[1:]]

    outputHistory = [ [] ] + [ [valK[n]] for n in range(1, len(valK)) ]
    #because the slot other than the first slot already iterated,
    #the pointer for the slot other tan the first get index 1.
    #and the first get index 0
    outputHistoryPointer = [ 0 ] + [1 for n in range(1, len(outputHistory))]

    for x in slotIterator(objK,valK,outputHistory,outputHistoryPointer):
        yield ''.join(x)

#remember, passing list in python in pass by reference,
#so we don't need to bother returning the changed value
#of the list too
def slotIterator(obj,val,outputHistory,outputHistoryPointer,n=0):
    while not n == len(obj):
        try:
            try:
                val[n] = outputHistory[n][outputHistoryPointer[n]]
            except IndexError:
                val[n] = next(obj[n])
                outputHistory[n].append(val[n])
            #need to add the pointer before the yield
            #if not, the pointer won't change
            outputHistoryPointer[n] += 1
            yield val
        except StopIteration:
            outputHistoryPointer[n] = 0
            val[n] = outputHistory[n][0]
            try:
                #after the other slot finished gives all possible pattern,
                #this slot have to move to the
                outputHistoryPointer[n] += 1
                yield next(slotIterator(obj,val,outputHistory,outputHistoryPointer,n+1))
            except StopIteration:
                break

def bracketPatternMaker(n):
    for x in incrementNextRightSlotAlgorithm(n):
        for y in slotObjects(x):
            yield y

#input

print("Input the number of brackets: ")
data = dict()

while True:
    x = int(input())

    if not x in data:
        data[x] = bracketPatternMaker(x)

    try:
        n = 0;
        while True:
            pattern = next(data[x])
            print(pattern)
            n += 1
    except StopIteration:
        data[x] = bracketPatternMaker(x)
        print("The total of mathematically valid pattern for ", x, " bracket is :", n)

bracket-pattern-generator.py

def incrementNextRightSlotAlgorithm(n): 
    if n == 1:
        yield [1]
    elif n == 0:
        yield []
    else:
        for x in range(n,0,-1):
            for y in incrementNextRightSlotAlgorithm(n-x):
                yield([x]+y)

def toBracket(n):
    if n == 1:
        yield '()'
    else:
        for x in bracketPatternMaker(n-1):
            yield('('+ x +')')

def slotObjects(array):
    objK = [toBracket(n) for n in array]
    #the reason we dont iterate the first slotObject is
    #because the slotIterator method will do the 
    #iteration to the object at the first index
    valK = [objK[0]] + [next(a) for a in objK[1:]]

    for x in slotIterator(objK,valK,array):
        yield ''.join(x)

def slotIterator(obj,val,lis,n = 0):
    while not n == len(obj):
        try:
            val[n] = next(obj[n])
            yield val
        except StopIteration:
            obj[n] = toBracket(lis[n])
            val[n] = next(obj[n])
            try:
                yield next(slotIterator(obj,val,lis,n+1))
            except StopIteration:
                break

def bracketPatternMaker(n):
    for x in incrementNextRightSlotAlgorithm(n):
        for y in slotObjects(x):
            yield y

#input

print("Input the number of brackets: ")
data = dict()

while True:
    x = int(input())

    if not x in data:
        data[x] = bracketPatternMaker(x)

    try:
        n = 0;
        while True:
            print(next(data[x]))
            n += 1
    except StopIteration:
        data[x] = bracketPatternMaker(x)
        print("The total of mathematically valid pattern for ", x, " bracket is :", n)