从1到7的整数以相等的概率生成

给定一个函数foo()以相等的概率返回1到5的整数，仅使用foo()编写一个函数以相等的概率返回1到7的整数。最小化对foo()方法的调用次数。另外，不允许使用任何其他库函数，也不允许使用浮点运算。
解决方案 ：
我们知道foo()返回1到5的整数。如何确保1到7的整数以相等的概率出现?
如果我们以某种方式以相等的概率生成从1到7的整数(例如7、14、21，…)，则可以使用模除以7，然后加1以得到等号从1到7的数字可能性。
我们可以使用以下表达式从1到21产生相等的概率。

5*foo() + foo() -5 

让我们看看如何使用上面的表达式。
1.对于第一个foo()的每个值，第二个foo()的值可以有5种可能的组合。因此，总共可能有25种组合。
2.上式返回的值范围是1到25，每个整数恰好出现一次。
3.如果方程的值小于22，则将模除以7，然后加1。否则，再次递归调用该方法。因此，返回每个整数的概率变为1/7。
下面的程序显示该表达式返回从1到25的每个整数一次。

C++

#include 
 
int main()
{
    int first, second;
    for ( first=1; first<=5; ++first )
        for ( second=1; second<=5; ++second )
            printf ("%d \n", 5*first + second - 5);
    return 0;
}

Java

// Java code to demonstrate
// expression returns each integer
// from 1 to 25 exactly once
 
class GFG {
    public static void main(String[] args)
    {
        int first, second;
        for ( first=1; first<=5; ++first )
            for ( second=1; second<=5; ++second )
            System.out.printf ("%d \n", 5*first + second - 5);
    }
}
 
// This code is contributed by
// Smitha Dinesh Semwal

Python3

# Python3 code to demonstrate
# expression returns each integer
# from 1 to 25 exactly once
 
if name == '__main__':
     
    for first in range(1, 6):
        for second in range(1, 6):
                print(5 * first + second - 5)
 
# This code is contributed by Smitha Dinesh Semwal.

C#

// C# code to demonstrate expression returns
// each integer from 1 to 25 exactly once
using System;
 
class GFG {
     
    public static void Main()
    {
        int first, second;
 
        for ( first = 1; first <= 5; ++first )
            for ( second = 1; second <= 5; ++second )
                Console.WriteLine ( 5*first + second - 5);
    }
}
 
// This code is contributed by Sam007.

Javascript

 
// Javascript Program to demonstrate
// expression returns each integer
// from 1 to 25 exactly once
 
 
// Driver Code
 
    let first, second;
    for ( first=1; first<=5; ++first )
        for ( second=1; second<=5; ++second ) {
             document.write( 5*first + second - 5);
             document.write("<br />");
        }
 

输出 ：

1
2
.
.
24
25

下面的程序描述了如何使用foo()以相等的概率返回1到7。

C++

// C++ program to Generate integer from
// 1 to 5 with equal probability
#include 
 
// given method that returns 1 to 5 with equal probability
int foo()
{
    // some code here
}
 
int my_rand() // returns 1 to 7 with equal probability
{
    int i;
    i = 5*foo() + foo() - 5;
    if (i < 22)
        return i%7 + 1;
    return my_rand();
}
// Driver code
int main()
{
    printf ("%d ", my_rand());
    return 0;
}

Java

// Java program to Generate integer from
// 1 to 5 with equal probability
class GfG
{
 
// given method that returns 1 to 5 with equal probability
static int foo()
{
    // some code here
    return 0;
}
 
// returns 1 to 7 with equal probability
public static int my_rand() 
{
    int i;
    i = 5*foo() + foo() - 5;
    if (i < 22)
        return i%7 + 1;
    return my_rand();
}
 
// Driver code
public static void main (String[] args) {
 
    System.out.println(my_rand());
}
}

Python3

# Python3 program to Generate integer
# from 1 to 5 with equal probability
# given method that returns 1 to 5
# with equal probability
def foo():
 
    # some code here
    return 0;
 
# returns 1 to 7 with equal probability
def my_rand():
    i = 0;
    i = (5 * foo()) + (foo() - 5);
    if (i < 22):
        if(i < 0):
            return (i % 7 - 7) + 1;
        else:
            return (i % 7) + 1;
             
    return my_rand();
 
# Driver code
if __name__ == '__main__':
    print(my_rand());
 
# This code contributed by PrinciRaj1992

C＃

// C# program to Generate integer from
// 1 to 5 with equal probability
using System;
class GfG
{
  
// given method that returns 1 to 5 with equal probability
static int foo()
{
    // some code here
    return 0;
}
  
// returns 1 to 7 with equal probability
public static int my_rand() 
{
    int i;
    i = 5*foo() + foo() - 5;
    if (i < 22)
        return i%7 + 1;
    return my_rand();
}
  
// Driver code
public static void Main () {
  
    Console.Write(my_rand()+"\n");
}
}

Java脚本

 
// Javascript program to Generate integer from
// 1 to 5 with equal probability
 
    // given method that returns 1 to 5 with equal probability
    function foo()
    {
        // some code here
        return 0;
    }
     
    // returns 1 to 7 with equal probability
    function my_rand()
    {
        let i;
        i = 5*foo() + foo() - 5;
        if (i < 22)
            return i%7 + 1;
        return my_rand();
    }
     
    // Driver code
    document.write(my_rand());
     
    // This code is contributed by rag2127
     

输出：

-4