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# Creating permutations by randomly selecting values from a list

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Last Modified: 2020-08-05
Is it possible in python to create x number of 5 value permutations from a list of 100 values ?

using each number only once (until all the numbers were exhausted or until there were less than 5 ? )

so if the list was 1..100
to create
35 87 12 94 54
34 19 76 50 32

More detail to this question

ok so we have the values 1 to 20
the question is, how to randomly choose values in groups of 5 until there are no values left and choosing each number only once.
so, choosing
3 18 7 12 15 would eliminate those values from being chosen again, leaving 15 numbers to choose from
1 2   4 5 6   8 9 10 11    13 14    16 17    19 20
Then to make the next permutation, or group of numbers in the same random way leaving only 10 numbers to choose from and so on until none are left

Is this possible, and if so how would I do it ?

my apology also to pepr , I was not clear in the original question
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Senior Developer
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Commented:
I'm not sure whether I should answer this.. cause this was and is one of my test questions in coachings and seminars..

Can you tell us about the problem and the reason for the question?
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Commented:
There is the module itertools and the function permutations inside. It is part of the standard distribution of Python; so, there is no need to install any other package.

The following code just prints the generated lists from the list [1, ..., 100] generated by the range(1, 101) function. However, you can use whatever input list. You probably want to break the program using Ctrl+C as it produces a lot of permutations:
import itertools

##print(list(range(1, 101))) # you can uncomment to see the generated list

for lst in itertools.permutations(range(1, 101), 5):
print(lst)


Anyway, the generator is rather systematic, the results are not randomized. The problem with randomized results is that you need to remember the values that were already generated. So, you should add what exactly is the purpose.

For random samples (here without checking whether the sample does not repeat), you can use the standard random module and its sample generator, and wrap it to, say, tuple. Like this:
import random

pool = list(range(1, 101))
#print(pool)

for n in range(5):
print(tuple(random.sample(pool, 5)))

You get the results like this
(16, 18, 69, 70, 83)
(36, 29, 22, 42, 27)
(66, 35, 93, 25, 84)
(5, 20, 70, 80, 48)
(74, 49, 63, 28, 60)


If you need only "few" (really meaning not extremely many), you can remember the already generated tuples in a set. Here the pool was restricted to few to show how it behaves:

import random

pool = list(range(1, 6))
#print(pool)

observed = set()
for n in range(100):
result = tuple(random.sample(pool, 5))
while result in observed:
print(f'\t{result} again...')
result = tuple(random.sample(pool, 5))
observed.add(result)
print(result)

You should observe something like...

