Greetings,

**Newton School** cordially invites you to be a part of our monthly coding challenge. This month, the challenge is going to take place on eve of **27th February, 2021 at 9PM IST**. The duration of the contest is **150 minutes**.

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Registrations for contest is open till start of contest.

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I hope you all will participate and enjoy the contest.

Regards,

Newton School Team.

Clashes with Lunchtime :(

Can someone please share their solution idea for the 5th and 6th problem?

For the 5th problem.

Fix the position of the unique person and the distance between the nearest power ranger to the left. Then, we can get possible ways to arrange the others in O(1) (with precalculation). It reduces to equation of form:

(a1 + a2 + a3 + .... + aP = something, ai >= 0 for all i).

Number of solutions for this is a well-known combinatorial result.

We can simply iterate over all possible values of distance and finally multiply the result by N. Also handle the cases when there are not enough seats available.

I solved it with combinatorics, but it became very complex for me. Can it be solved with dp?

There is also a closed-form formula: $$$\frac{N}{P}\binom{N-P\cdot C-1}{P-1}(N-P)$$$

Adapt the solution given here and multiply by $$$N-P$$$.