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# Reverse a subarray to maximize sum of even-indexed elements of given array

• Difficulty Level : Hard
• Last Updated : 02 Aug, 2021

Given an array arr[], the task is to maximize the sum of even-indexed elements by reversing a subarray and print the maximum sum obtained.

Examples:

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Input: arr[] = {1, 2, 1, 2, 1}
Output:
Explanation:
Sum of initial even-indexed elements = a + a + a = 1 + 1 + 1 = 3
Reversing subarray {1, 2, 1, 2} modifies the array to {2, 1, 2, 1, 1}.
Hence, the maximized sum = 2 + 2 + 1 = 5

Input: arr[] = {7, 8, 4, 5, 7, 6, 8, 9, 7, 3}
Output: 37

Naive Approach:
The simplest approach to solve the problem is to generate all the possible permutations by reversal of elements one by one and calculate the sum at even indices for each permutation. Print the maximum possible sum among all the permutations.

Time Complexity: O(N3
Auxiliary Space: O(N)

Efficient Approach:
The above approach can be further optimized to O(N) computational complexity by using Dynamic Programming to check the maximum difference by rotation of arrays.
Follow the steps below to solve the problem:

• Compare the elements at odd index with even index and also keep track of them.
• Initialize two arrays leftDP[] and rightDP[].
• For every odd index, leftDP[] stores the difference of the element at current index with the element on its left and rightDP[] stores that of the right.
• If the difference calculated for the previous index is positive, add it to the current difference:

if(dp[i – 1] > 0)
dp[i] = dp[i-1] + curr_diff

• Otherwise, store the current difference:

dp[i] = curr_diff;

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function to return maximized sum``// at even indices``int` `maximizeSum(``int` `arr[], ``int` `n)``{``    ``int` `sum = 0;``    ``for``(``int` `i = 0; i < n; i = i + 2)``        ``sum += arr[i];` `    ``// Stores difference with``    ``// element on the left``    ``int` `leftDP[n / 2];` `    ``// Stores difference with``    ``// element on the right``    ``int` `rightDP[n / 2];` `    ``int` `c = 0;` `    ``for``(``int` `i = 1; i < n; i = i + 2)``    ``{``        ` `        ``// Compute and store``        ``// left difference``        ``int` `leftDiff = arr[i] - arr[i - 1];` `        ``// For first index``        ``if` `(c - 1 < 0)``            ``leftDP = leftDiff;` `        ``else``        ``{``            ` `            ``// If previous difference``            ``// is positive``            ``if` `(leftDP > 0)``                ``leftDP = leftDiff + leftDP;` `            ``// Otherwise``            ``else``                ``leftDP[i] = leftDiff;``        ``}` `        ``int` `rightDiff;` `        ``// For the last index``        ``if` `(i + 1 >= n)``            ``rightDiff = 0;` `        ``// Otherwise``        ``else``            ``rightDiff = arr[i] - arr[i + 1];` `        ``// For first index``        ``if` `(c - 1 < 0)``            ``rightDP = rightDiff;``        ``else``        ``{``            ` `            ``// If the previous difference``            ``// is positive``            ``if` `(rightDP > 0)``                ``rightDP = rightDiff +``                             ``rightDP;``            ``else``                ``rightDP = rightDiff;``        ``}``        ``c++;``    ``}``    ``int` `maxi = 0;``    ``for``(``int` `i = 0; i < n / 2; i++)``    ``{``        ``maxi = max(maxi, max(leftDP[i],``                            ``rightDP[i]));``    ``}``    ``return` `maxi + sum;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 7, 8, 4, 5, 7,``                  ``6, 8, 9, 7, 3 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);``    ``int` `ans = maximizeSum(arr, n);``    ` `    ``cout << (ans);``}` `// This code is contributed by chitranayal`

