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Random numbers

Random numbers. Random  completely unpredictable. No way to determine in advance what value will be chosen from a set of equally probable elements. Impossible with any program! However we can generate seemingly random numbers, called pseudorandom numbers.

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Random numbers

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  1. Random numbers • Random  completely unpredictable.No way to determine in advance what value will be chosen from a set of equally probable elements. • Impossible with any program! • However we can generate seemingly random numbers, called pseudorandom numbers. • The functionrand()returns a non-negative number between 0 and RAND_MAX • It is defined in stdlib.h

  2. Random numbers /* * This program prints a list of 10 random * integers between 0 and RAND_MAX */ #include<iostream> int main () { for (int i=0; i<10; i++) std::cout << rand() << std::endl; return 0; }

  3. Random numbers • The very first call to rand() uses an initial value to generate a pseudorandom number. • That value is called the seed. • Each subsequent call to rand() uses the result of the previous call as the starting value. s rand() 1804289383 1804289383 rand() 846930886 846930886 rand() 1681692777

  4. Random numbers • Starting always with the same seed will give the same sequence of numbers. • In order to get a different sequence every time the program is run, we must make sure to set a different seed every time. • The only thing that changes between executions is the time  use the current time as the seed.

  5. Random numbers • Set the seed for rand() with the function: • To set the current time as the seed, use the time() function: • Libraries needed:#include<cstdlib> /* for rand(), srand() */#include<ctime> /* for time() */ void srand(int seed) void srand((int) time(NULL))

  6. Random numbers • Example: int main () { srand((int)time(NULL)); for (int i=0; i<10; i++) { cout << "You rolled a " << rand()%6+1 << endl; } return 0; } CAREFUL! Only use srand() once and never place it in a loop. srand() sets the seed to the current second so if it is called repeatedly within the same second (e.g. due to a loop), it will keep resetting the seed to the same value.

  7. Random numbers • When should you not set a variable seed? When you develop your project, you may want to be able to get the same sequence of numbers for debugging purposes.

  8. Random numbers • What if we want a specific range? • Example: simulate dice rolling • we need a random integer between 1 and 6 • answer: use modulus operator • rand() % 6;generates a random integer between 0 and 5 • rand() % 6 + 1; generates a random integer between 1 and 6 • To generate a random integer between low and high: low + rand() % (high - low + 1)

  9. Random numbers • What if we want a random floating point number within some range? • Step 1: map rand() to the 0 1 range rand() / RAND_MAX is between 0 and 1rand() / (RAND_MAX+1) is between 0 and 1, not including 1 • Step 2: scale the result to desired range similarly to how we did it for integers. • To generate a floating point number between low and high: low + ( rand() / RAND_MAX ) % (high - low)

  10. Random numbers • Example: Simulating a die roll: • Example: Simulating a coin toss: int roll; roll = rand()%6; cout << "You rolled a " << roll << ". Roll again? (y/n)"; int toss; if (rand()%2 == 0) cout << "Heads!"; else cout << "Tails!";

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