Permutations without itertools for two values (using recursion!) - python

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')

Related

How to Reverse an array in groups in python?

I am trying to reverse the array in groups but I am getting this error:
:---- for i in arr: TypeError: 'NoneType' object is not iterable.
What's wrong with my code?
def reverseSubarray(arr,n,k):
if k == 1:
return
i = 0
while i < n:
l = i
r = min(i+k-1, n-1)
while l < r:
temp = arr[l]
arr[l] = arr[r]
arr[r] = temp
l += 1
r -= 1
i += k
return arr
def main():
n = int(input().strip())
string = input().strip().split()
arr=[]
for j in string:
arr.append(int(j.strip()))
k=int(input().strip())
arr = reverseSubarray(arr,n,k)
for i in arr:
print(i,end=' ')
if __name__ == "__main__":
main()
So the problem is that you're actually returning None. This happens because most likely you're giving k=1 so it will go to that line where you return nothing, which will return this error when trying to iterate.
You can treat the problem with a try-catch block on arr=reverseSubarray(arr,n,k) that will return a message like k cannot be 1
You can reverse an array in groups in python as given below,
def reverseSubarray(arr, N, K):
for i in range(0, len(arr),K):
l=arr[i:i+K]
l.reverse()
arr[i:i+K] =l
return arr
While your error was indeed coming from the fact that your function is returning None as other answers have pointed out, you have also written the function in a very non-pythonic style. Here is an example of how you could rewrite it more succintly:
def reverseInGroups(self, arr, N, K):
for i in range(0, N, K):
arr[i:i+K] = reversed(arr[i:i+K])
return arr
range(0, N, K) will return an iterator that goes from 0 to N-1 in steps of K. In other word, i will successively have value: 0, K, 2K, 3K, 4K, etc. until the last multiple of K that is less than N. Here is the documentation for more details.
arr[i:i+K] will refer to the slice of arr between indices i and i+K-1 or, put another way, [arr[i], arr[i+1], arr[i+2], ..., arr[i+K-1]]. It stops at i+K-1 so that you can naturally use arr[i:i+K] and arr[i+K:] without counting arr[i+K] twice.
reversed... reverses an iterator. Here's the doc.

Generate a dictionary of all possible Kakuro solutions

I'm just starting out with Python and had an idea to try to generate a dictionary of all the possible solutions for a Kakuro puzzle. There are a few posts out there about these puzzles, but none that show how to generate said dictionary. What I'm after is a dictionary that has keys from 3-45, with their values being tuples of the integers which sum to the key (so for example mydict[6] = ([1,5],[2,4],[1,2,3])). It is essentially a Subset Sum Problem - https://mathworld.wolfram.com/SubsetSumProblem.html
I've had a go at this myself and have it working for tuples up to three digits long. My method requires a loop for each additional integer in the tuple, so would require me to write some very repetitive code! Is there a better way to do this? I feel like i want to loop the creation of loops, if that is a thing?
def kakuro():
L = [i for i in range(1,10)]
mydict = {}
for i in L:
L1 = L[i:]
for j in L1:
if i+j in mydict:
mydict[i+j].append((i,j))
else:
mydict[i+j] = [(i,j)]
L2 = L[j:]
for k in L2:
if i+j+k in mydict:
mydict[i+j+k].append((i,j,k))
else:
mydict[i+j+k] = [(i,j,k)]
for i in sorted (mydict.keys()):
print(i,mydict[i])
return
my attempt round 2 - getting better!
def kakurodict():
from itertools import combinations as combs
L = [i for i in range(1,10)]
mydict={}
mydict2={}
for i in L[1:]:
mydict[i] = list(combs(L,i))
for j in combs(L,i):
val = sum(j)
if val in mydict2:
mydict2[val].append(j)
else:
mydict2[val] = [j]
return mydict2
So this is written with the following assumptions.
dict[n] cannot have a list with the value [n].
Each element in the subset has to be unique.
I hope there is a better solution offered by someone else, because when we generate all subsets for values 3-45, it takes quite some time. I believe the time complexity of the subset sum generation problem is 2^n so if n is 45, it's not ideal.
import itertools
def subsetsums(max):
if (max < 45):
numbers = [x for x in range(1, max)]
else:
numbers = [x for x in range(1, 45)]
result = [list(seq) for i in range(len(numbers), 0, -1) for seq in itertools.combinations(numbers, i) if sum(seq) == max]
return(result)
mydict = {}
for i in range(3, 46):
mydict[i] = subsetsums(i)
print(mydict)

