Weighted random numbers

What I do when I need to weight numbers is using a random number for the weight.

For example: I need that generate random numbers from 1 to 3 with the following weights:

• 10% of a random number could be 1
• 30% of a random number could be 2
• 60% of a random number could be 3

Then I use:

weight = rand() % 10;

switch( weight ) {

    case 0:
        randomNumber = 1;
        break;
    case 1:
    case 2:
    case 3:
        randomNumber = 2;
        break;
    case 4:
    case 5:
    case 6:
    case 7:
    case 8:
    case 9:
        randomNumber = 3;
        break;
}

With this, randomly it has 10% of the probabilities to be 1, 30% to be 2 and 60% to be 3.

You can play with it as your needs.

Hope I could help you, Good Luck!

This is my understanding of a "weighted random", I've been using this recently. (Code is in Python but can be implemented in other langs)

Let's say you want to pick a random person and they don't have equal chances of being selected You can give each person a "weight" or "chance" value:

choices = [("Ade", 60), ("Tope", 50), ("Maryamu", 30)]

You use their weights to calculate a score for each then find the choice with the highest score

highest = [None, 0]
for p in choices:
    score = math.floor(random.random() * p[1])
    if score > highest[1]:
        highest[0] = p
        highest[1] = score

print(highest)

For Ade the highest score they can get is 60, Tope 50 and so on, meaning that Ade has a higher chance of generating the largest score than the rest.

You can use any range of weights, the greater the difference the more skewed the distribution. E.g if Ade had a weight of 1000 they will almost always be chosen.

Test

votes = [{"name": "Ade", "votes": 0}, {"name": "Tope", "votes": 0}, {"name": "Maryamu", "votes": 0]
for v in range(100):
        
        highest = [None, 0]
        for p in choices:
            score = math.floor(random.random() * p[1])
            
            if score > highest[1]:
                highest[0] = p
                highest[1] = score

        candidate = choices(index(highest[0])) # get index of person
        votes[candidate]["count"] += 1 # increase vote count
print(votes)

// votes printed at the end. your results might be different
[{"name": "Ade", "votes": 45}, {"name": "Tope", "votes": 30}, {"name": "Maryamu", "votes": 25}]

Issues

It looks like the more the voters, the more predictable the results. Welp

Hope this gives someone an idea...

I have just implemented the given solution by "will"

#include <iostream>
#include <map>

using namespace std;


template < class T >
class WeightedRandomSample
{
public:
    void SetWeigthMap( map< T , unsigned int >& WeightMap )
    {
        m_pMap = &WeightMap;
    }
    
    T GetRandomSample()
    {
        unsigned int sum_of_weight = GetSumOfWeights();
        unsigned int rnd = (rand() % sum_of_weight);
        map<T , unsigned int>& w_map = *m_pMap;
        typename map<T , unsigned int>::iterator it;
        for(it = w_map.begin() ; it != w_map.end() ; ++it )
        {
            unsigned int w = it->second;
            if(rnd < w)
                return (it->first);
            rnd -= w;
        }
        //assert(!"should never get here");
        T* t = NULL;
        return *(t);
    }
    
    unsigned int GetSumOfWeights()
    {
        if(m_pMap == NULL)
            return 0;
        unsigned int sum = 0;
        map<T , unsigned int>& w_map = *m_pMap;
        typename map<T , unsigned int>::iterator it;
        
        for(it = w_map.begin() ; it != w_map.end() ; ++it )
        {
            sum += it->second;
        }
        return sum;
    }

    
protected:
    map< T , unsigned int>* m_pMap = NULL;
    
};

typedef pair<int , int> PAIR_INT_INT;
typedef map<PAIR_INT_INT ,unsigned int> mul_table_weighted_map;

int main()
{
    
    mul_table_weighted_map m;
    m[PAIR_INT_INT(2,3)] = 10;
    m[PAIR_INT_INT(4,5)] = 20;
    m[PAIR_INT_INT(2,5)] = 10;
    
    WeightedRandomSample<PAIR_INT_INT> WRS;
    WRS.SetWeigthMap(m);
    unsigned int sum_of_weight = WRS.GetSumOfWeights();
    cout <<"Sum of weights : " << sum_of_weight << endl;
    
    unsigned int number_of_test = 10000;
    cout << "testing " << number_of_test << " ..." << endl;
    map<PAIR_INT_INT , unsigned int> check_map;
    for(int i = 0 ; i < number_of_test ; i++)
    {
        PAIR_INT_INT res = WRS.GetRandomSample();
        check_map[res]++;
        //cout << i+1 << ": random = " << res.first << " * " << res.second << endl;
    }
    cout << "results: " << endl;
    
    for(auto t : check_map)
    {
        PAIR_INT_INT p = t.first;
        unsigned int expected = (number_of_test * m[p]) / sum_of_weight;
        cout << " pair " << p.first << " * " << p.second 
            << ", counted = " << t.second
            << ", expected = " << expected
            << endl;
    }

    return 0;
}