Number of ways to reach a number using increments of 1 and 2 (consecutive 2s are not allowed)

The problem states that given a number or a score, we need to find the number of ways to reach it using increments of 1 and 2 with a constraint that consecutive 2s aren't allowed. We will solve this using Dynamic Programming in linear time O(N).

Consider the example

4 1+1+1+1 1+2+1 1+1+2 2+1+1

Note: Consecutive 2s does not imply that we can't use more than two 2s in forming the number, the number of 2s aren't restricted, only the order is. As long as they don't swing together that is fine.

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