std::uniform_int_distribution class in C++
Last Updated :
11 Jul, 2025
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 probability.
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:
CPP
// 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-a];
}
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:
CPP
// 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.html.html
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