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Permutations without itertools for two values (using recursion!)

Stackoverflow, I am once again asking for your help.
I'm aware there are other threads about this but I'll explain what makes my assignment different.
Basically my function would get a list of 0s and 1s, and return all the possible orders for the string. For example for "0111" we will get "0111", "1011", "1101", "1110".
Here's my code:
def permutations(string):
if len(string) == 1:
return [string]
lst = []
for j in range(len(string)):
remaining_elements = ''.join([string[i] for i in range(len(string)) if i != j])
mini_perm = permutations(remaining_elements)
for perm in mini_perm:
new_str = string[j] + perm
if new_str not in lst:
lst.append(new_str)
return lst
The problem is when I run a string like "000000000011" it takes a very long time to process. There is supposed to be a more efficient way to do it because it's just two numbers. So I shouldn't be using the indexes?
Please help me if you can figure out a more efficient say to do this.
(I am allowed to use loops just have to use recursion as well!)

Here is an example for creating permutations with recursion that is more efficient:
def permute(string):
string = list(string)
n = len(string)
# Base conditions
# If length is 0 or 1, there is only 1 permutation
if n in [0, 1]:
return [string]
# If length is 2, then there are only two permutations
# Example: [1,2] and [2,1]
if n == 2:
return [string, string[::-1]]
res = []
# For every number in array, choose 1 number and permute the remaining
# by calling permute recursively
for i in range(n):
permutations = permute(string[:i] + string[i+1:])
for p in permutations:
res.append([''.join(str(n) for n in [string[i]] + p)])
return res
This should also work for permute('000000000011') - hope it helps!

You can also use collections.Counter with a recursive generator function:
from collections import Counter
def permute(d):
counts = Counter(d)
def get_permuations(c, s = []):
if len(s) == sum(counts.values()):
yield ''.join(s)
else:
for a, b in c.items():
for i in range(1, b+1):
yield from get_permuations({**c, a:b - i}, s+([a]*i))
return list(set(get_permuations(counts)))
print(permute("0111"))
print(permute("000000000011"))
Output:
['0111', '1110', '1101', '1011']
['010000100000', '100000000001', '010000001000', '000000100001', '011000000000', '100000000010', '001001000000', '000000011000', '100000001000', '100000100000', '100001000000', '001000100000', '100010000000', '000000001100', '000100000100', '010010000000', '000000000011', '000000100010', '101000000000', '110000000000', '100000010000', '000100001000', '000001001000', '000000000101', '000000100100', '010000000001', '001000000100', '001000000010', '000110000000', '000011000000', '000001100000', '000000110000', '001000000001', '000010001000', '000100100000', '000001000001', '000010000001', '001100000000', '000100000001', '001000001000', '010000000100', '010000010000', '000000010001', '001000010000', '010001000000', '100000000100', '100100000000', '000000001001', '010100000000', '000010100000', '010000000010', '000000001010', '000010000100', '001010000000', '000000010010', '000001000010', '000100000010', '000101000000', '000000010100', '000100010000', '000000000110', '000001000100', '000010010000', '000000101000', '000001010000', '000010000010']

posting an answer someone gave me. Thanks for your responses!:
def permutations(zeroes, ones, lst, perm):
if zeroes == 0 and ones == 0:
lst.append(perm)
return
elif zeroes < 0 or ones < 0:
return
permutations(zeroes - 1, ones, lst, perm + '0')
permutations(zeroes, ones - 1, lst, perm + '1')

looping through loops in python?

