Sequences with no wells X41088
A sequence of numbers has a well if it contains three consecutive numbers such that that the endpoints add up more than twice the one in the middle.
Formally, (x1, x2 , … , xn) has a well if it exists at least an i with 1 ≤ i < n − 1 such that xi + xi+2 > 2· xi+1.
Write a program that, given an integer n ≥ 1, writes all sequences with no well that can be obtained by reordering the sequence (1, 2, … , n).
Input
The input consists of an integer n ≥ 1.
Output
Write all sequences with no well that can be obtained by reordering the sequence (1, 2, …, n). You can write the sequences in any order.
Public test cases
Input
3
Output
(1,2,3) (1,3,2) (2,3,1) (3,2,1)
Input
2
Output
(1,2) (2,1)
Input
4
Output
(1,2,3,4) (1,3,4,2) (1,4,3,2) (2,3,4,1) (2,4,3,1) (4,3,2,1)
Input
1
Output
(1)
Information
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- English
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- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++ Python