Codeforces 1741E Sending a Sequence - From Intuition to Prefix States

The value $b_i$ itself suggests a block length $L$. Using that $L$, you can try two roles for $b_i$:

• It might be the length at the right end of a block.

• It might be the length at the left end of a block. Each of these cases tells you how you can jump from one prefix length to another. The whole problem becomes a reachability question on prefix positions:

• Position $0$ means the empty prefix.

• You start from prefix $0$.

• You make jumps according to valid blocks.

• If you can reach prefix $n$, then the answer is YES, otherwise NO. That is exactly what you will represent with dynamic programming.