## Java

 `// Java Program to implement``// the above approach``import` `java.io.*;` `class` `GFG {` `    ``// Function to return maximized sum``    ``// at even indices``    ``public` `static` `int` `maximizeSum(``int``[] arr)``    ``{` `        ``int` `n = arr.length;``        ``int` `sum = ``0``;``        ``for` `(``int` `i = ``0``; i < n; i = i + ``2``)``            ``sum += arr[i];` `        ``// Stores difference with``        ``// element on the left``        ``int` `leftDP[] = ``new` `int``[n / ``2``];` `        ``// Stores difference with``        ``// element on the right``        ``int` `rightDP[] = ``new` `int``[n / ``2``];` `        ``int` `c = ``0``;` `        ``for` `(``int` `i = ``1``; i < n; i = i + ``2``) {` `            ``// Compute and store``            ``// left difference``            ``int` `leftDiff = arr[i]``                           ``- arr[i - ``1``];` `            ``// For first index``            ``if` `(c - ``1` `< ``0``)``                ``leftDP = leftDiff;` `            ``else` `{` `                ``// If previous difference``                ``// is positive``                ``if` `(leftDP > ``0``)``                    ``leftDP = leftDiff``                                ``+ leftDP;` `                ``// Otherwise``                ``else``                    ``leftDP[i] = leftDiff;``            ``}` `            ``int` `rightDiff;` `            ``// For the last index``            ``if` `(i + ``1` `>= arr.length)``                ``rightDiff = ``0``;` `            ``// Otherwise``            ``else``                ``rightDiff = arr[i]``                            ``- arr[i + ``1``];` `            ``// For first index``            ``if` `(c - ``1` `< ``0``)``                ``rightDP = rightDiff;``            ``else` `{` `                ``// If the previous difference``                ``// is positive``                ``if` `(rightDP > ``0``)``                    ``rightDP = rightDiff``                                 ``+ rightDP;``                ``else``                    ``rightDP = rightDiff;``            ``}``            ``c++;``        ``}``        ``int` `max = ``0``;``        ``for` `(``int` `i = ``0``; i < n / ``2``; i++) {``            ``max = Math.max(max,``                           ``Math.max(``                               ``leftDP[i],``                               ``rightDP[i]));``        ``}` `        ``return` `max + sum;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``7``, ``8``, ``4``, ``5``, ``7``, ``6``,``                      ``8``, ``9``, ``7``, ``3` `};``        ``int` `ans = maximizeSum(arr);``        ``System.out.println(ans);``    ``}``}`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to return maximized sum``# at even indices``def` `maximizeSum(arr):` `    ``n ``=` `len``(arr)``    ``sum` `=` `0` `    ``for` `i ``in` `range``(``0``, n, ``2``):``        ``sum` `+``=` `arr[i]` `    ``# Stores difference with``    ``# element on the left``    ``leftDP ``=` `[``0``] ``*` `(n)` `    ``# Stores difference with``    ``# element on the right``    ``rightDP ``=` `[``0``] ``*` `(n)` `    ``c ``=` `0``    ``for` `i ``in` `range``(``1``, n, ``2``):` `        ``# Compute and store``        ``# left difference``        ``leftDiff ``=` `arr[i] ``-` `arr[i ``-` `1``]` `        ``# For first index``        ``if` `(c ``-` `1` `< ``0``):``            ``leftDP[i] ``=` `leftDiff``        ``else``:` `            ``# If previous difference``            ``# is positive``            ``if` `(leftDP[i] > ``0``):``                ``leftDP[i] ``=` `(leftDiff ``+``                             ``leftDP[i ``-` `1``])` `            ``# Otherwise``            ``else``:``                ``leftDP[i] ``=` `leftDiff` `        ``rightDiff ``=` `0` `        ``# For the last index``        ``if` `(i ``+` `1` `>``=` `len``(arr)):``            ``rightDiff ``=` `0``            ` `        ``# Otherwise``        ``else``:``            ``rightDiff ``=` `arr[i] ``-` `arr[i ``+` `1``]` `        ``# For first index``        ``if` `(c ``-` `1` `< ``0``):``            ``rightDP[i] ``=` `rightDiff``        ``else``:` `            ``# If the previous difference``            ``# is positive``            ``if` `(rightDP[i] > ``0``):``                ``rightDP[i] ``=` `(rightDiff ``+``                              ``rightDP[i ``-` `1``])``            ``else``:``                ``rightDP[i] ``=` `rightDiff``                ` `        ``c ``+``=` `1` `    ``maxm ``=` `0` `    ``for` `i ``in` `range``(n ``/``/` `2``):``        ``maxm ``=` `max``(maxm, ``max``(leftDP[i],``                            ``rightDP[i]))` `    ``return` `maxm ``+` `sum` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[ ``7``, ``8``, ``4``, ``5``, ``7``,``            ``6``, ``8``, ``9``, ``7``, ``3` `]``    ``ans ``=` `maximizeSum(arr)` `    ``print``(ans)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to implement``// the above approach``using` `System;` `class` `GFG{` `// Function to return maximized sum``// at even indices``public` `static` `int` `maximizeSum(``int``[] arr)``{``    ``int` `n = arr.Length;``    ``int` `sum = 0;``    ` `    ``for``(``int` `i = 0; i < n; i = i + 2)``        ``sum += arr[i];` `    ``// Stores difference with``    ``// element on the left``    ``int` `[]leftDP = ``new` `int``[n / 2];` `    ``// Stores difference with``    ``// element on the right``    ``int` `[]rightDP = ``new` `int``[n / 2];` `    ``int` `c = 0;` `    ``for``(``int` `i = 1; i < n; i = i + 2)``    ``{``        ` `        ``// Compute and store``        ``// left difference``        ``int` `leftDiff = arr[i] - arr[i - 1];` `        ``// For first index``        ``if` `(c - 1 < 0)``            ``leftDP = leftDiff;``            ` `        ``else``        ``{``            ` `            ``// If previous difference``            ``// is positive``            ``if` `(leftDP > 0)``                ``leftDP = leftDiff +``                            ``leftDP;``                            ` `            ``// Otherwise``            ``else``                ``leftDP = leftDiff;``        ``}` `        ``int` `rightDiff;` `        ``// For the last index``        ``if` `(i + 1 >= arr.Length)``            ``rightDiff = 0;` `        ``// Otherwise``        ``else``            ``rightDiff = arr[i] - arr[i + 1];` `        ``// For first index``        ``if` `(c - 1 < 0)``            ``rightDP = rightDiff;``            ` `        ``else``        ``{``            ` `            ``// If the previous difference``            ``// is positive``            ``if` `(rightDP > 0)``                ``rightDP = rightDiff +``                             ``rightDP;``            ``else``                ``rightDP = rightDiff;``        ``}``        ``c++;``    ``}``    ` `    ``int` `max = 0;``    ` `    ``for``(``int` `i = 0; i < n / 2; i++)``    ``{``        ``max = Math.Max(max,``                       ``Math.Max(leftDP[i],``                               ``rightDP[i]));``    ``}``    ``return` `max + sum;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 7, 8, 4, 5, 7, 6,``                  ``8, 9, 7, 3 };``    ``int` `ans = maximizeSum(arr);``    ` `    ``Console.WriteLine(ans);``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`37`

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

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