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# Rearrange an array to minimize sum of product of consecutive pair elements

We are given an array of even size, we have to sort the array in such a way that the sum of product of alternate elements is minimum also we have to find that minimum sum.

Examples:

```Input : arr[] = {9, 2, 8, 4, 5, 7, 6, 0}
Output : Minimum sum of the product of
consecutive pair elements: 74
Sorted arr[] for minimum sum:
{9, 0, 8, 2, 7, 4, 6, 5}
Explanation : We get 74 using below
calculation in rearranged array.
9*0 + 8*2 + 7*4 + 6*5 = 74

Input : arr[] = {1, 2, 1, 4, 0, 5, 6, 0}
Output : Minimum sum of the product of
consecutive pair elements: 6
Sorted arr[] for minimum sum:
{6, 0, 5, 0, 4, 1, 2, 1}
Explanation : We get 6 using below:
6*0 + 5*0 + 4*1 + 2*1 = 6```

This problem is a variation of Minimize the sum of product of two arrays with permutations allowed

For rearranging the array in such a way that we should get the sum of the product of consecutive element pairs is minimum we should have all even index element in decreasing and odd index element in increasing order with all n/2 maximum elements as even indexed and next n/2 elements as odd indexed or vice-versa.

Now, for that our idea is simple, we should sort the main array and further create two auxiliary arrays evenArr[] and oddArr[] respectively. We traverse input array and put n/2 maximum elements in evenArr[] and next n/2 elements in oddArr[]. Then we sort evenArr[] in descending and oddArr[] in ascending order. Finally, copy evenArr[] and oddArr[] element by element to get the required result and should calculate the minimum required sum.

Below is the implementation of above approach :

## C++

 `// C++ program to sort an array such that``// sum of product of alternate element``// is minimum.``#include ``using` `namespace` `std;` `int` `minSum(``int` `arr[], ``int` `n)``{``    ``// create evenArr[] and oddArr[]``    ``vector<``int``> evenArr;``    ``vector<``int``> oddArr;` `    ``// sort main array in ascending order``    ``sort(arr, arr+n );` `    ``// Put elements in oddArr[] and evenArr[]``    ``// as per desired value.``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``if` `(i < n/2)``            ``oddArr.push_back(arr[i]);``        ``else``            ``evenArr.push_back(arr[i]);``    ``}` `    ``// sort evenArr[] in descending order``    ``sort(evenArr.begin(), evenArr.end(), greater<``int``>());` `    ``// merge both sub-array and``    ``// calculate minimum sum of``    ``// product of alternate elements``    ``int` `i = 0, sum = 0;``    ``for` `(``int` `j=0; j

## Java

 `// Java program to sort an array such that``// sum of product of alternate element``// is minimum.` `import` `java.util.Arrays;``import` `java.util.Collections;``import` `java.util.Comparator;``import` `java.util.Vector;` `class` `GFG {` `    ``static` `int` `minSum(``int` `arr[], ``int` `n) {``        ``// create evenArr[] and oddArr[]``        ``Vector evenArr = ``new` `Vector<>();``        ``Vector oddArr = ``new` `Vector<>();` `        ``// sort main array in ascending order``        ``Arrays.sort(arr);` `        ``// Put elements in oddArr[] and evenArr[]``        ``// as per desired value.``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``if` `(i < n / ``2``) {``                ``oddArr.add(arr[i]);``            ``} ``else` `{``                ``evenArr.add(arr[i]);``            ``}``        ``}` `        ``// sort evenArr[] in descending order``        ``Comparator comparator = Collections.reverseOrder();``        ``Collections.sort(evenArr,comparator);` `        ``// merge both sub-array and``        ``// calculate minimum sum of``        ``// product of alternate elements``        ``int` `i = ``0``, sum = ``0``;``        ``for` `(``int` `j = ``0``; j < evenArr.size(); j++) {``            ``arr[i++] = evenArr.get(j);``            ``arr[i++] = oddArr.get(j);``            ``sum += evenArr.get(j) * oddArr.get(j);``        ``}` `        ``return` `sum;``    ``}` `// Driver program``    ``public` `static` `void` `main(String[] args) {` `        ``int` `arr[] = {``1``, ``5``, ``8``, ``9``, ``6``, ``7``, ``3``, ``4``, ``2``, ``0``};``        ``int` `n = arr.length;``        ``System.out.println(``"Minimum required sum = "``                                  ``+ minSum(arr, n));``        ``System.out.println(``"Sorted array in required format : "``);``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``System.out.print(arr[i] + ``" "``);``        ``}` `    ``}` `}`

## Python3

 `# Python 3 program to sort an array such``# that sum of product of alternate element``# is minimum.``def` `minSum(arr, n):` `    ``# create evenArr[] and oddArr[]``    ``evenArr ``=` `[]``    ``oddArr ``=` `[]` `    ``# sort main array in ascending order``    ``arr.sort()` `    ``# Put elements in oddArr[] and``    ``# evenArr[] as per desired value.``    ``for` `i ``in` `range``(n):``    ` `        ``if` `(i < n ``/``/` `2``):``            ``oddArr.append(arr[i])``        ``else``:``            ``evenArr.append(arr[i])` `    ``# sort evenArr[] in descending order``    ``evenArr.sort(reverse ``=` `True``)` `    ``# merge both sub-array and``    ``# calculate minimum sum of``    ``# product of alternate elements``    ``i ``=` `0``    ``sum` `=` `0``    ``for` `j ``in` `range``(``len``(evenArr)):``        ``arr[i] ``=` `evenArr[j]``        ``i ``+``=` `1``        ``arr[i] ``=` `oddArr[j]``        ``i ``+``=` `1``        ``sum` `+``=` `evenArr[j] ``*` `oddArr[j]``    ` `    ``return` `sum` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``arr ``=` `[ ``1``, ``5``, ``8``, ``9``, ``6``, ``7``, ``3``, ``4``, ``2``, ``0` `]``    ``n ``=` `len``(arr)``    ``print``( ``"Minimum required sum ="``,``                      ``minSum(arr, n))``    ``print``(``"Sorted array in required format : "``,``                                      ``end ``=` `"")``    ``for` `i ``in` `range``(n):``        ``print``(arr[i], end ``=` `" "``)` `# This code is contributed by ita_c`

## C#

 `// Program to sort an array such that``// sum of product of alternate element``// is minimum.``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{``static` `int` `minSum(``int` `[]arr, ``int` `n)``{``    ``// create evenArr[] and oddArr[]``    ``List<``int``> evenArr = ``new` `List<``int``>();``    ``List<``int``> oddArr = ``new` `List<``int``>();``    ``int` `i;``    ` `    ``// sort main array in ascending order``    ``Array.Sort(arr);` `    ``// Put elements in oddArr[] and``    ``// evenArr[] as per desired value.``    ``for` `(i = 0; i < n; i++)``    ``{``        ``if` `(i < n / 2)``        ``{``            ``oddArr.Add(arr[i]);``        ``}``        ``else``        ``{``            ``evenArr.Add(arr[i]);``        ``}``    ``}` `    ``// sort evenArr[] in descending order``    ``evenArr.Sort();``    ``evenArr.Reverse();` `    ``// merge both sub-array and``    ``// calculate minimum sum of``    ``// product of alternate elements``    ``int` `k = 0, sum = 0;``    ``for` `(``int` `j = 0; j < evenArr.Count; j++)``    ``{``        ``arr[k++] = evenArr[j];``        ``arr[k++] = oddArr[j];``        ``sum += evenArr[j] * oddArr[j];``    ``}` `    ``return` `sum;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `[]arr = {1, 5, 8, 9, 6,``                 ``7, 3, 4, 2, 0};``    ``int` `n = arr.Length;``    ``Console.WriteLine(``"Minimum required sum = "` `+``                                 ``minSum(arr, n));``    ``Console.WriteLine(``"Sorted array in "` `+``                    ``"required format : "``);``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``Console.Write(arr[i] + ``" "``);``    ``}``}``}` `// This code contributed by 29AjayKumar`

## Javascript

 ``

Output

```Minimum required sum = 60
Sorted array in required format : 9 0 8 1 7 2 6 3 5 4 ```

Time Complexity: O(nlog(n))
Auxiliary Space: O(n)