# RandonInt()

## RandonInt()

A nested function call is when inside a function, you call the same function.\

We will now define a function RandomInt(

Now RandomInt(Random(Random(..........RandomInt(

RandomInt(

And RandomInt(RandomInt(N)) means nesting of 2 and thus so on....

You will be given a Number

You have to give the probability of getting a number =

We will now define a function RandomInt(

**N**). This function generates a random number between 0 and N-1 (inclusive) with equal probability.Now RandomInt(Random(Random(..........RandomInt(

**N**).....)))) is nested.RandomInt(

**N**) means nesting of 1.And RandomInt(RandomInt(N)) means nesting of 2 and thus so on....

You will be given a Number

**N**,**nesting**(the no of nestings) and**Target**.You have to give the probability of getting a number =

**Target**after**nestings**starting from number**N****SwitchCase**- Posts : 5

Join date : 2008-08-13

## Re: RandonInt()

I'm not able to figure out probability but considered following cases:

Let N be number, T be target and n be nestings

if n>=N and T>0 we cannot get T

if N>T (alsothen we cannot get T

if n> N-T ( N > T obviously ) ,we cannot get T

else

we can get T with probability is as follow

0: 1/N +1/2N + ....+ 1/nN

1:1/N +.........+ 1/(n-1)N

.

.

N-1: 1/N

Let N be number, T be target and n be nestings

if n>=N and T>0 we cannot get T

if N>T (alsothen we cannot get T

if n> N-T ( N > T obviously ) ,we cannot get T

else

we can get T with probability is as follow

0: 1/N +1/2N + ....+ 1/nN

1:1/N +.........+ 1/(n-1)N

.

.

N-1: 1/N

**ankurgutpa**- Posts : 44

Join date : 2008-08-10

Age : 32

Location : Tandon 72

## Re: RandonInt()

my understanding of the problem is simple(probably not right ).

target > N - number_of_nestings OR target < 0

P(target) = 0

0<= target <= N - number_of_nestings

this part needs more maths.... i am weak in it..

its not evenly distributed of course.because at the end,the outer most RandInt can get

so intuitively it feels like P(1) > P(2) > P(3) .....

somebody please solve this thing!!!

target > N - number_of_nestings OR target < 0

P(target) = 0

0<= target <= N - number_of_nestings

this part needs more maths.... i am weak in it..

its not evenly distributed of course.because at the end,the outer most RandInt can get

**anything less**than N - number_of_nestings as input.so intuitively it feels like P(1) > P(2) > P(3) .....

somebody please solve this thing!!!

Last edited by Ramprasadg on Tue Oct 14, 2008 9:09 pm; edited 1 time in total

**Ramprasadg**- Posts : 12

Join date : 2008-08-13

## Re: RandonInt()

P(N-1) != 1/N

see to get N-1 as target,every nested RandomINt must give N-1.

so the ans is (1/N-1)^no_of_nestings.

see to get N-1 as target,every nested RandomINt must give N-1.

so the ans is (1/N-1)^no_of_nestings.

**Ramprasadg**- Posts : 12

Join date : 2008-08-13

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