# Maximize difference between sum of even and odd-indexed elements of a subsequence

• Difficulty Level : Expert
• Last Updated : 20 May, 2021

Given an array arr[] consisting of N positive integers, the task is to find the maximum possible difference between the sum of even and odd-indexed elements of a subsequence from the given array.

Examples:

Input: arr[] = { 3, 2, 1, 4, 5, 2, 1, 7, 8, 9 }
Output: 15
Explanation:
Considering the subsequences { 3, 1, 5, 1, 9 } from the array
Sum of even-indexed array elements = 3 + 5 + 9 = 17
Sum of odd-indexed array elements = is 1 + 1 = 2
Therefore, the difference between the sum of even and odd-indexed elements present in the subsequence = (17 – 2) = 15, which is the maximum possible.

Input: arr[] = {1, 2, 3, 4, 5, 6}
Output: 6

Naive Approach: The simplest approach to solve this problem is to generate all possible subsequences of the given array and for each subsequence, calculate the difference between the sum of even and odd indexed elements of the subsequence. Finally, print the maximum difference obtained.

Time Complexity: O(2N)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is to store the local maxima at even indices of the subsequence and store the local minima at odd indices of the subsequence. Finally, print the difference between the sum of even and odd indices of the subsequence.
Follow the steps below to solve the problem:

• Initialize a variable, say maxDiff, to store the maximum difference between the sum of even and odd-indexed elements of a subsequence.
• Traverse the array arr[] and check if arr[i] > arr[i + 1] and arr[i] < arr[i – 1] or not. If found to be true, then update maxDiff += arr[i].
• Otherwise, check if arr[i] > arr[i + 1] and arr[i] < arr[i – 1] or not. If found to be true, then update maxDiff -= arr[i].
• Finally, print the value of maxDiff.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to find the maximum possible difference``// between sum of even and odd indices``int` `maxPossibleDiff(vector<``int``>& arr, ``int` `N)``{` `    ``// Convert arr[] into 1-based indexing``    ``arr.push_back(-1);` `    ``// Reverse the array``    ``reverse(arr.begin(), arr.end());` `    ``// Convert arr[] into 1 based index``    ``arr.push_back(-1);` `    ``// Reverse the array``    ``reverse(arr.begin(), arr.end());` `    ``// Stores maximum difference between``    ``// sum of even and odd indexed elements``    ``int` `maxDiff = 0;` `    ``// Traverse the array``    ``for` `(``int` `i = 1; i <= N; i++) {` `        ``// If arr[i] is local maxima``        ``if` `(arr[i] > arr[i - 1]``            ``&& arr[i] > arr[i + 1]) {` `            ``// Update maxDiff``            ``maxDiff += arr[i];``        ``}` `        ``// If arr[i] is local minima``        ``if` `(arr[i] < arr[i - 1]``            ``&& arr[i] < arr[i + 1]) {` `            ``// Update maxDiff``            ``maxDiff -= arr[i];``        ``}``    ``}``    ``cout << maxDiff;``}` `// Driver Code``int` `main()``{` `    ``vector<``int``> arr = { 3, 2, 1, 4, 5,``                        ``2, 1, 7, 8, 9 };` `    ``// Size of array``    ``int` `N = arr.size();` `    ``// Function Call``    ``maxPossibleDiff(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;` `class` `GFG{` `// Function to find the maximum possible``// difference between sum of even and``// odd indices``static` `void` `maxPossibleDiff(Vector arr, ``int` `N)``{``    ` `    ``// Convert arr[] into 1-based indexing``    ``arr.add(-``1``);` `    ``// Reverse the array``    ``Collections.reverse(arr);` `    ``// Convert arr[] into 1 based index``    ``arr.add(-``1``);` `    ``// Reverse the array``    ``Collections.reverse(arr);` `    ``// Stores maximum difference between``    ``// sum of even and odd indexed elements``    ``int` `maxDiff = ``0``;` `    ``// Traverse the array``    ``for``(``int` `i = ``1``; i <= N; i++)``    ``{``        ` `        ``// If arr.get(i) is local maxima``        ``if` `(arr.get(i) > arr.get(i - ``1``) &&``            ``arr.get(i) > arr.get(i + ``1``))``        ``{``            ` `            ``// Update maxDiff``            ``maxDiff += arr.get(i);``        ``}` `        ``// If arr.get(i) is local minima``        ``if` `(arr.get(i) < arr.get(i - ``1``) &&``            ``arr.get(i) < arr.get(i + ``1``))``        ``{``            ` `            ``// Update maxDiff``            ``maxDiff -= arr.get(i);``        ``}``    ``}``    ``System.out.print(maxDiff);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int``[] array = { ``3``, ``2``, ``1``, ``4``, ``5``,``                    ``2``, ``1``, ``7``, ``8``, ``9` `};``    ``Vector v = ``new` `Vector<>();``    ``for``(``int` `i :array)``    ``{``        ``v.add(i);``    ``}``    ` `    ``// Size of array``    ``int` `N = v.size();` `    ``// Function Call``    ``maxPossibleDiff(v, N);``}``}` `// This code is contributed by shikhasingrajput`

