Construct the Lexicographically Largest Valid Sequence
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Description
Given an integer n, find a sequence with elements in the range [1, n] that satisfies all of the following:
- The integer 1 occurs once in the sequence.
- Each integer between 2 and n occurs twice in the sequence.
- For every integer i between 2 and n, the distance between the two occurrences of i is exactly i.
The distance between two numbers on the sequence, a[i] and a[j], is the absolute difference of their indices, |j - i|.
Return the lexicographically largest sequence. It is guaranteed that under the given constraints, there is always a solution.
A sequence a is lexicographically larger than a sequence b (of the same length) if in the first position where a and b differ, sequence a has a number greater than the corresponding number in b. For example, [0,1,9,0] is lexicographically larger than [0,1,5,6] because the first position they differ is at the third number, and 9 is greater than 5.
Example 1:
Example 2:
Solution