한 줄에 rand6()을 사용하여 rand12() 구현
1부터 6까지의 난수를 동일한 확률로 반환하는 함수 rand6()가 주어지면 1부터 12까지의 난수를 동일한 확률로 반환하는 rand6()을 사용하여 단일 라이너 함수 rand12()를 구현합니다. 솔루션은 rand6() 메서드에 대한 호출 수를 최소화해야 합니다. 다른 라이브러리 함수 및 부동 소수점 연산을 사용할 수 없습니다.
아이디어는 표현을 사용하는 것입니다 rand6() + (rand6() % 2) * 6 . 1부터 12까지 동일한 확률로 난수를 반환합니다. 표현은 다음과 같습니다 -
// if rand6() is even if (rand6() % 2) return 6 + rand6(); else // if rand6() is odd return rand6();비슷한 방식으로 작동하는 아래 표현식 중 하나를 사용할 수도 있습니다.
- rand6() + !(rand6() % 2) * 6 또는
- rand6() + (rand6() & 1) * 6 또는
- rand6() + !(rand6() & 1) * 6
다음은 위의 접근 방식을 구현한 것입니다.
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 ]); }
산출:
100237 100202 99678 99867 100253 99929 100287 100449 99827 99298 100019 99954또 다른 해결책:
int rand12() { return (rand6() * 2) - (rand6() & 1); }
- 랜드6() * 2: 그러면 동일한 확률로 짝수 2 4 6 8 10과 12가 반환됩니다.
- 랜드6() & 1 : rand6()이 각각 짝수 또는 홀수인지에 따라 0 또는 1을 반환합니다. 그래서 표현은
- (rand6() * 2) - (rand6() & 1) : 1부터 12까지 동일한 확률로 난수를 반환합니다.
다음은 위의 접근 방식을 구현한 것입니다.
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 );
산출
Random number between 1 and 12: 7