I'm trying to solve this problem on the easy section of coderbyte and the prompt is:
Have the function ArrayAdditionI(arr) take the array of numbers stored in arr and return the string true if any combination of numbers in the array can be added up to equal the largest number in the array, otherwise return the string false. For example: if arr contains [4, 6, 23, 10, 1, 3] the output should return true because 4 + 6 + 10 + 3 = 23. The array will not be empty, will not contain all the same elements, and may contain negative numbers.
Here's my solution.
def ArrayAddition(arr):
arr = sorted(arr, reverse=True)
large = arr.pop(0)
storage = 0
placeholder = 0
for r in range(len(arr)):
for n in arr:
if n + storage == large: return True
elif n + storage < large: storage += n
else: continue
storage = 0
if placeholder == 0: placeholder = arr.pop(0)
else: arr.append(placeholder); placeholder = arr.pop(0)
return False
print ArrayAddition([2,95,96,97,98,99,100])
I'm not even sure if this is correct, but it seems to cover all the numbers I plug in. I'm wondering if there is a better way to solve this through algorithm which I know nothing of. I'm thinking a for within a for within a for, etc loop would do the trick, but I don't know how to do that.
What I have in mind is accomplishing this with A+B, A+C, A+D ... A+B+C ... A+B+C+D+E
e.g)
for i in range(len(arr):
print "III: III{}III".format(i)
storage = []
for j in range(len(arr):
print "JJ: II({}),JJ({})".format(i,j)
for k in range(len(arr):
print "K: I{}, J{}, K{}".format(i,j,k)
I've searched all over and found the suggestion of itertool, but I'm wondering if there is a way to write this code up more raw.
Thanks.

A recursive solution:
def GetSum(n, arr):
if len(arr) == 0 and n != 0:
return False
return (n == 0 or
GetSum(n, arr[1:]) or
GetSum(n-arr[0], arr[1:]))
def ArrayAddition(arr):
arrs = sorted(arr)
return GetSum(arrs[-1], arrs[:-1])
print ArrayAddition([2,95,96,97,98,99,100])
The GetSum function returns False when the required sum is non-zero and there are no items in the array. Then it checks for 3 cases:
If the required sum, n, is zero then the goal is achieved.
If we can get the sum with the remaining items after the first item is removed, then the goal is achieved.
If we can get the required sum minus the first element of the list on the rest of the list the goal is achieved.

Your solution doesn't work.
>>> ArrayAddition([10, 11, 20, 21, 30, 31, 60])
False
The simple solution is to use itertools to iterate over all subsets of the input (that don't contain the largest number):
def subsetsum(l):
l = list(l)
target = max(l)
l.remove(l)
for subset_size in xrange(1+len(l)):
for subset in itertools.combinations(l, subset_size):
if sum(subset) == target:
return True
return False
If you want to avoid itertools, you'll need to generate subsets directly. That can be accomplished by counting in binary and using the set bits to determine which elements to pick:
def subsetsum(l):
l = list(l)
target = max(l)
l.remove(l)
for subset_index in xrange(2**len(l)):
subtotal = 0
for i, num in enumerate(l):
# If bit i is set in subset_index
if subset_index & (1 << i):
subtotal += num
if subtotal == target:
return True
return False

Update: I forgot that you want to check all possible combinations. Use this instead:
def ArrayAddition(l):
for length in range(2, len(l)):
for lst in itertools.combinations(l, length):
if sum(lst) in l:
print(lst, sum(lst))
return True
return False
One-liner solution:
>>> any(any(sum(lst) in l for lst in itertools.combinations(l, length)) for length in range(2, len(l)))
Hope this helps!

Generate all the sums of the powerset and test them against the max
def ArrayAddition(L):
return any(sum(k for j,k in enumerate(L) if 1<<j&i)==max(L) for i in range(1<<len(L)))
You could improve this by doing some preprocessing - find the max first and remove it from L

One more way to do it...
Code:
import itertools
def func(l):
m = max(l)
rem = [itertools.combinations([x for x in l if not x == m],i) for i in range(2,len(l)-1)]
print [item for i in rem for item in i if sum(item)==m ]
if __name__=='__main__':
func([1,2,3,4,5])
Output:
[(1, 4), (2, 3)]
Hope this helps.. :)

If I understood the question correctly, simply this should return what you want:
2*max(a)<=sum(a)

Converting integer to digit list [duplicate]

This question already has answers here:
How to split an integer into a list of digits?
(10 answers)
Closed 4 months ago.
What is the quickest and cleanest way to convert an integer into a list?
For example, change 132 into [1,3,2] and 23 into [2,3]. I have a variable which is an int, and I want to be able to compare the individual digits so I thought making it into a list would be best, since I can just do int(number[0]), int(number[1]) to easily convert the list element back into int for digit operations.

