# Find a permutation of 2N numbers such that the result of given expression is exactly 2K

Given two integers **N** and **K**, the task is to find a permutation of first **2*N** natural numbers such that the following equation is satisfied.

**Note:** The value of **K** will always be less than or equal to **N**.

**Examples:**

Input :N = 1, K = 0Output :1 2 The result of the above expression will be: |1-2|-|1-2| =0Input :N = 2, K = 1Output :2 1 3 4 The result of the above expression will be: (|2-1|+|3-4|)-(|2-1+3-4|) = 2

**Approach:**

Consider the sorted permutation:

1, 2, 3, 4, 5, 6....

The result of the expression will come out to be exactly 0. If we swap any 2 indices **2i-1** and **2i**, the result will increase by exactly 2. So we need to make **K** such swaps.

Below is the implementation of the above approach:

## C++

`// C++ program to find the required permutation ` `// of first 2*N natural numbers ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the required permutation ` `// of first 2*N natural numbers ` `void` `printPermutation(` `int` `n, ` `int` `k) ` `{ ` ` ` `// Iterate in blocks of 2 ` ` ` `for` `(` `int` `i = 1; i <= n; i++) { ` ` ` `int` `x = 2 * i - 1; ` ` ` `int` `y = 2 * i; ` ` ` ` ` `// We need more increments, so print in reverse order ` ` ` `if` `(i <= k) ` ` ` `cout << y << ` `" "` `<< x << ` `" "` `; ` ` ` ` ` `// We have enough increments, so print in same order ` ` ` `else` ` ` `cout << x << ` `" "` `<< y << ` `" "` `; ` ` ` `} ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 2, k = 1; ` ` ` ` ` `printPermutation(n, k); ` ` ` ` ` `return` `0; ` `} ` |

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## Python3

`# Python3 program to find the required ` `# permutation of first 2*N natural numbers ` ` ` `# Function to find the required permutation ` `# of first 2*N natural numbers ` `def` `printPermutation(n, k) : ` ` ` ` ` `# Iterate in blocks of 2 ` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `+` `1` `) : ` ` ` `x ` `=` `2` `*` `i ` `-` `1` `; ` ` ` `y ` `=` `2` `*` `i; ` ` ` ` ` `# We need more increments, ` ` ` `# so print in reverse order ` ` ` `if` `(i <` `=` `k) : ` ` ` `print` `(y, x, end ` `=` `" "` `); ` ` ` ` ` `# We have enough increments, ` ` ` `# so print in same order ` ` ` `else` `: ` ` ` `print` `(x, y, end ` `=` `" "` `); ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `n ` `=` `2` `; k ` `=` `1` `; ` ` ` ` ` `printPermutation(n, k); ` ` ` `# This code is contributed by Ryuga ` |

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## C#

`using` `System; ` ` ` `// C# program to find the ` `// required permutation ` `// of first 2*N natural numbers ` ` ` `class` `GFG ` `{ ` ` ` ` ` `// Function to find the required permutation ` ` ` `// of first 2*N natural numbers ` ` ` `static` `void` `printPermutation(` `int` `n, ` `int` `k) ` ` ` `{ ` ` ` `// Iterate in blocks of 2 ` ` ` `for` `(` `int` `i = 1; i <= n; i++) ` ` ` `{ ` ` ` `int` `x = 2 * i - 1; ` ` ` `int` `y = 2 * i; ` ` ` ` ` `// We need more increments, ` ` ` `// so print in reverse order ` ` ` `if` `(i <= k) ` ` ` `Console.Write(y + ` `" "` `+ x + ` `" "` `); ` ` ` ` ` `// We have enough increments, ` ` ` `// so print in same order ` ` ` `else` ` ` `Console.Write(x + ` `" "` `+ y + ` `" "` `); ` ` ` `} ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `n = 2, k = 1; ` ` ` `printPermutation(n, k); ` ` ` `} ` `} ` ` ` `// This code is contributed by ` `// shashank_sharma ` |

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**Output:**

2 1 3 4

**Time Complexity:** O(N)

**Auxiliary Space**: O(1)

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