Associate Software Engineer

You have been given two integers ‘DAY_HOURS’ and ‘PARTS’. Where ‘DAY_HOURS’ is the number of hours in a day and a day can be divided into ‘PARTS’ equal parts. Your task is to find total instances of equivalent prime groups. Prime group refers to the group of elements (hours) which are prime and measure the same equivalent time since the start of the day.

For example, if we consider ‘DAY_HOURS’ to be 24 and ‘PARTS’ to be 2, then the day of total 24 hours is divided into 2 parts ( 1 - 12 ) and ( 13 - 24 ). 5 hours in the first part of the day is equivalent to 17, which is 5 hours into the second part of the day. And since 5 and 17 both are prime, they can be considered as a prime group.

Note:

1. Day starts with hour 1 and ends with hour  ‘DAY_HOURS’.

2. Each hour of the prime group should be in a different part of the day.

3. If there is no prime group then return zero.

4. ‘DAY_HOURS’ should be divisible by ‘PARTS’, meaning that the number of hours per part (DAY_HOURS/PARTS)  should be a natural number.

Example:

Let ‘DAY_HOURS’ = 20  and ‘PARTS’ = 2

Hence the view of our day would be in the following format: 

1  2  3  4  5  6  7  8  9 10      -  Part 1
11 12 13 14 15 16 17 18 19 20     -  Part 2

 1-11  Not a prime group because 1 is not prime.
 2-12  Not a prime group because 12 is not prime.
 3-13  Because both 3 and 13 are prime, it is an equivalent prime group.
 4-14  Not a prime group because 4 and 14 are not prime.
 5-15  Not a prime group because 15 is not prime.
 6-16  Not a prime group, because 6 and 16 are not prime.
 7-17  Because both 7 and 17 are prime, it is an equivalent prime group.
 8-18  Not a prime group, because 8 and 18 are, is not prime.
 9-19  Not a prime group because 9 is not prime.
 10-20 Not a prime group because both 10 and 20 are not prime.

 Hence there are 2 equivalent prime groups in the above format which are 3-13 and 7-17.

There are ‘N’ friends who have borrowed money from one another. Now, they wanted to settle their debts by giving or taking some money among themselves.

Your task is to design a series of transactions, such that the total cash flow among them is minimized.

For example:

Let there be three friends ‘A’, ‘B’, ‘C’  with debts-

• A has to pay $ 2000 to B.
• A has to pay $ 1000 to C.
• B has to pay $ 3000 to C.
• C has to pay $ 1000 to A.

Then their minimized cash flow system will be-

• A will finally pay $ 2000 to C.
• B will finally pay $ 1000 to C.

Thus, the total cash flow among them will be $ 3000.