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Write a function to generate a random number between 1
and 7. You have been given a function that generates a random number between 1 and 5.
The distribution between each of the numbers must be uniform.

Though both solutions are too close, but there is another method that can give 100% random depending on retRand1to5() function. Hint:

We know foo() returns integers from 1 to 5. How we can ensure that integers from 1 to 7 occur with equal probability? If we somehow generate integers from 1 to a-multiple-of-7 (like 7, 14, 21, …) with equal probability, we can use modulo division by 7 followed by adding 1 to get the numbers from 1 to 7 with equal probability.

We can generate from 1 to 21 with equal probability using the following expression.

This comment has been removed by the author.

ReplyDeleteint genRand1to7 ()

ReplyDelete{

int i = genRand1to5();

int j = genRand1to5();

return (i+j)%8 ;

}

It's not uniform.

DeleteWhat about :

ReplyDeleteLet f() is retRand1to5() and g() is getRand1to7() then as per @AditiPal

g() = (f()+f())%8;

what about:

n = f();

g() = n+(log of n base sqrt(5));

Wouldn't it provide a more uniform distribution.

Great discussion by Aditi and Aduait.

ReplyDeleteThough both solutions are too close, but there is another method that can give 100% random depending on retRand1to5() function. Hint:

We know foo() returns integers from 1 to 5. How we can ensure that integers from 1 to 7 occur with equal probability?

If we somehow generate integers from 1 to a-multiple-of-7 (like 7, 14, 21, …) with equal probability, we can use modulo division by 7 followed by adding 1 to get the numbers from 1 to 7 with equal probability.

We can generate from 1 to 21 with equal probability using the following expression.

5*foo() + foo() -5