std::uniform_int_distribution class in C++

In Probability, Discrete Uniform Distribution Function refers to the distribution with constant probability for discrete values over a range and zero probability outside the range. The probability density function P(x) for uniform discrete distribution in interval [a, b] is constant for discrete values in the range [a, b] and zero otherwise. Mathematically the function is defined as:

$f(x) = \begin{cases} \frac{1}{b-a}, & a\leq x \leq b\\ 0, & \text{otherwise}\\ \end{cases}$

C++ have introduced uniform_int_distribution class in the random library whose member function give random integer numbers or discrete values from a given input range with uniform probabilty.

Public member functions in uniform_int_distribution class:

operator(): This function returns a random number from the given range of distribution. The probability for any number to be obtained from this function is same. Operator() function takes constant time for generation.

Example:

// C++ code to demonstrate the working of 
// operator() function 
  
#include <iostream> 
  
// for uniform_int_distribution function 
#include <random> 
  
using namespace std; 
  
int main() 
{ 
    // Here default_random_engine object 
    // is used as source of randomness 
    // We can give seed also to default_random_engine 
    // if psuedorandom numbers are required 
    default_random_engine generator; 
  
    int a = 0, b = 9; 
  
    // Initializing of uniform_int_distribution class 
    uniform_int_distribution<int> distribution(a, b); 
  
    // number of experiments 
    const int num_of_exp = 10000; 
  
    int n = b - a + 1; 
    int p[n] = {}; 
    for (int i = 0; i < num_of_exp; ++i) { 
  
        // using operator() function 
        // to give random values 
        int number = distribution(generator); 
        ++p[number]; 
    } 
  
    cout << "Expected probability: "
         << float(1) / float(n) << endl; 
  
    cout << "uniform_int_distribution ("
         << a << ", " << b << ")" << endl; 
  
    // Displaying the probability of each number 
    // after generating values 10000 times. 
    for (int i = 0; i < n; ++i) 
        cout << a + i << ": "
             << (float)p[i] / (float)(num_of_exp) 
             << endl; 
  
    return 0; 
} 

Output:

Expected probability: 0.1
uniform_int_distribution (0, 9)
0: 0.0993
1: 0.1007
2: 0.0998
3: 0.0958
4: 0.1001
5: 0.1049
6: 0.0989
7: 0.0963
8: 0.1026
9: 0.1016

We could observe from the output that the probability of each number obtained from the random number is much closer to calculated probability.

a(): Returns the lower parameter of range. This specifies the lower bound of the range of values potentially returned by its member operator().
b(): Returns the higher parameter of range. This specifies the upper bound of the range of values potentially returned by its member operator().
max(): This function return the possible smallest upper bound of output possible from the operator() function.
min(): This function return the possible highest lower bound of output possible from the operator() function.
reset(): This function resets the distribution such that subsequent distributions are not dependent on the previously generated numbers.

Example:

// C++ code to demonstrate the working of 
// a(), b(), min(), max(), reset() function 
  
#include <iostream> 
  
// for uniform_int_distribution function 
#include <random> 
  
using namespace std; 
  
int main() 
{ 
    int a = 10, b = 100; 
  
    // Initializing of uniform_int_distribution class 
    uniform_int_distribution<int> distribution(a, b); 
  
    // Using a() and b() 
    cout << "Lower Bound"
         << " " << distribution.a() << endl; 
    cout << "Upper Bound"
         << " " << distribution.b() << endl; 
  
    // Using min() and max() 
    cout << "Minimum possible output"
         << " " << distribution.min() << endl; 
    cout << "Maximum possible output"
         << " " << distribution.max() << endl; 
  
    // Using reset() 
    distribution.reset(); 
    return 0; 
} 

Output:

Lower Bound 10
Upper Bound 100
Minimum possible output 10
Maximum possible output 100

Reference: https://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution

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