Implementeu rand12() utilitzant rand6() en una línia
Donada una funció rand6() que retorna nombres aleatoris de l'1 al 6 amb la mateixa probabilitat, implementeu la funció d'una línia rand12() utilitzant rand6() que retorna nombres aleatoris de l'1 al 12 amb la mateixa probabilitat. La solució hauria de minimitzar el nombre de trucades al mètode rand6(). No es permet l'ús de cap altra funció de biblioteca i l'aritmètica de coma flotant.
La idea és utilitzar l'expressió rand6() + (rand6() % 2) * 6 . Retorna nombres aleatoris de l'1 al 12 amb la mateixa probabilitat. L'expressió equival a -
// if rand6() is even if (rand6() % 2) return 6 + rand6(); else // if rand6() is odd return rand6();També podem utilitzar qualsevol de les expressions següents que funcionin de manera similar:
- rand6() + !(rand6() % 2) * 6 o
- rand6() + (rand6() i 1) * 6 o
- rand6() + !(rand6() i 1) * 6
A continuació es mostra la implementació de l'enfocament anterior:
C++ #include // for rand and srand #include // for time #include using namespace std ; // Function that returns random numbers from 1 to 6 with // equal probability int rand6 () { // rand() will generate random numbers between 0 and // RAND_MAX with equal probability rand() % 6 returns // number from 0 to 5 with equal probability (rand() % // 6) + 1 returns number from 1 to 6 with equal // probability return ( rand () % 6 ) + 1 ; } // The function uses rand6() to return random numbers from 1 // to 12 with equal probability int rand12 () { return rand6 () + ( rand6 () % 2 ) * 6 ; } // Driver code to test above functions int main () { // Initialize random number generator srand ( time ( NULL )); int N = 12 ; int freq [ N + 1 ] = { 0 }; // call rand12() multiple times and store its results for ( int i = 0 ; i < N * 100000 ; i ++ ) freq [ rand12 ()] ++ ; // print frequency of numbers 1-12 for ( int i = 1 ; i <= N ; i ++ ) cout < < freq [ i ] < < ' ' ; return 0 ; }
Java import java.util.Random ; public class RandomNumbers { public static int rand6 () { Random random = new Random (); //nextInt(6) generates a random number from 0 to 5 return random . nextInt ( 6 ) + 1 ; } public static int rand12 () { return rand6 () + ( rand6 () % 2 ) * 6 ; } public static void main ( String [] args ) { int N = 12 ; int [] freq = new int [ N + 1 ] ; // Initialize random number generator Random random = new Random (); // Call rand12() multiple times and store its results for ( int i = 0 ; i < N * 100000 ; i ++ ) { freq [ rand12 () ]++ ; } // Print the frequency of numbers 1-12 for ( int i = 1 ; i <= N ; i ++ ) { System . out . print ( freq [ i ] + ' ' ); } } }
Python import random # Create a single instance of Random for better performance rand = random . Random () # Function that returns random numbers from 1 to 6 with equal probability def rand6 (): return rand . randint ( 1 6 ) # The function uses rand6() to return random numbers from 1 to 12 with equal probability def rand12 (): return rand6 () + ( rand6 () % 2 ) * 6 # Driver code to test above functions if __name__ == '__main__' : N = 12 iterations = 100000 freq = [ 0 ] * ( N + 1 ) # call rand12() multiple times and store its results for _ in range ( iterations ): freq [ rand12 ()] += 1 # print frequency of numbers 1-12 for i in range ( 1 N + 1 ): print freq [ i ] # Wait for user input to keep the console window open try : raw_input ( 'Press Enter to exit' ) except EOFError : pass
C# using System ; class Program { // Create a single instance of Random for better performance static Random rand = new Random (); // Function that returns random numbers from 1 to 6 with equal probability static int Rand6 () { return rand . Next ( 1 7 ); } // The function uses Rand6() to return random numbers from 1 to 12 with equal probability static int Rand12 () { return Rand6 () + ( Rand6 () % 2 ) * 6 ; } // Driver code to test above functions static void Main () { int N = 12 ; int iterations = 100000 ; int [] freq = new int [ N + 1 ]; // call Rand12() multiple times and store its results for ( int i = 0 ; i < iterations ; i ++ ) freq [ Rand12 ()] ++ ; // print frequency of numbers 1-12 for ( int i = 1 ; i <= N ; i ++ ) Console . Write ( freq [ i ] + ' ' ); Console . ReadLine (); // Added to keep the console window open until a key is pressed } }
