Construct the Lexicographically Largest Valid Sequence
Given an integer n, find a sequence with elements in the range [1, n] that satisfies all of the following:
- The integer
1occurs once in the sequence. - Each integer between
2andnoccurs twice in the sequence. - For every integer
ibetween2andn, the distance between the two occurrences ofiis exactlyi.
The distance between two numbers in 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.
Example 1
Input
n = 3Output
[3,1,2,3,2][2, 3, 2, 1, 3] is also a valid sequence, but [3, 1, 2, 3, 2] is the lexicographically largest valid sequence.
Example 2
Input
n = 5Output
[5,3,1,4,3,5,2,4,2]The sequence satisfies all occurrence and distance requirements and is the lexicographically largest valid sequence for n = 5.
Constraints
- 1 <= n <= 20