Probability of choosing two cities C++ - c++

Question

I'm making a program where I have a list of 34 cities and I am wanting to give each of these cities a probability of being chosen.
So I have:
vector<float> vec;
int s;
cin >> s;
srand(s);
for (int k=0; k < 34; k++)
{
float p1= (float)rand()/(float)((unsigned)RAND_MAX+1);
vec.push_back(p1);
}
So that gives each city a probability. The problem I am now having is I want to then do a random number generator that will choose two of these cities. So, for example city1 will have a 5%, city2 a 2%, city3, a 3%, etc. How can I randomly choose two of these cities based off the probabilities given?

Answer 1

I did this in genetic algorithm.
for your cities consider a line of 10 units.
now from 0-5 units on line are city1 6-7 for city2 and 8-9 for city3.
now choose a number at random from 0-9.
and found out in which cities range it comes in.

Answer 2

At first glance my solution will be :
Create a number equals to all city's probability
Create a random number, with max random number is equal to the previous number
Take the random number, and go throught your city vector and take the one who is corresponding.
Example :
City 1 : 5%
City 2 : 8%
City 3 : 2%
City 4 : 5%
City 5 : 12%
Create a number -> Number a = 32 (5+8+2+5+12)
Generate a number with : 1 <= number
Assume that the number is equal to 12
City 1 is choose if : 1 <= number <= 5 (So not)
City 2 is choose if : 6 <= number <= 13 (So yes)
City 2 is choose.
If you have any questions about that, you are welcome :)
Edit :
Well i will give you some more explaination.
Take this code :
for (int k=0; k < 10; k++)
{
float p1= (float)rand()/(float)((unsigned)RAND_MAX+1);
vec.push_back(p1);
}
Assume now that vec contain the following informations :
5
3
8
5
12
14
8
5
6
18
With each number correspond to the probability to choose a city.
5 -> 5% probability to choose (City1)
3 -> 3% probability to choose (City2)
8 -> 8% probability to choose (City3)
... etc
Now i will give you some code and i will explain it :
int nbReference = 0;
for (auto it = vec.begin() ; it != vec.end() ; ++it)
{
nbReference += *it;
}
nbReference = rand(nbReference);
int i = 0;
int cityProbability = 0;
for (auto it = vec.begin() ; it != vec.end() ; ++it)
{
cityProbability = *it;
if ((i + cityProbability) > nbReference)
{
return (i + 1);
}
i += cityProbability;
}
First i create a number equals to the addition of all city's probability
int nbReference = 0;
for (auto it = vec.begin() ; it != vec.end() ; ++it)
{
nbReference += *it;
}
Second, i generate a number that is respect the following range -> 0 < nbReference
Third, i create a loop that take all city one by one and quit when we got right city.
How does we know when a city is good?
Let's take an example!
With our previous probability
5 3 8 5 12 14 8 5 6 18
NbReference is equals to (5+3+8+5+12+14+8+5+6+18) so 84
To each city we are going to put a range equals to his probability plus all of previous city's probability. Let me show you :
5 -> Range 0 to 4 (0 to 4 = 5 ---> 5%)
3 -> Range 5 to 8 (5 to 8 = 3 ---> 3%)
8 -> Range 9 to 17
5 -> Range 18 to 22
... etc
If the number that we create here
nbReference = rand(nbReference);
Is in a city range, so that city is choosed.
Example : If the number is 16, city3 is choosed!
5 -> Range 0 to 4 Number is 16 so NOPE
3 -> Range 5 to 8 Number is 16 so NOPE
8 -> Range 9 to 17 Number is 16 so YES!
5 -> Range 18 to 22
... etc
Does is this helpfull? :)
Any questions? You are welcome

Answer 3

Maybe this code can help you (follows partially WhozCraig advice)
#include <iostream>
#include <random>
#include <algorithm>
int main(int argc, const char * argv[])
{
using namespace std::chrono;
system_clock::time_point tp = system_clock::now();
system_clock::duration dtn = tp.time_since_epoch();
std::default_random_engine generator(static_cast<int>(dtn.count()));
//Generate 34 cities
std::uniform_real_distribution<double> gen_distribution(0,1);
auto getProb = std::bind ( gen_distribution, generator );
std::vector<double> citiesProb;
double probSum(0.0);
double cityProb(0.0);
for (int k=0; k < 34; k++)
{
cityProb = getProb();
probSum += cityProb;
citiesProb.push_back(cityProb);
}
//Pick 7 cities
std::uniform_real_distribution<double> pick_distribution(0,probSum);
auto pickCity = std::bind ( pick_distribution, generator );
double chooseCity;
double probBasket;
for (int k=0; k < 7; ++k)
{
probBasket = 0.0;
chooseCity = pickCity();
for (int i = 0; i < citiesProb.size(); ++i)
{
if (chooseCity >= probBasket && chooseCity < probBasket + citiesProb[i])
{
std::cout << "City with index " << i << " picked" << std::endl;
}
probBasket += citiesProb[i];
}
}
return 0;
}
How it works:
city1 5%(0.05), city2 25%(0.25), city3 8%(0.08), city4 10%(0.1)
then
probSum = 0.05 + 0.25 + 0.08 + 0.1 = 0.48
then choose a number between 0 and 0.48 (named pickProb) and
if pickProb is between 0 and 0.05 pick city1 (prob = 0.05/0.48 = 10%)
if pickProb is between 0.05 and 0.30 pick city2 (prob = 0.25/0.48 = 52%)
if pickProb is between 0.30 and 0.38 pick city3 (prob = 0.08/0.48 = 16%)
if pickProb is between 0.38 and 0.48 pick city4 (prob = 0.1/0.48 = 20%)
if probSum = 1.0 then city1 is picked with probability 5%, city2 is picked with probability 25% and so on.