Convert the integer to string first, and then use map to apply int on it:
>>> num = 132
>>> map(int, str(num)) #note, This will return a map object in python 3.
[1, 3, 2]
or using a list comprehension:
>>> [int(x) for x in str(num)]
[1, 3, 2]

There are already great methods already mentioned on this page, however it does seem a little obscure as to which to use. So I have added some mesurements so you can more easily decide for yourself:
A large number has been used (for overhead) 1111111111111122222222222222222333333333333333333333
Using map(int, str(num)):
import timeit
def method():
num = 1111111111111122222222222222222333333333333333333333
return map(int, str(num))
print(timeit.timeit("method()", setup="from __main__ import method", number=10000)
Output: 0.018631496999999997
Using list comprehension:
import timeit
def method():
num = 1111111111111122222222222222222333333333333333333333
return [int(x) for x in str(num)]
print(timeit.timeit("method()", setup="from __main__ import method", number=10000))
Output: 0.28403817900000006
Code taken from this answer
The results show that the first method involving inbuilt methods is much faster than list comprehension.
The "mathematical way":
import timeit
def method():
q = 1111111111111122222222222222222333333333333333333333
ret = []
while q != 0:
q, r = divmod(q, 10) # Divide by 10, see the remainder
ret.insert(0, r) # The remainder is the first to the right digit
return ret
print(timeit.timeit("method()", setup="from __main__ import method", number=10000))
Output: 0.38133582499999996
Code taken from this answer
The list(str(123)) method (does not provide the right output):
import timeit
def method():
return list(str(1111111111111122222222222222222333333333333333333333))
print(timeit.timeit("method()", setup="from __main__ import method", number=10000))
Output: 0.028560138000000013
Code taken from this answer
The answer by Duberly González Molinari:
import timeit
def method():
n = 1111111111111122222222222222222333333333333333333333
l = []
while n != 0:
l = [n % 10] + l
n = n // 10
return l
print(timeit.timeit("method()", setup="from __main__ import method", number=10000))
Output: 0.37039988200000007
Code taken from this answer
Remarks:
In all cases the map(int, str(num)) is the fastest method (and is therefore probably the best method to use). List comprehension is the second fastest (but the method using map(int, str(num)) is probably the most desirable of the two.
Those that reinvent the wheel are interesting but are probably not so desirable in real use.

The shortest and best way is already answered, but the first thing I thought of was the mathematical way, so here it is:
def intlist(n):
q = n
ret = []
while q != 0:
q, r = divmod(q, 10) # Divide by 10, see the remainder
ret.insert(0, r) # The remainder is the first to the right digit
return ret
print intlist(3)
print '-'
print intlist(10)
print '--'
print intlist(137)
It's just another interesting approach, you definitely don't have to use such a thing in practical use cases.

n = int(raw_input("n= "))
def int_to_list(n):
l = []
while n != 0:
l = [n % 10] + l
n = n // 10
return l
print int_to_list(n)

If you have a string like this: '123456'
and you want a list of integers like this: [1,2,3,4,5,6], use this:
>>>s = '123456'
>>>list1 = [int(i) for i in list(s)]
>>>print(list1)
[1,2,3,4,5,6]
or if you want a list of strings like this: ['1','2','3','4','5','6'], use this:
>>>s = '123456'
>>>list1 = list(s)
>>>print(list1)
['1','2','3','4','5','6']

