std::mt19937 Class in C++

std::mt19937(since C++11) class is a very efficient pseudo-random number generator and is defined in a random header file. It produces 32-bit pseudo-random numbers using the well-known and popular algorithm named Mersenne twister algorithm. std::mt19937 class is basically a type of std::mersenne_twister_engine class. 

typedef mersenne_twister_engine<uint_fast32_t,
 32,624,397,31,0x9908b0df,11,0xffffffff,7,0x9d2c5680,15,0xefc60000,18,1812433253>
 mt19937;

Syntax :

mt19937 mt1(seed_value);

Here mt1 is an instance of the mt19937 class and it takes a seed value to generate an entire sequence.

Significance Of The Name mt19937 

mt19937 stands for mersenne twister with a long period of 2¹⁹⁹³⁷ - 1 which means mt19937 produces a sequence of 32-bit integers that only repeats itself after 2¹⁹⁹³⁷ - 1 number have been generated.

Similarities Between mt19937 And rand() & srand():

The std::mt19937 does two things -

• When an std::mt19937 object is instantiated, it takes an argument which is used to generate seed value(like srand()).
• By using operator(), it generates a random number (like rand()).

Below is the example to demonstrate the similarities:

// C++ program for demonstrating 
// similaritites
#include <ctime>
#include <iostream>
#include <random>
using namespace std;

int main()
{
  // Initializing the sequence 
  // with a seed value
  // similar to srand()
  mt19937 mt(time(nullptr)); 

  // Printing a random number
  // similar to rand()
  cout << mt() << '\n'; 
  return 0;
}

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Being a type of std::mersenne_twister_engine class it has the same member functions which mersenne_twister_engine does. Here is the list of some important member functions -

1. (constructor): constructs the mt19937 object. It takes either a seed value of result type or a seed sequence object(Similar to srand() function).

Example :

// C++ program to implement 
// the above concept

// This header file is 
// for time
#include <ctime> 
#include <iostream>
#include <random>
using namespace std;

int main()
{
  // Using the constructor to
  // initialize with a seed value
  mt19937 mt(time(nullptr)); 

  // Operator() is used to 
  // generate random numbers
  cout << mt() << '\n';
  return 0;
}

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2. min(): returns the minimum value operator() can return (which is zero).

Example:

// C++ program for the 
// min()
#include <ctime>
#include <iostream>
#include <random>
using namespace std;

// Driver code
int main()
{
  // Initializing mt19937
  // object
  mt19937 mt(time(nullptr));

  // Prints the minimum value 
  // which is 0
  cout << "the minimum integer it can generate is " << 
           mt.min() << endl; 
  return 0;
}

the minimum integer it can generate is 0

3. max(): returns maximum value operator() can return ( which is  2³² - 1 = 4294967295 )

Example :

// C++ program to demonstrate 
// max()
#include <ctime>
#include <iostream>
#include <random>
using namespace std;

// Driver code
int main()
{
  // Initializing mt19937
  // object
  mt19937 mt(time(nullptr)); 
  
  // Prints the maximum value
  // which is 4294967295
  cout << "mt19937 can generate random numbers upto " << 
           mt.max() << endl; 
  return 0;
}

mt19937 can generate random numbers upto 4294967295

4. seed(): reinitializes the seed value of the object either by taking a seed value of result type or by taking a seed sequence object.

Example :

// C++ program to demonstrate
// seed()
#include <iostream>
#include <random>
using namespace std;

// Driver code
int main()
{
  // Defining the 
  // mt19937 object
  mt19937 mt; 
  
  // Initializing a random 
  // sequence with a seed value
  mt.seed(45218965); 
  
  cout << "some random numbers generated by mt19937 are:" << 
           endl;
  
  for (int i = 5; i > 0; i--) 
  {
    cout << mt() << ' ';
  }
  return 0;
}

some random numbers generated by mt19937 are:
3334444225 240363925 3350157104 146869560 639267854

5. operator(): it generates pseudo-random integers.(similar to rand() function).

Example:

// C++ program to demonstrate
// operator()
#include <ctime>
#include <iostream>
#include <random>
using namespace std;

// Driver code
int main()
{
  // Initializing mt19937
  // object
  mt19937 mt(time(nullptr));
  
  for (int i = 0; i < 5; i++) 
  {
    // operator() is used to
    // generate random numbers
    cout << mt() << ' '; 
  }
  return 0;
}

3529725061 3019704141 2006641117 725527349 3631905871

There are also non-member functions overloaded to work with std::mt19937 object. These are - 

• operator<<() - This is overloaded so that we can directly print the value generated by the mt19937 object to the output stream.
• operator>>() - it is used to extract seed value from input.

Here is a simple example to generate a pseudo-random number by taking a seed value from the user - 

Using operator<<() and operator>>() :

Example :

// C++ program to demonstrate 
// operator>>() and <<operator()
#include <ctime>
#include <iostream>
#include <random>
using namespace std;

// Driver code
int main()
{
  mt19937 mt;
  cout << "enter a integer to begin" << 
           endl;
  
  // operator>>() is used to get 
  // a seed value from the user
  cin >> mt; 
  
  // <<operator() is used to print 
  // the random integer
  cout << "a random number " << 
           mt() << " is generated";
  
  return 0;
}

enter a integer to begin
a random number 3499211612 is generated

Why Use mt19937 Instead Of rand() ?

Although the rand() function can be used in a small range, it is inefficient for generating real-world like random numbers. A careful person can observe the repetitions of the random numbers generated by rand() which is very risky. Whereas std::mt19937 has the following advantages - 

1. It has a very long period compared to the rand(). It will take a longer time. If an implementation of the Mersenne twister could generate 1,000,000,000 (one billion) pseudo-random numbers every second, a program that generated pseudo-random numbers would need to run about 1.3684 × 105,985 years to repeat the random sequence. So it is safe to assume that an observer will never guess the number.
2. Many random number generators can be initiated simultaneously with different seed values. Here is an example -

// C++ program to demonstrate
// above approach
#include <iostream>
#include <random>
using namespace std;

// Driver code
int main()
{
  mt19937 mt1(10000);
  mt19937 mt2(100000);

  cout << mt1() << endl;
  cout << mt2() << endl;
  return 0;
}

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