Given two integers N and K where K < N, the task is to generate a permutation of integers from 1 to N such that the absolute difference of all the consecutive integers give exactly K distinct integers.
Input: N = 3, K = 2
Output: 1 3 2
|1 – 3| = 2 and |3 – 2| = 1 which gives 2 distinct integers (2 and 1)
Input: N = 5, K = 4
Output: 1 5 2 4 3
|1 – 5| = 4, |5 – 2| = 3, |2 – 4| = 2 and |4 – 3| = 1 gives 4 distinct integers i.e. 4, 3, 2 and 1
Approach: The problem can be easily solved by simple observation. At the odd indices place increasing sequence 1, 2, 3, … and at the even indices place the decreasing sequence N, N-1, N-2, … and so on.
For N = 10, a permutation with distinct integers for consecutive absolute difference can be 1 10 2 9 3 8 4 7 5 6. The consecutive absolute difference gives integers 9, 8, 7 and so on.
So, first print K integers of such a sequence then make the rest of the differences equal to 1. The code is quite self explanatory.
Below is the implementation of the above approach:
1 10 2 9 8 7 6 5 4 3
- Print combinations of distinct numbers which add up to give sum N
- Pair of prime numbers with a given sum and minimum absolute difference
- Absolute difference between the Product of Non-Prime numbers and Prime numbers of an Array
- Absolute Difference between the Sum of Non-Prime numbers and Prime numbers of an Array
- Number of distinct integers obtained by lcm(X, N)/X
- Check whether a number can be represented as sum of K distinct positive integers
- Minimum absolute difference between N and a power of 2
- Count pairs in an array such that the absolute difference between them is ≥ K
- Largest subset where absolute difference of any two element is a power of 2
- Check if array can be divided into two sub-arrays such that their absolute difference is K
- Remove Minimum coins such that absolute difference between any two piles is less than K
- Pair with minimum absolute difference after solving each query
- Count maximum elements of an array whose absolute difference does not exceed K
- Find the good permutation of first N natural numbers
- Find permutation of first N natural numbers that satisfies the given condition
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