Use list on a number converted to string:
In [1]: [int(x) for x in list(str(123))]
Out[2]: [1, 2, 3]

>>>list(map(int, str(number))) #number is a given integer
It returns a list of all digits of number.

you can use:
First convert the value in a string to iterate it, Them each value can be convert to a Integer value = 12345
l = [ int(item) for item in str(value) ]

By looping it can be done the following way :)
num1= int(input('Enter the number'))
sum1 = num1 #making a alt int to store the value of the orginal so it wont be affected
y = [] #making a list
while True:
if(sum1==0):#checking if the number is not zero so it can break if it is
break
d = sum1%10 #last number of your integer is saved in d
sum1 = int(sum1/10) #integer is now with out the last number ie.4320/10 become 432
y.append(d) # appending the last number in the first place
y.reverse()#as last is in first , reversing the number to orginal form
print(y)
Answer becomes
Enter the number2342
[2, 3, 4, 2]

num = 123
print(num)
num = list(str(num))
num = [int(i) for i in num]
print(num)

num = list(str(100))
index = len(num)
while index > 0:
index -= 1
num[index] = int(num[index])
print(num)
It prints [1, 0, 0] object.

Takes an integer as input and converts it into list of digits.
code:
num = int(input())
print(list(str(num)))
output using 156789:
>>> ['1', '5', '6', '7', '8', '9']

counting odd numbers in a list python

This is a part of my homework assignment and im close to the final answer but not quite yet. I need to write a function that counts odd numbers in a list.
Create a recursive function count_odd(l) which takes as its only argument a list of integers. The function will return a count of the number of list elements that are odd, i.e., not evenly divisible by 2.\
>>> print count_odd([])
0
>>> print count_odd([1, 3, 5])
3
>>> print count_odd([2, 4, 6])
0
>>> print count_odd([0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144])
8
Here is what i have so far:
#- recursive function count_odd -#
def count_odd(l):
"""returns a count of the odd integers in l.
PRE: l is a list of integers.
POST: l is unchanged."""
count_odd=0
while count_odd<len(l):
if l[count_odd]%2==0:
count_odd=count_odd
else:
l[count_odd]%2!=0
count_odd=count_odd+1
return count_odd
#- test harness
print count_odd([])
print count_odd([1, 3, 5])
print count_odd([2, 4, 6])
print count_odd([0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144])
Can u help explain what im missing. The first two test harness works fine but i cant get the final two. Thanks!

Since this is homework, consider this pseudo-code that just counts a list:
function count (LIST)
if LIST has more items
// recursive case.
// Add one for the current item we are counting,
// and call count() again to process the *remaining* items.
remaining = everything in LIST except the first item
return 1 + count(remaining)
else
// base case -- what "ends" the recursion
// If an item is removed each time, the list will eventually be empty.
return 0
This is very similar to what the homework is asking for, but it needs to be translate to Python and you must work out the correct recursive case logic.
Happy coding.

def count_odd(L):
return (L[0]%2) + count_odd(L[1:]) if L else 0

Are slices ok? Doesn't feel recursive to me, but I guess the whole thing is kind of against usual idioms (i.e. - recursion of this sort in Python):
def countOdd(l):
if l == list(): return 0 # base case, empty list means we're done
return l[0] % 2 + countOdd(l[1:]) # add 1 (or don't) depending on odd/even of element 0. recurse on the rest
x%2 is 1 for odds, 0 for evens. If you are uncomfortable with it or just don't understand it, use the following in place of the last line above:
thisElement = l[0]
restOfList = l[1:]
if thisElement % 2 == 0: currentElementOdd = 0
else: currentElementOdd = 1
return currentElementOdd + countOdd(restOfList)
PS - this is pretty recursive, see what your teacher says if you turn this in =P
>>> def countOdd(l):
... return fold(lambda x,y: x+(y&1),l,0)
...
>>> def fold(f,l,a):
... if l == list(): return a
... return fold(f,l[1:],f(a,l[0]))