JavaScript function rand6 () { // Generates a random number from 1 to 6 return Math . floor ( Math . random () * 6 ) + 1 ; } function rand12 () { return rand6 () + ( rand6 () % 2 ) * 6 ; } const N = 12 ; const freq = new Array ( N + 1 ). fill ( 0 ); // Call rand12() multiple times and store its results for ( let i = 0 ; i < N * 100000 ; i ++ ) { freq [ rand12 ()] ++ ; } // Print the frequency of numbers 1-12 for ( let i = 1 ; i <= N ; i ++ ) { console . log ( freq [ i ]); }
Sortida:
100237 100202 99678 99867 100253 99929 100287 100449 99827 99298 100019 99954Una altra solució:
int rand12() { return (rand6() * 2) - (rand6() & 1); }
- rand6() * 2: Això tornarà els nombres parells 2 4 6 8 10 i 12 amb la mateixa probabilitat i
- rand6() i 1 : Això tornarà 0 o 1 basat en rand6() és parell o senar respectivament. Així l'expressió
- (rand6() * 2) - (rand6() i 1) : Això retornarà nombres aleatoris de l'1 al 12 amb la mateixa probabilitat.
A continuació es mostra la implementació de l'enfocament anterior:
C++ #include #include #include // Assume rand6 generates a random integer between 1 and 6 int rand6 () { return rand () % 6 + 1 ; } int rand12 () { return ( rand6 () * 2 ) - ( rand6 () & 1 ); } int main () { // Seed the random number generator srand ( time ( 0 )); // Generate a random number between 1 and 12 int randomNum = rand12 (); // Print the random number std :: cout < < 'Random number between 1 and 12: ' < < randomNum < < std :: endl ; return 0 ; }
Java import java.util.Random ; public class Main { private static final Random rand = new Random (); // Assume rand6 generates a random integer between 1 and 6 public static int rand6 () { return rand . nextInt ( 6 ) + 1 ; } public static int rand12 () { return ( rand6 () * 2 ) - ( rand6 () & 1 ); } public static void main ( String [] args ) { // Generate a random number between 1 and 12 int randomNum = rand12 (); // Print the random number System . out . println ( 'Random number between 1 and 12: ' + randomNum ); } }
Python import random def rand6 (): ''' Generates a random integer between 1 and 6 inclusive. Returns: int: A random integer between 1 and 6. ''' return random . randint ( 1 6 ) def rand12 (): ''' Generates a random integer between 1 and 12 inclusive. Returns: int: A random integer between 1 and 12. ''' # Generate two random numbers between 1 and 6 num1 = rand6 () num2 = rand6 () # Calculate the result using the formula: (2 * num1) - (num2 & 1) result = ( 2 * num1 ) - ( num2 & 1 ) # Ensure the result is within the range of 1 to 12 if result > 12 : result = result % 12 return result if __name__ == '__main__' : # Seed the random number generator random . seed () # Generate a random number between 1 and 12 random_num = rand12 () # Print the random number print ( 'Random number between 1 and 12:' random_num )
JavaScript /** * Generates a random integer between 1 and 6 inclusive. * * @returns {number} A random integer between 1 and 6. */ function rand6 () { return Math . floor ( Math . random () * 6 ) + 1 ; } /** * Generates a random integer between 1 and 12 inclusive. * * @returns {number} A random integer between 1 and 12. */ function rand12 () { // Generate two random numbers between 1 and 6 let num1 = rand6 (); let num2 = rand6 (); // Calculate the result using the formula: (2 * num1) - (num2 & 1) let result = ( 2 * num1 ) - ( num2 % 2 ); // Ensure the result is within the range of 1 to 12 if ( result > 12 ) { result = result % 12 ; if ( result === 0 ) { result = 12 ; } } return result ; } // Generate a random number between 1 and 12 let randomNum = rand12 (); // Print the random number console . log ( 'Random number between 1 and 12:' randomNum );
Sortida
Random number between 1 and 12: 7
