1718. Construct the Lexicographically Largest Valid Sequence
Description
Given an integer n
, find a sequence that satisfies all of the following:
- The integer
1
occurs once in the sequence. - Each integer between
2
andn
occurs twice in the sequence. - For every integer
i
between2
andn
, the distance between the two occurrences ofi
is exactlyi
.
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:
Input: n = 3 Output: [3,1,2,3,2] Explanation: [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 = 5 Output: [5,3,1,4,3,5,2,4,2]
Constraints:
1 <= n <= 20
Solutions
Solution 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 |
|