How Can Boost's Random Number Generator Be Used for Weighted Random Number Selection?

Weighted Random Number Generation

Choosing random numbers with specific probabilities is a common task in programming. Boost's random number generator provides a convenient way to select items with weighted probabilities.

Consider the scenario where you want to pick a random number between 1 and 3 with the following weights:

• 1: 90%
• 2: 56%
• 3: 4%

Algorithm

Boost does not have built-in functionality for weighted random number generation. However, there is a simple algorithm that can be applied:

1. Calculate the Total Weight: Sum the weights of all items.
2. Generate a Random Number: Choose a random number between 0 and the total weight.
3. Iterate Through Weights: Go through each item's weight, subtracting it from the random number until the number becomes less than the current item's weight.
4. Return Item: The item corresponding to the position where the random number became negative is the chosen item.

Code Example

In Boost, using the random_device and mt19937 random number generator:

std::mt19937 rng(std::random_device{}());
int total_weight = 90 + 56 + 4;
for (int i = 0; i < total_weight; i++) {
    int random_number = rng() % total_weight;
    int current_weight = 90;
    if (random_number < current_weight) {
        return 1;
    }
    current_weight += 56;
    if (random_number < current_weight) {
        return 2;
    }
    return 3; // Reached the end of the weights
}

Optimizations

If weights rarely change and random picks are frequent, an optimization can be applied by storing the cumulative weight sum in each item. This allows for a more efficient binary search approach.

Additionally, if the number of items is unknown but the weights are known, reservoir sampling can be adapted for weighted random number generation.

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