All of the prior answers are subdividing the problem into subproblems of size 1 and size n-1. Several people noted that the recursive stack might easily blow out. This solution should keep the recursive stack size at O(log n):
def count_odd(series):
l = len(series) >> 1
if l < 1:
return series[0] & 1 if series else 0
else:
return count_odd(series[:l]) + count_odd(series[l:])

The goal of recursion is to divide the problem into smaller pieces, and apply the solution to the smaller pieces. In this case, we can check if the first number of the list (l[0]) is odd, then call the function again (this is the "recursion") with the rest of the list (l[1:]), adding our current result to the result of the recursion.

def count_odd(series):
if not series:
return 0
else:
left, right = series[0], series[1:]
return count_odd(right) + (1 if (left & 1) else 0)

Tail recursion
def count_odd(integers):
def iter_(lst, count):
return iter_(rest(lst), count + is_odd(first(lst))) if lst else count
return iter_(integers, 0)
def is_odd(integer):
"""Whether the `integer` is odd."""
return integer % 2 != 0 # or `return integer & 1`
def first(lst):
"""Get the first element from the `lst` list.
Return `None` if there are no elements.
"""
return lst[0] if lst else None
def rest(lst):
"""Return `lst` list without the first element."""
return lst[1:]
There is no tail-call optimization in Python, so the above version is purely educational.
The call could be visualize as:
count_odd([1,2,3]) # returns
iter_([1,2,3], 0) # could be replaced by; depth=1
iter_([2,3], 0 + is_odd(1)) if [1,2,3] else 0 # `bool([1,2,3])` is True in Python
iter_([2,3], 0 + True) # `True == 1` in Python
iter_([2,3], 1) # depth=2
iter_([3], 1 + is_odd(2)) if [2,3] else 1
iter_([3], 1 + False) # `False == 0` in Python
iter_([3], 1) # depth=3
iter_([], 1 + is_odd(3)) if [3] else 1
iter_([], 2) # depth=4
iter_(rest([]), 2 + is_odd(first([])) if [] else 2 # bool([]) is False in Python
2 # the answer
Simple trampolining
To avoid 'max recursion depth exceeded' errors for large arrays all tail calls in recursive functions can be wrapped in lambda: expressions; and special trampoline() function can be used to unwrap such expressions. It effectively converts recursion into iterating over a simple loop:
import functools
def trampoline(function):
"""Resolve delayed calls."""
#functools.wraps(function)
def wrapper(*args):
f = function(*args)
while callable(f):
f = f()
return f
return wrapper
def iter_(lst, count):
#NOTE: added `lambda:` before the tail call
return (lambda:iter_(rest(lst), count+is_odd(first(lst)))) if lst else count
#trampoline
def count_odd(integers):
return iter_(integers, 0)
Example:
count_odd([1,2,3])
iter_([1,2,3], 0) # returns callable
lambda:iter_(rest(lst), count+is_odd(first(lst))) # f = f()
iter_([2,3], 0+is_odd(1)) # returns callable
lambda:iter_(rest(lst), count+is_odd(first(lst))) # f = f()
iter_([3], 1+is_odd(2)) # returns callable
lambda:iter_(rest(lst), count+is_odd(first(lst))) # f = f()
iter_([], 1+is_odd(3))
2 # callable(2) is False

I would write it like this:
def countOddNumbers(numbers):
sum = 0
for num in numbers:
if num%2!=0:
sum += numbers.count(num)
return sum

not sure if i got your question , but as above something similar:
def countOddNumbers(numbers):
count=0
for i in numbers:
if i%2!=0:
count+=1
return count

Generator can give quick result in one line code:
sum((x%2 for x in nums))

