Given an integer N, the task is to print a good permutation of first N natural numbers. Let’s denote the ith element of the permutation be pi.
A good permutation is a permutation such that for all 1 ≤ i ≤ N the following equations hold true,
- ppi = i
- pi != i
Basically above expressions mean, no value is equal to its position.
If no such good permutation exists then print -1.
Input: N = 1
No good permutation exists.
Input: N = 2
Output: 2 1
Position of 2 is 1 and position of 1 is 2.
Approach: Consider permutation p such that pi = i. Actually, p is a sequence of numbers from 1 to N and ppi = i.
Now the only trick is to change the permutation to satisfy the second equation i.e. pi != i. Let’s swap every two consecutive elements. More formally, for each k: 2k ≤ n let's swap p2k – 1 and p2k. It’s easy to see that the obtained permutation satisfies both the equations for every n with the only exception: when n is odd, there is no answer and we should print -1.
Below is the implementation of the above approach:
2 1 4 3
- Find the number of sub arrays in the permutation of first N natural numbers such that their median is M
- Find permutation of first N natural numbers that satisfies the given condition
- Find the permutation of first N natural numbers such that sum of i % Pi is maximum possible
- Find the K-th Permutation Sequence of first N natural numbers
- Increasing permutation of first N natural numbers
- Number of valid indices in the permutation of first N natural numbers
- Minimum cost to make an Array a permutation of first N natural numbers
- Count array elements that can be maximized by adding any permutation of first N natural numbers
- Sort permutation of N natural numbers using triple cyclic right swaps
- Find m-th summation of first n natural numbers.
- Program to find sum of first n natural numbers
- Find the average of first N natural numbers
- Find maximum N such that the sum of square of first N natural numbers is not more than X
- Find all divisors of first N natural numbers
- Find if given number is sum of first n natural numbers
- Print all Good numbers in given range
- Minimum number of given operations required to convert a permutation into an identity permutation
- Minimum number of adjacent swaps required to convert a permutation to another permutation by given condition
- Find the largest good number in the divisors of given number N
- Find all good indices in the given Array
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