e:\__Python\EuropaMacDonald\ee29190546>py c.py
(4, 2, 3, 1, 5)
(4, 5, 3, 2, 1)
(2, 4, 3, 1, 5)
(5, 2, 4, 1, 3)
(1, 4, 3, 5, 2)
(3, 5, 2, 1, 4)
(2, 3, 4, 5, 1)
(4, 1, 2, 5, 3)
(5, 2, 1, 3, 4)
(1, 2, 3, 4, 5)
(4, 5, 3, 1, 2)
(4, 1, 2, 5, 3) again...
(3, 4, 1, 2, 5)
(2, 4, 3, 5, 1)
(4, 5, 1, 3, 2)
(1, 3, 4, 2, 5)
(5, 1, 4, 2, 3)
(1, 2, 4, 5, 3)
(2, 1, 5, 4, 3)
(4, 1, 3, 5, 2)
(1, 2, 3, 5, 4)
(5, 3, 4, 1, 2)
(1, 5, 4, 3, 2)
(4, 1, 2, 3, 5)
(2, 4, 5, 3, 1)
(1, 5, 2, 4, 3)
(4, 2, 1, 5, 3)
(4, 2, 5, 3, 1)
(3, 2, 5, 4, 1)
(4, 2, 5, 3, 1) again...
(4, 1, 3, 2, 5)
(3, 4, 5, 1, 2)
(4, 2, 5, 1, 3)
(1, 5, 4, 2, 3)
(5, 2, 3, 4, 1)
(4, 3, 1, 5, 2)
(1, 3, 5, 2, 4)
(2, 4, 5, 3, 1) again...
(2, 4, 1, 3, 5)
(2, 3, 1, 5, 4)
(5, 4, 1, 2, 3)
(3, 4, 5, 2, 1)
(3, 2, 5, 4, 1) again...
(4, 5, 2, 1, 3)
(2, 1, 3, 4, 5)
(5, 1, 2, 4, 3)
(1, 4, 2, 5, 3)
(5, 2, 4, 3, 1)
(3, 1, 5, 4, 2)
(1, 3, 5, 2, 4) again...
(4, 3, 2, 5, 1)
(5, 1, 4, 3, 2)
(4, 3, 5, 1, 2)
(1, 3, 2, 5, 4)
(4, 2, 1, 5, 3) again...
(3, 2, 5, 1, 4)
(2, 3, 5, 1, 4)
(1, 4, 2, 5, 3) again...
(2, 5, 3, 4, 1)
(1, 3, 5, 2, 4) again...
(4, 2, 5, 3, 1) again...
(2, 3, 1, 4, 5)
(5, 4, 3, 1, 2)
(5, 3, 4, 2, 1)
(4, 1, 3, 5, 2) again...
(2, 3, 1, 4, 5) again...
(4, 1, 3, 2, 5) again...
(1, 2, 5, 3, 4)
(5, 2, 1, 3, 4) again...
(1, 4, 2, 5, 3) again...
(5, 2, 3, 4, 1) again...
(4, 2, 1, 5, 3) again...
(3, 1, 5, 2, 4)
(2, 3, 5, 1, 4) again...
(1, 5, 4, 3, 2) again...
(1, 3, 4, 5, 2)
(1, 2, 4, 5, 3) again...
(4, 1, 3, 2, 5) again...
(3, 1, 5, 2, 4) again...
(4, 1, 5, 3, 2)
(3, 4, 5, 1, 2) again...
(1, 2, 3, 5, 4) again...
(4, 1, 3, 2, 5) again...
(2, 1, 4, 3, 5)
(2, 1, 5, 4, 3) again...
(4, 3, 2, 5, 1) again...
(3, 5, 2, 1, 4) again...
(2, 5, 4, 3, 1)
etc.

Senior Developer
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Commented:
Let's start by clarifying your needs:

Do you need combinations (k-combinations over S), where order does not matter. E.g. 2 from 3 {a,b,c} => {a,b}, {a,c}, {b,c}.

Or permutations (precisely k-permutation of n), where order matters. E.g. 2 frm 3 {a,b,c} => (a,b), (a,c), (b,a), (b,c), (c,a), (c b).

The problem is 5 of 100 are 100! / (100-5)! possible permutations (~9 billion (10^9)). Calculating them and drawing a random one is pretty inefficient. So I'm not sure whether this is the correct approach.
Chief slayer of dragons

Commented:
Ste5an I apologise, I see the error in how I have asked that question.
(I have also edited the original question for future clarity)

ok so we have the values 1 to 20
the question is, how to randomly choose values in groups of 5 until there are no values left and choosing each number only once.
so, choosing
3 18 7 12 15 would eliminate those values from being chosen again, leaving 15 numbers to choose from
1 2   4 5 6   8 9 10 11    13 14    16 17    19 20
Then to make the next permutation, or group of numbers in the same random way leaving only 10 numbers to choose from and so on until none are left

Is this possible, and if so how would I do it ?
Research Engineer - Electrical
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Commented:
This one is on us!
(Get your first solution completely free - no credit card required)
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Commented:
OK, to add... Getting the sequence of the five elements could be done like that:
import random

lst = list(range(1, 101))   # the odered pool of values
random.shuffle(lst)         # shuffled randomly

while len(lst) > 0:         # while there is anything to get
print(lst[0:5])         # get the first five of them
del lst[0:5]            # remove the first five of them


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