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I have the following problem. I must sample from a discrete distribution that is changing at each sort.

Let me explain, with a "vivid" description, I draw a color ball from a bag. The probability associated with each color is different (for this part I could choose an alias method, for example, the Vose's algorithm). BUT, after I choose a paint can, I paint the ball with this color and I put it back in the bag. So, If I use a classical alias method, I have to initialize prob and alias each time and it takes time. So, I wonder if an algorithm derived from the alias method exists for this kind of problem. As only two probabilities are changed at each iteration, I could imagine that the initialization part could be done in a very efficient way.

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