# Generate an N-length permutation such that absolute difference between adjacent elements are present in the range [2, 4]

Given a positive integer **N**, the task is to construct a permutation of first **N** natural numbers** **such that the absolute difference between adjacent elements is either **2**, **3**, or **4**. If it is not possible to construct such a permutation, then print **“-1”**.

**Examples:**

Input:N = 4Output:3 1 4 2Explanation:

Consider a permutation {3, 1, 4, 2}. Now, the absolute difference between adjacent elements are {2, 3, 2}.

Input:N = 9Output:9 7 5 3 1 4 2 6 8

**Approach:** The given problem can be solved by grouping up consecutive even and odd elements together to construct the permutation. Follow the steps below to solve the problem:

- If the value of
**N**is less than**4**then print**-1**as it is impossible to construct a permutation according to the given conditions for**N**less than**4**. - Initialize a variable, say
**i**as**N**, and perform the following steps below:- If the value of
**i**is even, then decrement the value of**i**by**1**. - Iterate until the value of
**i**is at least**1**and print the value of**i**and decrement the value of**i**by**2**. - Print
**4**and**2**and update the value of**i**to**6**. - Iterate in the range
**[i, N]**and print the value of**i**and increment the value of**i**by**2**.

- If the value of

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to print the permutation of` `// size N with absolute difference of` `// adjacent elements in range [2, 4]` `void` `getPermutation(` `int` `N)` `{` ` ` `// If N is less than 4` ` ` `if` `(N <= 3) {` ` ` `cout << -1;` ` ` `return` `;` ` ` `}` ` ` `int` `i = N;` ` ` `// Check if N is even` ` ` `if` `(N % 2 == 0)` ` ` `i--;` ` ` `// Traverse through odd integers` ` ` `while` `(i >= 1) {` ` ` `cout << i << ` `" "` `;` ` ` `i -= 2;` ` ` `}` ` ` `cout << 4 << ` `" "` `<< 2 << ` `" "` `;` ` ` `// Update the value of i` ` ` `i = 6;` ` ` `// Traverse through even integers` ` ` `while` `(i <= N) {` ` ` `cout << i << ` `" "` `;` ` ` `i += 2;` ` ` `}` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `N = 9;` ` ` `getPermutation(N);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` ` ` `// Function to print the permutation of` `// size N with absolute difference of` `// adjacent elements in range [2, 4]` `static` `void` `getPermutation(` `int` `N)` `{` ` ` ` ` `// If N is less than 4` ` ` `if` `(N <= ` `3` `)` ` ` `{` ` ` `System.out.print(-` `1` `);` ` ` `return` `;` ` ` `}` ` ` `int` `i = N;` ` ` `// Check if N is even` ` ` `if` `(N % ` `2` `== ` `0` `)` ` ` `i--;` ` ` `// Traverse through odd integers` ` ` `while` `(i >= ` `1` `)` ` ` `{` ` ` `System.out.print(i + ` `" "` `);` ` ` `i -= ` `2` `;` ` ` `}` ` ` `System.out.print(` `4` `+ ` `" "` `+ ` `2` `+` `" "` `);` ` ` `// Update the value of i` ` ` `i = ` `6` `;` ` ` `// Traverse through even integers` ` ` `while` `(i <= N)` ` ` `{` ` ` `System.out.print(i + ` `" "` `);` ` ` `i += ` `2` `;` ` ` `}` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `9` `;` ` ` ` ` `getPermutation(N);` `} ` `}` `// This code is contributed by sanjoy_62` |

## Python3

`# Python3 program for the above approach` `# Function to print permutation of` `# size N with absolute difference of` `# adjacent elements in range [2, 4]` `def` `getPermutation(N):` ` ` ` ` `# If N is less than 4` ` ` `if` `(N <` `=` `3` `):` ` ` `print` `(` `-` `1` `)` ` ` `return` ` ` `i ` `=` `N` ` ` `# Check if N is even` ` ` `if` `(N ` `%` `2` `=` `=` `0` `):` ` ` `i ` `-` `=` `1` ` ` `# Traverse through odd integers` ` ` `while` `(i >` `=` `1` `):` ` ` `print` `(i, end ` `=` `" "` `)` ` ` `i ` `-` `=` `2` ` ` `print` `(` `4` `, ` `2` `, end ` `=` `" "` `)` ` ` `# Update the value of i` ` ` `i ` `=` `6` ` ` `# Traverse through even integers` ` ` `while` `(i <` `=` `N):` ` ` `print` `( i, end ` `=` `" "` `)` ` ` `i ` `+` `=` `2` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `N ` `=` `9` ` ` `getPermutation(N)` ` ` `# This code is contributed by mohit kumar 29.` |

## C#

`// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG{` ` ` `// Function to print the permutation of` `// size N with absolute difference of` `// adjacent elements in range [2, 4]` `static` `void` `getPermutation(` `int` `N)` `{` ` ` ` ` `// If N is less than 4` ` ` `if` `(N <= 3)` ` ` `{` ` ` ` ` `Console.Write(-1);` ` ` `return` `;` ` ` `}` ` ` `int` `i = N;` ` ` `// Check if N is even` ` ` `if` `(N % 2 == 0)` ` ` `i--;` ` ` `// Traverse through odd integers` ` ` `while` `(i >= 1)` ` ` `{` ` ` `Console.Write(i + ` `" "` `);` ` ` `i -= 2;` ` ` `}` ` ` `Console.Write(4 + ` `" "` `+ 2 +` `" "` `);` ` ` `// Update the value of i` ` ` `i = 6;` ` ` `// Traverse through even integers` ` ` `while` `(i <= N)` ` ` `{` ` ` `Console.Write(i +` `" "` `);` ` ` `i += 2;` ` ` `}` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `N = 9;` ` ` ` ` `getPermutation(N);` `}` `}` `// This code is contributed by SURENDRA_GANGWAR` |

## Javascript

`<script>` `// JavaScript program for the above approach` `// Function to print the permutation of` `// size N with absolute difference of` `// adjacent elements in range [2, 4]` `function` `getPermutation(N)` `{` ` ` ` ` `// If N is less than 4` ` ` `if` `(N <= 3)` ` ` `{` ` ` `document.write(-1);` ` ` `return` `;` ` ` `}` ` ` `let i = N;` ` ` `// Check if N is even` ` ` `if` `(N % 2 == 0)` ` ` `i--;` ` ` `// Traverse through odd integers` ` ` `while` `(i >= 1)` ` ` `{` ` ` `document.write(i + ` `" "` `);` ` ` `i -= 2;` ` ` `}` ` ` `document.write(4 + ` `" "` `+ 2 + ` `" "` `);` ` ` `// Update the value of i` ` ` `i = 6;` ` ` `// Traverse through even integers` ` ` `while` `(i <= N)` ` ` `{` ` ` `document.write(i + ` `" "` `);` ` ` `i += 2;` ` ` `}` `}` `// Driver Code` `let N = 9;` `getPermutation(N);` `// This code is contributed by Potta Lokesh` `</script>` |

**Output:**

9 7 5 3 1 4 2 6 8

**Time Complexity:** O(N)**Auxiliary Space:** O(1)