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++
// 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(1100) 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:
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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.