Implementujte rand3() pomocou rand2()
Vzhľadom na funkciu rand2(), ktorá vracia 0 alebo 1 s rovnakou pravdepodobnosťou, implementujte rand3() pomocou rand2(), ktorá vracia 0 1 alebo 2 s rovnakou pravdepodobnosťou. Minimalizujte počet volaní metódy rand2(). Tiež nie je povolené použitie akejkoľvek inej funkcie knižnice a aritmetiky s pohyblivou rádovou čiarkou.
Cieľom je použiť výraz 2 * rand2() + rand2() . Vráti 0 1 2 3 s rovnakou pravdepodobnosťou. Aby to vrátilo 0 1 2 s rovnakou pravdepodobnosťou, eliminujeme nežiaducu udalosť 3.
Nižšie je uvedená implementácia vyššie uvedenej myšlienky -
// C++ Program to print 0 1 or 2 with equal // probability #include using namespace std ; // Random Function to that returns 0 or 1 with // equal probability int rand2 () { // 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 0 1 or 2 with // equal probability 1 with 75% int rand3 () { // returns 0 1 2 or 3 with 25% probability int r = 2 * rand2 () + rand2 (); if ( r < 3 ) return r ; return rand3 (); } // Driver code to test above functions int main () { // Initialize random number generator srand ( time ( NULL )); for ( int i = 0 ; i < 100 ; i ++ ) cout < < rand3 (); return 0 ; }
Java // Java Program to print 0 1 or 2 with equal // probability import java.util.Random ; class GFG { // Random Function to that returns 0 or 1 with // equal probability static int rand2 () { // 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. Random rand = new Random (); return ( rand . nextInt () & 1 ); } // Random Function to that returns 0 1 or 2 with // equal probability 1 with 75% static int rand3 () { // returns 0 1 2 or 3 with 25% probability int r = 2 * rand2 () + rand2 (); if ( r < 3 ) return r ; return rand3 (); } // Driver code public static void main ( String [] args ) { for ( int i = 0 ; i < 100 ; i ++ ) System . out . print ( rand3 ()); } } // This code is contributed by divyesh072019.
Python3 # Python3 Program to print 0 1 or 2 with equal # Probability import random # Random Function to that returns 0 or 1 with # equal probability def rand2 (): # randint(0100) function will generate odd or even # number [1100] with equal probability. If rand() # generates odd number the function will # return 1 else it will return 0 tmp = random . randint ( 1 100 ) return tmp % 2 # Random Function to that returns 0 1 or 2 with # equal probability 1 with 75% def rand3 (): # returns 0 1 2 or 3 with 25% probability r = 2 * rand2 () + rand2 () if r < 3 : return r return rand3 () # Driver code to test above functions if __name__ == '__main__' : for i in range ( 100 ): print ( rand3 () end = '' ) #This code is contributed by sahilshelangia
C# // C# Program to print 0 1 or 2 with equal // probability using System ; class GFG { // Random Function to that returns 0 or 1 with // equal probability static int rand2 () { // 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. Random rand = new Random (); return ( rand . Next () & 1 ); } // Random Function to that returns 0 1 or 2 with // equal probability 1 with 75% static int rand3 () { // returns 0 1 2 or 3 with 25% probability int r = 2 * rand2 () + rand2 (); if ( r < 3 ) return r ; return rand3 (); } // Driver code static void Main () { for ( int i = 0 ; i < 100 ; i ++ ) Console . Write ( rand3 ()); } } // This code is contributed by divyeshrabadiya07.
PHP // PHP Program to print 0 1 or // 2 with equal probability // Random Function to that // returns 0 or 1 with // equal probability function rand2 () { // 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 0 1 or 2 with // equal probability 1 with 75% function rand3 () { // returns 0 1 2 or 3 // with 25% probability $r = 2 * rand2 () + rand2 (); if ( $r < 3 ) return $r ; return rand3 (); } // Driver Code // Initialize random // number generator srand ( time ( NULL )); for ( $i = 0 ; $i < 100 ; $i ++ ) echo rand3 (); // This code is contributed by aj_36 ?>
JavaScript < script > // Javascript program to print 0 1 or 2 with equal // probability // Random Function to that returns 0 or 1 with // equal probability function rand2 () { // Math.random()*2 function generates // 0 and 1 with equal probability return Math . floor ( Math . random () * 2 ); } // Random Function to that returns 0 1 or 2 with // equal probability 1 with 75% function rand3 () { // returns 0 1 2 or 3 with 25% probability var r = 2 * rand2 () + rand2 (); if ( r < 3 ) return r ; return rand3 (); } var ans = '' ; //to store the output for ( var i = 0 ; i < 100 ; i ++ ) ans += rand3 (); document . write ( ans ); // This code is contributed by shruti456rawal < /script>
výstup:
2111011101112002111002020210112022022022211100100121202021102100010200121121210122011022111020
Ďalšie riešenie -
Ak x = rand2() a y = rand2() x + y vráti 0 a 2 s 25% pravdepodobnosťou a 1 s 50% pravdepodobnosťou. Aby sa pravdepodobnosť 1 rovnala pravdepodobnosti 0 a 2, t. j. 25 %, odstránime jednu nežiaducu udalosť, ktorá má za následok x + y = 1, t. j. buď (x = 1 y = 0) alebo (x = 0 y = 1).
int rand3() { int x y; do { x = rand2(); y = rand2(); } while (x == 0 && y == 1); return x + y; }
Upozorňujeme, že vyššie uvedené riešenia prinesú rôzne výsledky zakaždým, keď ich spustíme.