python itertools permutations with tied values

I want to find efficiently permutations of a vector which has tied values.
E.g., if perm_vector = [0,0,1,2] I would want to obtain as output all combinations of [0,0,1,2], [0,0,2,1], [0,1,2,0] and so on, but I don't want to obtain [0,0,1,2] twice which is what the standard itertools.permutations(perm_vector) would give.
I tried the following but it works really SLOW when perm_vector grows in len:
vectors_list = []
for it in itertools.permutations(perm_vector):
vectors_list.append(list(it))
df_vectors_list = pd.DataFrame( vectors_list)
df_gb = df_vectors_list.groupby(list(df_vectors_list.columns))
vectors_list = pd.DataFrame(df_gb.groups.keys()).T
The question is of more general "speed-up" nature, actually. The main time is spent on creating the permutations of long vectors - even without the duplicity, creation of permutations of a vector of 12 unique values takes a "infinity". Is there a possibility to call the itertools iteratively without accessing the entire permutations data but working on bunches of it?
Try this if perm_vector is small:
import itertools as iter
{x for x in iter.permutations(perm_vector)}
This should give you unique values, because now it becomes a set, which by default delete duplications.
If perm_vector is large, you might want to try backtracking:
def permu(L, left, right, cache):
for i in range(left, right):
L[left], L[i] = L[i], L[left]
L_tuple = tuple(L)
if L_tuple not in cache:
permu(L, left + 1, right, cache)
L[left], L[i] = L[i], L[left]
cache[L_tuple] = 0
cache = {}
permu(perm_vector, 0, len(perm_vector), cache)
cache.keys()
How about this:
from collections import Counter
def starter(l):
cnt = Counter(l)
res = [None] * len(l)
return worker(cnt, res, len(l) - 1)
def worker(cnt, res, n):
if n < 0:
yield tuple(res)
else:
for k in cnt.keys():
if cnt[k] != 0:
cnt[k] = cnt[k] - 1
res[n] = k
for r in worker(cnt, res, n - 1):
yield r
cnt[k] = cnt[k] + 1

Is there a way to check if a list is a sublist of another list? [duplicate]

