Generate unique random integers

Generating unique random integers is an important task in various domains. Examples include data sampling, simulations, and even lottery picks. Products have come a long way from when one had to write a fair amount of code to do the needful. Below are two solutions, one in MS Excel and the other in Python.

Suppose we want 6 random numbers from the range 1 to 54. Here the population is the list of 54 integers between 1 and 54 and the sample size is 6.

The intuitive way to do pick random numbers is to repeatedly generate numbers between 1 and 54 and check that it is not already selected . However, this gets extremely wasteful as the sample size approaches the population size. Imagine the extreme case where we want to pick 54 random numbers between 1 and 54. There's nothing random about the last pick. So, repeatedly generating a number between 1 and 54 and checking if it is already selected is...well, wasteful.

It's easier to sort the list of 54 numbers in random order and pick the top 6.

In Excel, the below function does the needful:

=LAMBDA(_Min,_Max,_NbrVals,
? ? LET(_Range,_Max-_Min+1,
? ? ? ? INDEX(SORTBY(SEQUENCE(_Range,,_Min),RANDARRAY(_Range)),SEQUENCE(_NbrVals))
? ? ? ? ))        

How does it work?

1. The SEQUENCE(_Range,,_Min) generates the integers between _Min and _Max. That would be 1 and 54 in the above example.
2. The RANDARRAY(_Range) generates an array of random numbers of the same size as above - 54 elements in the above example.
3. The SORTBY sorts the numbers from 1 in the order of the random numbers. This essentially randomizes the list of integers.
4. The SEQUENCE(_NbrVals) generates the numbers 1,2,...,_NbrVals - this would be 1,2,..,6 in the above example.
5. The INDEX() function picks the first _NbrVals values (6 in the above example - see 4 above) from the *randomized* list of integers from SORTBY (from 3 above).

Of course, even better would be if we had a function that did the needful for us. And, in Python, random.sample does just that.

import random
print(random.sample(range(1, 54+1),k=6))

[47, 20, 54, 38, 41, 12]        

For more on this function see random — Generate pseudo-random numbers — Python 3.11.1 documentation

Do you have occasion to generate unique random integers? How do you do so?

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