Given an integer N. The task is to find the permutation of first N natural numbers such that the absolute difference between any two consecutive numbers > 1. If no such permutation is possible then print -1.
Input: N = 5
Output: 5 3 1 4 2
Input: N = 3
Approach: There may be many such arrangements possible but one of the most common and greedy approach is to arrange all odd numbers in decreasing (or increasing) order and after that arrange all even numbers in decreasing (or increasing) order. Note that if N = 3 or N = 2 then there will be no such arrangement possible and if N = 1 then the sequence will consist of a single element i.e. 1.
Below is the implementation of the above approach:
5 3 1 4 2
- Check whether the sum of absolute difference of adjacent digits is Prime or not
- Count maximum elements of an array whose absolute difference does not exceed K
- Maximum sum of difference of adjacent elements
- Absolute Difference between the Sum of Non-Prime numbers and Prime numbers of an Array
- Count possible combinations of pairs with adjacent elements from first N numbers
- Replace elements with absolute difference of smallest element on left and largest element on right
- Arrange numbers to form a valid sequence
- Arrange given numbers to form the smallest number
- Minimum absolute difference between N and a power of 2
- Sort an array according to absolute difference with given value
- Calculate Stirling numbers which represents the number of ways to arrange r objects around n different circles
- Find the node whose absolute difference with X gives maximum value
- Find the node whose absolute difference with X gives minimum value
- Pair with minimum absolute difference after solving each query
- Rearrange numbers in an array such that no two adjacent numbers are same
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