Given an array of **n** elements. Consider array as circular array i.e element after a_{n} is a_{1}. The task is to find maximum sum of the difference between consecutive elements with rearrangement of array element allowed i.e after rearrangement of element find |a_{1} – a_{2}| + |a_{2} – a_{3}| + …… + |a_{n – 1} – a_{n}| + |a_{n} – a_{1}|.

Examples:

Input : arr[] = { 4, 2, 1, 8 } Output : 18 Rearrange given array as : { 1, 8, 2, 4 } Sum of difference between consecutive element = |1 - 8| + |8 - 2| + |2 - 4| + |4 - 1| = 7 + 6 + 2 + 3 = 18. Input : arr[] = { 10, 12, 15 } Output : 10

The idea is to use Greedy Approach and try to bring elements having greater difference closer.

Consider the sorted permutation of the given array a_{1}, a_{1}, a_{2},…., a_{n – 1}, a_{n} such that a_{1} < a_{2} < a_{3}…. < a_{n – 1} < a_{n}.

Now, to obtain the answer having maximum sum of difference between consecutive element, arrange element in following manner:

a_{1}, a_{n}, a_{2}, a_{n-1},…., a_{n/2}, a_{(n/2) + 1}

We can observe that the arrangement produces the optimal answer, as all a_{1}, a_{2}, a_{3},….., a_{(n/2)-1}, a_{n/2} are subtracted twice while a_{(n/2)+1} , a_{(n/2)+2}, a_{(n/2)+3},….., a_{n – 1}, a_{n} are added twice.

Note – a_{(n/2)+1} This term is considered only for even n because for odd n, it is added once and substracted once and hence cancels out.

## C++

`// C++ program to maximize the sum of difference ` `// between consecutive elements in circular array ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Return the maximum Sum of difference between ` `// consecutive elements. ` `int` `maxSum(` `int` `arr[], ` `int` `n) ` `{ ` ` ` `int` `sum = 0; ` ` ` ` ` `// Sorting the array. ` ` ` `sort(arr, arr + n); ` ` ` ` ` `// Subtracting a1, a2, a3,....., a(n/2)-1, an/2 ` ` ` `// twice and adding a(n/2)+1, a(n/2)+2, a(n/2)+3,. ` ` ` `// ...., an - 1, an twice. ` ` ` `for` `(` `int` `i = 0; i < n/2; i++) ` ` ` `{ ` ` ` `sum -= (2 * arr[i]); ` ` ` `sum += (2 * arr[n - i - 1]); ` ` ` `} ` ` ` ` ` `return` `sum; ` `} ` ` ` `// Driver Program ` `int` `main() ` `{ ` ` ` `int` `arr[] = { 4, 2, 1, 8 }; ` ` ` `int` `n = ` `sizeof` `(arr)/` `sizeof` `(arr[0]); ` ` ` `cout << maxSum(arr, n) << endl; ` ` ` `return` `0; ` `} ` |

## Java

`// Java program to maximize the sum of difference ` `// between consecutive elements in circular array ` `import` `java.io.*; ` `import` `java.util.Arrays; ` ` ` `class` `MaxSum ` `{ ` ` ` `// Return the maximum Sum of difference between ` ` ` `// consecutive elements. ` ` ` `static` `int` `maxSum(` `int` `arr[], ` `int` `n) ` ` ` `{ ` ` ` `int` `sum = ` `0` `; ` ` ` ` ` `// Sorting the array. ` ` ` `Arrays.sort(arr); ` ` ` ` ` `// Subtracting a1, a2, a3,....., a(n/2)-1, ` ` ` `// an/2 twice and adding a(n/2)+1, a(n/2)+2, ` ` ` `// a(n/2)+3,....., an - 1, an twice. ` ` ` `for` `(` `int` `i = ` `0` `; i < n/` `2` `; i++) ` ` ` `{ ` ` ` `sum -= (` `2` `* arr[i]); ` ` ` `sum += (` `2` `* arr[n - i - ` `1` `]); ` ` ` `} ` ` ` ` ` `return` `sum; ` ` ` `} ` ` ` ` ` `// Driver Program ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `arr[] = { ` `4` `, ` `2` `, ` `1` `, ` `8` `}; ` ` ` `int` `n = arr.length; ` ` ` `System.out.println(maxSum(arr, n)); ` ` ` `} ` `} ` `/*This code is contributed by Prakriti Gupta*/` |

## Python3

`# Python3 program to maximize the sum of difference ` `# between consecutive elements in circular array ` ` ` `# Return the maximum Sum of difference ` `# between consecutive elements ` `def` `maxSum(arr, n): ` ` ` `sum` `=` `0` ` ` ` ` `# Sorting the array ` ` ` `arr.sort() ` ` ` ` ` `# Subtracting a1, a2, a3,....., a(n/2)-1, an/2 ` ` ` `# twice and adding a(n/2)+1, a(n/2)+2, a(n/2)+3,. ` ` ` `# ...., an - 1, an twice. ` ` ` `for` `i ` `in` `range` `(` `0` `, ` `int` `(n ` `/` `2` `)) : ` ` ` `sum` `-` `=` `(` `2` `*` `arr[i]) ` ` ` `sum` `+` `=` `(` `2` `*` `arr[n ` `-` `i ` `-` `1` `]) ` ` ` ` ` `return` `sum` ` ` ` ` `# Driver Program ` `arr ` `=` `[` `4` `, ` `2` `, ` `1` `, ` `8` `] ` `n ` `=` `len` `(arr) ` `print` `(maxSum(arr, n)) ` ` ` `# This code is contributed by Shreyanshi Arun. ` |

## C#

`// C# program to maximize the sum of difference ` `// between consecutive elements in circular array ` `using` `System; ` ` ` `class` `MaxSum { ` ` ` ` ` `// Return the maximum Sum of difference ` ` ` `// between consecutive elements. ` ` ` `static` `int` `maxSum(` `int` `[] arr, ` `int` `n) ` ` ` `{ ` ` ` `int` `sum = 0; ` ` ` ` ` `// Sorting the array. ` ` ` `Array.Sort(arr); ` ` ` ` ` `// Subtracting a1, a2, a3, ....., a(n/2)-1, ` ` ` `// an/2 twice and adding a(n/2)+1, a(n/2)+2, ` ` ` `// a(n/2)+3, ....., an - 1, an twice. ` ` ` `for` `(` `int` `i = 0; i < n / 2; i++) { ` ` ` `sum -= (2 * arr[i]); ` ` ` `sum += (2 * arr[n - i - 1]); ` ` ` `} ` ` ` ` ` `return` `sum; ` ` ` `} ` ` ` ` ` `// Driver Program ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `[] arr = { 4, 2, 1, 8 }; ` ` ` `int` `n = arr.Length; ` ` ` `Console.WriteLine(maxSum(arr, n)); ` ` ` `} ` `} ` ` ` `//This Code is contributed by vt_m. ` |

Output :

18

**Time Complexity: **O(nlogn).

**Auxiliary Space :** O(1)

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