computer science Math Programming Python Statistics Utility Functions

Solution for the Random Selection Challenge

A few days ago, I wrote up two small Python Challenges. Several people have presented solutions for the first challenge, and I also posted my solution in the comments there.

However, the second challenge remained unsolved, and I will present a solution for it in this post.

Challenges Math Programming Python

Small Python Challenge No. 3 – Random Selection

This time I’ll give two related problems, both not too hard.

Lets warm up with the first:

You have a mapping between items and probabilities. You need to choose each item with its probability.

For example, consider the items [‘good’, ‘bad’, ‘ugly’], with probabilities of [0.5, 0.3, 0.2] accordingly. Your solution should choose good with probability 50%, bad with 30% and ugly with 20%.

I came to this challenge because just today I had to solve it, and it seems like a common problem. Hence, it makes sense to ask ‘what is the best way?’.

The second problem is slightly harder:

Assume a bell shaped function p(x) that you can ‘solve’. This means that given a value y, you can get all x such that p(x)=y. For example, sin(x)^2 in [0,pi] is such a function. Given a function such as Python’s random.random() that yields a uniform distribution of values in [0,1), write a function that yields a distribution proportional to p(x) in the appropriate interval.

For example, consider the function p(x) = e^(-x^2) in [-1,1]. Since p(0) = 1, and p(0.5)~0.779, the value 0 should be p(0)/p(0.5)~1.28 times more common than 0.5.

As usual, the preferred solutions are the elegant ones. Go!

note: please post your solutions in the comments, using [ python]…[ /python] tags (but without the spaces in the tags).