Genera 0 y 1 con 25% y 75% de probabilidad
Dada una función rand50() que devuelve 0 o 1 con la misma probabilidad, escriba una función que devuelva 1 con un 75% de probabilidad y 0 con un 25% de probabilidad usando rand50() únicamente. Minimiza el número de llamadas al método rand50(). Tampoco se permite el uso de ninguna otra función de biblioteca ni la aritmética de punto flotante.
La idea es utilizar O bit a bit . Un OR bit a bit toma dos bits y devuelve 0 si ambos bits son 0, mientras que en caso contrario el resultado es 1. Por lo tanto, tiene un 75% de probabilidad de que devuelva 1.
A continuación se muestra la implementación de la idea anterior:
C++ // Program to print 1 with 75% probability and 0 // with 25% probability #include using namespace std ; // Random Function to that returns 0 or 1 with // equal probability int rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return rand () & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise OR bool rand75 () { return rand50 () | rand50 (); } // Driver code to test above functions int main () { // Initialize random number generator srand ( time ( NULL )); for ( int i = 0 ; i < 50 ; i ++ ) cout < < rand75 (); return 0 ; }
Java // Java program to print 1 with 75% probability and 0 // with 25% probability class GFG { // Random Function to that returns 0 or 1 with // equal probability static int rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return ( int ) ( 10 * Math . random ()) & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise OR static int rand75 () { return rand50 () | rand50 (); } // Driver code public static void main ( String [] args ) { // Initialize random number generator //srand(time(null)); for ( int i = 0 ; i < 50 ; i ++ ) { System . out . print ( rand75 ()); } } } // This code is contributed by 29AjayKumar
Python3 # Program to print 1 with 75% probability and 0 # with 25% probability from random import randrange # Random Function to that returns 0 or 1 with # equal probability def rand50 (): # The randrange function will generate integer # between the half closed interval at end # Here by passing parameter as 02 # the function will generate integer between 0 and 1 return ( int )( randrange ( 0 2 )) & 1 # Random Function to that returns 1 with 75% # probability and 0 with 25% probability using # Bitwise OR def rand75 (): return rand50 () | rand50 () # Driver code to test above functions for i in range ( 0 50 ): print ( rand75 () end = '' ) # This code is contributed by meetgor.
C# // C# program to print 1 with 75% probability and 0 // with 25% probability using System ; public class GFG { // Instantiate random number generator static Random rand = new Random (); // Random Function to that returns 0 or 1 with // equal probability static int rand50 () { // rand() function will generate 1 or 0 // with equal probability return rand . Next ( 0 2 ); } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise OR static int rand75 () { return rand50 () | rand50 (); } public static void Main ( string [] args ) { for ( int i = 0 ; i < 50 ; i ++ ) { Console . Write ( rand75 ()); } } } //this code is contributed by phasing17
PHP // Program to print 1 with 75% probability // and 0 with 25% probability // Random Function to that returns 0 or // 1 with equal probability function rand50 () { // rand() function will generate // odd or even number with equal // probability. If rand() generates // odd number the function will // return 1 else it will return 0. return rand () & 1 ; } // Random Function to that returns // 1 with 75% probability and 0 // with 25% probability using // Bitwise OR function rand75 () { return rand50 () | rand50 (); } // Driver Code // Initialize random // number generator srand ( time ( NULL )); for ( $i = 0 ; $i < 50 ; $i ++ ) echo rand75 (); // This code is contributed m_kit ?>
JavaScript < script > // Program to print 1 with 75% probability and 0 // with 25% probability // Random Function to that returns 0 or 1 with // equal probability function rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return Math . floor ( Math . random () * 10 ) & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise OR function rand75 () { return rand50 () | rand50 (); } // Driver code to test above functions // Initialize random number generator for ( let i = 0 ; i < 50 ; i ++ ) document . write ( rand75 ()); // This code is contributed by gfgking < /script>
Producción
11101010110101011010000101011110100010111110101111
Complejidad del tiempo: O(1)
Espacio Auxiliar: O(1)
En líneas similares también podemos usar Bit a bit Y . Como devuelve 0 con un 75% de probabilidad, tenemos que invertir el resultado.
// Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise AND bool rand75() { return !(rand50() & rand50()); } A continuación se muestra la implementación de la idea anterior:
C++ #include using namespace std ; // Random Function to that returns 0 or 1 with // equal probability int rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return rand () & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise AND bool rand75 () { return ! ( rand50 () & rand50 ()); } // Driver code to test above functions int main () { // Initialize random number generator srand ( time ( NULL )); for ( int i = 0 ; i < 50 ; i ++ ) cout < < rand75 (); return 0 ; }
Java class GFG { // Random Function to that returns 0 or 1 with // equal probability static int rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return ( int ) ( 10 * Math . random ()) & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise AND static int rand75 () { return ( rand50 () & rand50 ()) ^ 1 ; } // Driver code public static void main ( String [] args ) { // Initialize random number generator //srand(time(null)); for ( int i = 0 ; i < 50 ; i ++ ) { System . out . print ( rand75 ()); } } }
Python3 from random import randrange # Random Function to that returns 0 or 1 with # equal probability def rand50 (): return (( int )( randrange ( 0 2 )) & 1 ) def rand75 (): return ( rand50 () & rand50 ()) ^ 1 for i in range ( 0 50 ): print ( rand75 () end = '' )
C# // C# program to implement the approach using System ; class GFG { // Random Function to that returns 0 or 1 with // equal probability static int rand50 () { // Instantiate random number generator using // system-supplied value as seed. var rand = new Random (); // rand() function will generate 0 or 1 // number with equal probability. return rand . Next ( 0 2 ); } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise AND static int rand75 () { return ( rand50 () & rand50 ()) ^ 1 ; } // Driver code public static void Main ( string [] args ) { // Initialize random number generator // srand(time(null)); for ( int i = 0 ; i < 50 ; i ++ ) { Console . Write ( rand75 ()); } } } // This code is contributed by phasing17
JavaScript // JavaScript program to implement the approach // Random Function to that returns 0 or 1 with // equal probability function rand50 () { return ( Math . floor ( Math . random () * 2 ) & 1 ); } function rand75 () { return ( rand50 () & rand50 ()) ^ 1 ; } for ( var i = 0 ; i < 50 ; i ++ ) process . stdout . write ( rand75 (). toString ()); //This code is contributed by phasing17
Producción
11111111000111101111110011111110011110111111010111
Podemos reemplazar los operadores Bitwise OR y Bitwise AND con Operadores O y Y también -
// Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // OR or AND operator int rand75() { return !(rand50() && rand50()); // return rand50() || rand50() } También podemos lograr el resultado usando el operador de desplazamiento a la izquierda y Bitwise XOR -
C++ // Program to print 1 with 75% probability and 0 // with 25% probability #include using namespace std ; // Random Function to that returns 0 or 1 with // equal probability int rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return rand () & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // left shift and Bitwise XOR int rand75 () { // x is one of {0 1} int x = rand50 (); x = x < < 1 ; // x is now one of {00 10} x = x ^ rand50 (); // x is now one of {00 01 10 11} return ( x > 0 ) ? 1 : 0 ; } // Driver code to test above functions int main () { // Initialize random number generator srand ( time ( NULL )); for ( int i = 0 ; i < 50 ; i ++ ) cout < < rand75 (); return 0 ; }
Java // Java program to print 1 with 75% probability and 0 // with 25% probability class GFG { // Random Function to that returns 0 or 1 with // equal probability static int rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return ( int ) ( 10 * Math . random ()) & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // left shift and Bitwise XOR static int rand75 () { // x is one of {0 1} int x = rand50 (); x = x < < 1 ; // x is now one of {00 10} x = x ^ rand50 (); // x is now one of {00 01 10 11} return ( x > 0 ) ? 1 : 0 ; } // Driver code public static void main ( String [] args ) { for ( int i = 0 ; i < 50 ; i ++ ) System . out . print ( rand75 ()); } } // This code is contributed by 29AjayKumar
Python3 # Program to print 1 with 75% probability and 0 # with 25% probability from random import randrange # Random Function to that returns 0 or 1 with # equal probability def rand50 (): # rand range function generates a integer between # the provided ranges which is half closed interval # It will generate integer 0 or 1 if passed 02 as parameter return ( int )( randrange ( 0 2 )) & 1 # Random Function to that returns 1 with 75% # probability and 0 with 25% probability using # left shift and Bitwise XOR def rand75 (): # x is one of {0 1} x = rand50 () x = x < < 1 # x is now one of {00 10} x = x ^ rand50 () # x is now one of {00 01 10 11} return 1 if ( x > 0 ) else 0 # Driver code to test above functions for i in range ( 0 50 ): print ( rand75 () end = '' ) # This code is contributed by meetgor.
C# // C# program to print 1 with 75% probability and 0 // with 25% probability using System ; public class GFG { // Random Function to that returns 0 or 1 with // equal probability static Random rnd = new Random (); static int rand50 () { // Next(2) will generate 0 or 1 with equal probability return rnd . Next ( 2 ); } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // left shift and Bitwise XOR static int rand75 () { // x is one of {0 1} int x = rand50 (); x = x < < 1 ; // x is now one of {00 10} x = x ^ rand50 (); // x is now one of {00 01 10 11} return ( x > 0 ) ? 1 : 0 ; } static public void Main (){ for ( int i = 0 ; i < 50 ; i ++ ) Console . Write ( rand75 ()); } } // This code is contributed by shruti456rawal
PHP // Program to print 1 with // 75% probability and 0 // with 25% probability // Random Function to that // returns 0 or 1 with // equal probability function rand50 () { // rand() function will // generate odd or even // number with equal // probability. If rand() // generates odd number // the function will return // 1 else it will return 0. return rand () & 1 ; } // Random Function to that // returns 1 with 75% // probability and 0 with // 25% probability using // left shift and Bitwise XOR function rand75 () { // x is one of {0 1} $x = rand50 (); $x = $x < < 1 ; // x is now one // of {00 10} $x = $x ^ rand50 (); // x is now one of // {00 01 10 11} return ( $x > 0 ) ? 1 : 0 ; } // Driver code // Initialize random // number generator srand ( time ( NULL )); for ( $i = 0 ; $i < 50 ; $i ++ ) echo rand75 (); // This code is contributed // by ajit ?>
JavaScript < script > // Javascript program to print 1 with 75% probability and 0 // with 25% probability // Random Function to that returns 0 or 1 with // equal probability function rand50 () { // rand() function will generate odd or even // number with equal probability. If rand() // generates odd number the function will // return 1 else it will return 0. return Math . floor (( 10 * Math . random ())) & 1 ; } // Random Function to that returns 1 with 75% // probability and 0 with 25% probability using // Bitwise OR function rand75 () { // x is one of {0 1} let x = rand50 (); x = x < < 1 ; // x is now one of {00 10} x = x ^ rand50 (); // x is now one of {00 01 10 11} return ( x > 0 ) ? 1 : 0 ; } // Driver code for ( let i = 0 ; i < 50 ; i ++ ) { document . write ( rand75 ()); } // This code is contributed by rag2127 < /script>
Producción
10110100111011011110111100101111110111100001111111
Complejidad del tiempo: O(1)
Espacio Auxiliar: O(1)
Tenga en cuenta que las soluciones anteriores producirán diferentes resultados cada vez que los ejecutamos.
