Monday, March 24, 2014

Given a series (2,3,4,5,6,8,9,10,12,15,...) where the elements are in multiple of 2,3 and 5. Find the nth element of this sequence

Problem:
Assume given sequence :
2,3,4,5,6,8,9,10,12,15...
All these numbers are multiples of either 2 , 3, or 5 (and no other numbers).
Find the nth element of this sequence. (This is the interview question in flipkart)

Solution:
This can be thought in recursive terms. But to begin with, we can clearly see, 2.5=10 is part of series, but 2.7=14 is not part of series. So, while generation of numbers we have to make sure that divisor is not part of numbers like 7,11,13 etc.

Java code
public int GetNumberFromSequence(int n)
{
    if(n==1)
        return 2;
    if(n>1)
    for(int i=1;;i++)
    {
        int possibleNumber=GetNumberFromSequence(n-1)+i;
if(IsAllowedNumber(possibleNumber))
     return possibleNumber;
else 
    continue;
}
    
}
public bool IsAllowedNumber(int possibleNumber)
{

    for(int n: primesExcept_2_3_5  )
        if(possibleNumber%n == 0)
            return false;
        else
        if(n>possibleNumber)
            return true;    
}

Thanks

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