I want to write a function that determines if a sublist exists in a larger list.
list1 = [1,0,1,1,1,0,0]
list2 = [1,0,1,0,1,0,1]
#Should return true
sublistExists(list1, [1,1,1])
#Should return false
sublistExists(list2, [1,1,1])
Is there a Python function that can do this?
Let's get a bit functional, shall we? :)
def contains_sublist(lst, sublst):
n = len(sublst)
return any((sublst == lst[i:i+n]) for i in xrange(len(lst)-n+1))
Note that any() will stop on first match of sublst within lst - or fail if there is no match, after O(m*n) ops
If you are sure that your inputs will only contain the single digits 0 and 1 then you can convert to strings:
def sublistExists(list1, list2):
return ''.join(map(str, list2)) in ''.join(map(str, list1))
This creates two strings so it is not the most efficient solution but since it takes advantage of the optimized string searching algorithm in Python it's probably good enough for most purposes.
If efficiency is very important you can look at the Boyer-Moore string searching algorithm, adapted to work on lists.
A naive search has O(n*m) worst case but can be suitable if you cannot use the converting to string trick and you don't need to worry about performance.
No function that I know of
def sublistExists(list, sublist):
for i in range(len(list)-len(sublist)+1):
if sublist == list[i:i+len(sublist)]:
return True #return position (i) if you wish
return False #or -1
As Mark noted, this is not the most efficient search (it's O(n*m)). This problem can be approached in much the same way as string searching.
My favourite simple solution is following (however, its brutal-force, so i dont recommend it on huge data):
>>> l1 = ['z','a','b','c']
>>> l2 = ['a','b']
>>>any(l1[i:i+len(l2)] == l2 for i in range(len(l1)))
True
This code above actually creates all possible slices of l1 with length of l2, and sequentially compares them with l2.
Detailed explanation
Read this explanation only if you dont understand how it works (and you want to know it), otherwise there is no need to read it
Firstly, this is how you can iterate over indexes of l1 items:
>>> [i for i in range(len(l1))]
[0, 1, 2, 3]
So, because i is representing index of item in l1, you can use it to show that actuall item, instead of index number:
>>> [l1[i] for i in range(len(l1))]
['z', 'a', 'b', 'c']
Then create slices (something like subselection of items from list) from l1 with length of2:
>>> [l1[i:i+len(l2)] for i in range(len(l1))]
[['z', 'a'], ['a', 'b'], ['b', 'c'], ['c']] #last one is shorter, because there is no next item.
Now you can compare each slice with l2 and you see that second one matched:
>>> [l1[i:i+len(l2)] == l2 for i in range(len(l1))]
[False, True, False, False] #notice that the second one is that matching one
Finally, with function named any, you can check if at least one of booleans is True:
>>> any(l1[i:i+len(l2)] == l2 for i in range(len(l1)))
True
The efficient way to do this is to use the Boyer-Moore algorithm, as Mark Byers suggests. I have done it already here: Boyer-Moore search of a list for a sub-list in Python, but will paste the code here. It's based on the Wikipedia article.
The search() function returns the index of the sub-list being searched for, or -1 on failure.
def search(haystack, needle):
"""
Search list `haystack` for sublist `needle`.
"""
if len(needle) == 0:
return 0
char_table = make_char_table(needle)
offset_table = make_offset_table(needle)
i = len(needle) - 1
while i < len(haystack):
j = len(needle) - 1
while needle[j] == haystack[i]:
if j == 0:
return i
i -= 1
j -= 1
i += max(offset_table[len(needle) - 1 - j], char_table.get(haystack[i]));
return -1
def make_char_table(needle):
"""
Makes the jump table based on the mismatched character information.
"""
table = {}
for i in range(len(needle) - 1):
table[needle[i]] = len(needle) - 1 - i
return table
def make_offset_table(needle):
"""
Makes the jump table based on the scan offset in which mismatch occurs.
"""
table = []
last_prefix_position = len(needle)
for i in reversed(range(len(needle))):
if is_prefix(needle, i + 1):
last_prefix_position = i + 1
table.append(last_prefix_position - i + len(needle) - 1)
for i in range(len(needle) - 1):
slen = suffix_length(needle, i)
table[slen] = len(needle) - 1 - i + slen
return table
def is_prefix(needle, p):
"""
Is needle[p:end] a prefix of needle?
"""
j = 0
for i in range(p, len(needle)):
if needle[i] != needle[j]:
return 0
j += 1
return 1
def suffix_length(needle, p):
"""
Returns the maximum length of the substring ending at p that is a suffix.
"""
length = 0;
j = len(needle) - 1
for i in reversed(range(p + 1)):
if needle[i] == needle[j]:
length += 1
else:
break
j -= 1
return length
Here is the example from the question:
def main():
list1 = [1,0,1,1,1,0,0]
list2 = [1,0,1,0,1,0,1]
index = search(list1, [1, 1, 1])
print(index)
index = search(list2, [1, 1, 1])
print(index)
if __name__ == '__main__':
main()
Output:
2
-1
Here is a way that will work for simple lists that is slightly less fragile than Mark's
def sublistExists(haystack, needle):
def munge(s):
return ", "+format(str(s)[1:-1])+","
return munge(needle) in munge(haystack)
def sublistExists(x, y):
occ = [i for i, a in enumerate(x) if a == y[0]]
for b in occ:
if x[b:b+len(y)] == y:
print 'YES-- SUBLIST at : ', b
return True
if len(occ)-1 == occ.index(b):
print 'NO SUBLIST'
return False
list1 = [1,0,1,1,1,0,0]
list2 = [1,0,1,0,1,0,1]
#should return True
sublistExists(list1, [1,1,1])
#Should return False
sublistExists(list2, [1,1,1])
Might as well throw in a recursive version of #NasBanov's solution
def foo(sub, lst):
'''Checks if sub is in lst.
Expects both arguments to be lists
'''
if len(lst) < len(sub):
return False
return sub == lst[:len(sub)] or foo(sub, lst[1:])
def sublist(l1,l2):
if len(l1) < len(l2):
for i in range(0, len(l1)):
for j in range(0, len(l2)):
if l1[i]==l2[j] and j==i+1:
pass
return True
else:
return False
I know this might not be quite relevant to the original question but it might be very elegant 1 line solution to someone else if the sequence of items in both lists doesn't matter. The result below will show True if List1 elements are in List2 (regardless of order). If the order matters then don't use this solution.
List1 = [10, 20, 30]
List2 = [10, 20, 30, 40]
result = set(List1).intersection(set(List2)) == set(List1)
print(result)
Output
True
if iam understanding this correctly, you have a larger list, like :
list_A= ['john', 'jeff', 'dave', 'shane', 'tim']
then there are other lists
list_B= ['sean', 'bill', 'james']
list_C= ['cole', 'wayne', 'jake', 'moose']
and then i append the lists B and C to list A
list_A.append(list_B)
list_A.append(list_C)
so when i print list_A
print (list_A)
i get the following output
['john', 'jeff', 'dave', 'shane', 'tim', ['sean', 'bill', 'james'], ['cole', 'wayne', 'jake', 'moose']]
now that i want to check if the sublist exists:
for value in list_A:
value= type(value)
value= str(value).strip('<>').split()[1]
if (value == "'list'"):
print "True"
else:
print "False"
this will give you 'True' if you have any sublist inside the larger list.

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)

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