考虑负载/重量的概率资源选择

Question

说我有一张地图：

现在，我需要使用weighted random selection随机选择资源。但是，负载最高的资源应该具有最低的选择概率[例如，R2应该具有最低的概率]。那么，我现在正在做的计算概率是：

At first taking sum of values of the map say, totalWeight:

    totalWeight = 1+3+1+1 = 6 (for above example)

    newTotalWeight = (totalWeight - load of R1) + .... + (totalWeight - load of R4)    
                                   = totalWeight * (noOfElements-1)
                                   = 6 * (4-1) = 18
    Finally,
    p(selecting a resource R) = (totalWeight - current load of R) / newTotalWeight 

        So, for above example:
        p(selecting R1) = (6 - 1) / 18 = 5/18
        p(selecting R2) = (6 - 3) / 18 = 3/18
        p(selecting R3) = (6 - 1) / 18 = 5/18
        p(selecting R4) = (6 - 1) / 18 = 5/18

        p(R1, R2, R3, R4) = (5/18, 3/18, 5/18, 5/18)

这正是我想要的。现在，离散逆变换方法：

Generate U~U(0,1)
if U <= p(R1) selectedResource = R1; 
if p(R1) < U <= (p(R1) + p(R2)) selectedResource = R2; 
.......

可用于选择资源。

但我正在使用BOOST的{_ 3}}的discrete_distribution。

现在，每当资源负载发生变化时，我会使用上面的等式重新计算每个资源的概率，并重复整个过程。

我做得对吗还是有其他有效的方法吗？

Answer 1

你在找这个：

boost::mt19937 mt(42);
boost::random::discrete_distribution<int, Weight> dist({1,3,1,1});
auto genR = [&] { return static_cast<Resource>(dist(mt)); };

for (int i = 0; i<10; ++i)
    std::cout << genR() << "\n";

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#include <boost/random.hpp>
#include <boost/random/discrete_distribution.hpp>
#include <boost/random/piecewise_linear_distribution.hpp>

enum Resource { R1, R2, R3, R4, R5 };
using Weight = int;

std::ostream& operator<<(std::ostream& os, Resource r) {
    return os << "R" << std::to_string(1+r);
}

int main()
{
    using namespace std;

    boost::mt19937 mt(42);
    boost::random::discrete_distribution<int, Weight> dist({1,3,1,1});  
    auto genR = [&] { return static_cast<Resource>(dist(mt)); };

    for (int i = 0; i<10; ++i)
        std::cout << genR() << "\n";
}

打印例如

R2
R4
R1
R1
R1
R4
R3
R1
R1
R2