Python recursive program to prime factorize a number

I wrote the following program to prime factorize a number:
import math
def prime_factorize(x,li=[]):
until = int(math.sqrt(x))+1
for i in xrange(2,until):
if not x%i:
li.append(i)
break
else: #This else belongs to for
li.append(x)
print li #First print statement; This is what is returned
return li
prime_factorize(x/i,li)
if __name__=='__main__':
print prime_factorize(300) #Second print statement, WTF. why is this None
Following is the output I get:
[2, 2, 3, 5, 5]
None
Altho', the returned value is printed properly, the after returned value seems to be printing none, all the time. What am I missing?
Also, how can I improve the program (continuing to use the recursion)

Your prime_factorize function doesn't have a return statement in the recursive case -- you want to invoke "return prime_factorize(x/i,li)" on its last line. Try it with a prime number (so the recursive call isn't needed) to see that it works in that case.
Also you probably want to make the signature something like:
def prime_factorize(x,li=None):
if li is None: li = []
otherwise you get wrong results when calling it two or more times:
>>> prime_factorize(10)
[2, 5]
>>> prime_factorize(4)
[2, 5, 2, 2]
>>> prime_factorize(19)
[2, 5, 2, 2, 19]

If you want to do it completely recursive, I'd recommend this code, it does return the correct answer and the way it works is pretty clear.
If you want to make the program as efficient as possible I'd recommend you to stick to one of your previous methods.
def primeFact (i, f):
if i < f:
return []
if i % f == 0:
return [f] + primeFact (i / f, 2)
return primeFact (i, f + 1)
This is a completely recursive way of solving your problem
>>> primeFact (300, 2)
[2, 2, 3, 5, 5]
>>> primeFact (17, 2)
[17]
>>> primeFact (2310, 2)
[2, 3, 5, 7, 11]

#Anthony's correctly answered your original question about print. However, in the spirit of the several tips that were also offered, here's a simple refactorization using tail recursion removal:
def prime_factorize(x):
li = []
while x >= 2:
until = int(math.sqrt(x))+1
for i in xrange(2,until):
if not x%i:
li.append(i)
break
else:
li.append(x)
return li
x //= i
This doesn't address the crucial performance issues (big-O behavior is the same as for your original solution) -- but since Python itself doesn't do tail-recursion optimization, it's important to learn to do it manually.
"Change the [non-base-case] recursive steps 'return thisfun(newargs)' into args=newargs; continue and put the whole body into a while True: loop" is the basic idea of tail-recursion optimization. Here I've also made li a non-arg (no reason for it to be an arg), put a condition on the while, and avoided the continue since the recursive step was at the end of the body anyway.
This formulation would be a good basis from which to apply further optimizing refactorings (sqrt avoidance, memoization, ...) to reach towards better performance.

A more functional-style version.
def prime_factorize( number ):
def recurse( factors, x, n ):
if x<2: return factors # 0,1 dont have prime factors
if n > 1+x**0.5: # reached the upper limit
factors.append( x ) # the only prime left is x itself
return factors
if x%n==0: # x is a factor
factors.append( n )
return recurse( factors, x/n, n )
else:
return recurse( factors, x, n+1 )
return recurse( [], number, 2)
for num, factors in ((n, prime_factorize( n )) for n in range(1,50000)):
assert (num==reduce(lambda x,y:x*y, factors, 1)), (num, factors)
#print num, ":", factors

def primeFactorization(n):
""" Return the prime factors of the given number. """
factors = []
lastresult = n
while 1:
if lastresult == 1:
break
c = 2
while 1:
if lastresult % c == 0:
break
c += 1
factors.append(c)
lastresult /= c
return factors
is it fine.

def Pf(n,i):
if n%2==0:
print(2)
Pf(n/2,3)
elif n<i:
return 0
else:
if n%i==0:
print(i)
Pf(n/i,i)
else:
Pf(n,i+2)
n=int(input())
Pf(n,3)
check out this code