## Python3

 `#Python3 program to implement``#the above approach`  `#Function to find the maximum possible difference``#between sum of even and odd indices``def` `maxPossibleDiff(arr,  N):` `    ``#Convert arr[] o 1-based indexing``    ``arr.append(``-``1``)` `    ``#Reverse the array``    ``arr ``=` `arr[::``-``1``]` `    ``#Convert arr[] o 1 based index``    ``arr.append(``-``1``)` `    ``#Reverse the array``    ``arr ``=` `arr[::``-``1``]` `    ``#Stores maximum difference between``    ``#sum of even and odd indexed elements``    ``maxDiff ``=` `0` `    ``#Traverse the array``    ``for` `i ``in` `range``(``1``,N``+``1``):` `        ``#If arr[i] is local maxima``        ``if` `(arr[i] > arr[i ``-` `1``] ``and` `arr[i] > arr[i ``+` `1``]):` `            ``#Update maxDiff``            ``maxDiff ``+``=` `arr[i]` `        ``#If arr[i] is local minima``        ``if` `(arr[i] < arr[i ``-` `1``] ``and` `arr[i] < arr[i ``+` `1``]):` `            ``#Update maxDiff``            ``maxDiff ``-``=` `arr[i]``    ``print` `(maxDiff)` `#Driver Code``if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``3``, ``2``, ``1``, ``4``, ``5``, ``2``, ``1``, ``7``, ``8``, ``9``]` `    ``#Size of array``    ``N ``=` `len``(arr)` `    ``#Function Call``    ``maxPossibleDiff(arr, N)`

## C#

 `// C# program to implement``// the above approach``using` `System;``using` `System.Collections.Generic;` `public` `class` `GFG{` `// Function to find the maximum possible``// difference between sum of even and``// odd indices``static` `void` `maxPossibleDiff(List<``int``> arr, ``int` `N)``{``    ` `    ``// Convert []arr into 1-based indexing``    ``arr.Add(-1);` `    ``// Reverse the array``    ``arr.Reverse();` `    ``// Convert []arr into 1 based index``    ``arr.Add(-1);` `    ``// Reverse the array``    ``arr.Reverse();` `    ``// Stores maximum difference between``    ``// sum of even and odd indexed elements``    ``int` `maxDiff = 0;` `    ``// Traverse the array``    ``for``(``int` `i = 1; i <= N; i++)``    ``{``        ` `        ``// If arr[i] is local maxima``        ``if` `(arr[i] > arr[i - 1] &&``            ``arr[i] > arr[i + 1])``        ``{``            ` `            ``// Update maxDiff``            ``maxDiff += arr[i];``        ``}` `        ``// If arr[i] is local minima``        ``if` `(arr[i] < arr[i - 1] &&``            ``arr[i] < arr[i + 1])``        ``{``            ` `            ``// Update maxDiff``            ``maxDiff -= arr[i];``        ``}``    ``}``    ``Console.Write(maxDiff);``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int``[] array = { 3, 2, 1, 4, 5,``                    ``2, 1, 7, 8, 9 };``    ``List<``int``> v = ``new` `List<``int``>();``    ``foreach``(``int` `i ``in` `array)``    ``{``        ``v.Add(i);``    ``}``    ` `    ``// Size of array``    ``int` `N = v.Count;` `    ``// Function Call``    ``maxPossibleDiff(v, N);``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 `   `
Output:
`15`

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

My Personal Notes arrow_drop_up