One interesting observation is that ...
This solution works in $O(N)$ time.
viable/feasible 可行的、合法的
The given condition can be rephrased as follows: ...
By doing ..., we can restate the condition of the problem as follows: ...
... could be rephrased to say that ...
Now that we know sth. is unique, we can give it a notation.
The key observation in this problem is that ... The other observation we need is that ... These two observations lead us to a ... solution.