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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.
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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