Count max number of $$$1's$$$ you can place in the array. After placing the first $$$1$$$, it will take up $$$2*k-1$$$ slots, after then greedily filling $$$1$$$ to any of the ends will take up $$$k$$$ slots. Using this observation you can easily count the max number of $$$1's$$$ you can place in the array. Let this be $$$cnt$$$
So, the optimal length for repeating the subarray should be $$$max(ceil(\frac{n}{cnt}),k)$$$.

No greedy solution came to my mind. So I binary searched the answer and something similar to dp to find whether we can get the array by using a block of size in between [k,mid]. If we can move on to values less than equal to mid-1 otherwise go to values higher than mid+1. My solution

Handle n <= 6 by hand. We can use a brute force to observe that the maximum degree for n >= 7 is 4. The construction depends on n mod 4, but in all cases we can take the degree sequence to be some permutation of (1 2 3 4) repeated until we have n vertices. This degree sequence is valid because no prime number is a multiple of four. To realize this degree sequence, within each group of four vertices, we add the edges 1-4, 2-4, 2-3, 3-4. Then, we need one more edge incident to each of 3 and 4, so we connect each 3 to the next block’s 4. This also ensure that the graph will be connected.

This construction works as stated when n is divisible by 4. Otherwise, we can modify it slightly, e.g when n is 3 mod 4 the last block will contain only a 1, 2, and a 3, and we can reduce to two vertices requiring one edge each by adding edges 1-2 and 2-3.

As a more general note, I found it extremely helpful to write a brute force to generate the degree sequences. Doing so made it extremely easy to find that the answer is always 4 for sufficiently large n, and examining patterns in the output led me to the degree sequences in my eventual constructions. The only part I had to do by hand is the actual construction of a connected graph with the desired degree sequence, which is not especially difficult due to the periodicity of the sequences.

Hey, we'll be reaching out soon to the winners(1-2 weeks for Indian winners, 4-5 weeks for international winners) to get their details and transfer the prize money

Hey, we have reached out to the Indian winners, and we will be reaching out to International winners in a couple of days.