Python random list

Question

I am new to Python and have some problems creating random lists.

I am using random.sample(range(x, x), y) .

I want to get 4 lists with unique numbers starting from 1-4, so I used this

 a = random.sample(range(1, 5), 4) b = random.sample(range(1, 5), 4) c = random.sample(range(1, 5), 4) d = random.sample(range(1, 5), 4) 

So, I get, for example,

 a = 1, 3, 2, 4 b = 1, 4, 3, 2 c = 2, 3, 1, 4 d = 4, 2, 3, 1 

How can I make a column unique?

Answer 1

Lack of a clear mathematical theory, I don't trust anyone other than a multi-hit approach. In particular, approaches to the reverse approach may introduce a slight bias:

 from random import shuffle def isLatin(square): #assumes that square is an nxn list #where each row is a permutation of 1..n n = len(square[0]) return all(len(set(col)) == n for col in zip(*square)) def randSquare(n): row = [i for i in range(1,1+n)] square = [] for i in range(n): shuffle(row) square.append(row[:]) return square def randLatin(n): #uses a hit and miss approach while True: square = randSquare(n) if isLatin(square): return square 

Typical Output:

 >>> s = randLatin(4) >>> for r in s: print(r) [4, 1, 3, 2] [2, 3, 4, 1] [1, 4, 2, 3] [3, 2, 1, 4] 

Answer 2

Totally random then:

 def gen_matrix(): first_row = random.sample(range(1, 5), 4) tmp = first_row + first_row rows = [] for i in range(4): rows.append(tmp[i:i+4]) return random.sample(rows, 4) 

Answer 3

Probably the easiest way is to create a valid matrix, and then shuffle the rows and then shuffle the columns:

 import random def random_square(U): U = list(U) rows = [U[i:] + U[:i] for i in range(len(U))] random.shuffle(rows) rows_t = [list(i) for i in zip(*rows)] random.shuffle(rows_t) return rows_t 

Using:

 >>> random_square(range(1, 1+4)) [[2, 3, 4, 1], [4, 1, 2, 3], [3, 4, 1, 2], [1, 2, 3, 4]] 

This should be able to create any valid matrix with equal probability. After some reading, it seems like it still has a bias, although I still don't fully understand why for now.

Answer 4

Create a list of all elements, as well as filling in the line, delete the used element.

 import random def fill_line(length): my_list = list(range(length)) to_return = [] for i in range(length): x = random.choice(my_list) to_return.append(x) my_list.remove(x) return to_return x = [fill_line(4) for i in range(4)] print(x) 

Answer 5

I would build a random Latin square on 1) start with one random permutation, 2) fill the lines with turns 3) shuffle the lines 4) transpose the square 5) shuffle the lines again:

 from collections import deque from random import shuffle def random_latin_square(elements): elements = list(elements) shuffle(elements) square = [] for i in range(len(elements)): square.append(list(elements)) elements = elements[1:] + [elements[0]] shuffle(square) square[:] = zip(*square) shuffle(square) return square if __name__ == '__main__': from pprint import pprint square = random_latin_square('ABCD') pprint(square)