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std::uniform_int_distribution class in C++
• Last Updated : 31 May, 2021

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:

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:

1. 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   // for uniform_int_distribution function#include   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.

1. a(): Returns the lower parameter of range. This specifies the lower bound of the range of values potentially returned by its member operator().

2. b(): Returns the higher parameter of range. This specifies the upper bound of the range of values potentially returned by its member operator().

3. max(): This function return the possible smallest upper bound of output possible from the operator() function.

4. min(): This function return the possible highest lower bound of output possible from the operator() function.

5. 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   // for uniform_int_distribution function#include   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

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