# Longest alternating subsequence which has maximum sum of elements

• Last Updated : 19 Dec, 2022

Given a list of length N with positive and negative integers. The task is to choose the longest alternating subsequence of the given sequence (i.e. the sign of each next element is the opposite of the sign of the current element). Among all such subsequences, we have to choose one which has the maximum sum of elements and display that sum.

Examples:

Input: list = [-2 10 3 -8 -4 -1 5 -2 -3 1]
Output: 11
Explanation:
The largest subsequence with the greatest sum is [-2 10 -1 5 -2 1] with length 6.

Input: list=[12 4 -5 7 -9]
Output:
Explanation:
The largest subsequence with greatest sum is [12 -5 7 -9] with length 4.

Approach: The solution can be reached by the following approach:-

• To get alternating subsequences with maximum length and the largest sum, we will be traversing the whole list (length of list)-1 times for comparing signs of consecutive elements.
• During traversal, if we are getting more than 1 consecutive element of the same sign(exp. 1 2 4), then we will append the maximum element out of them to another list named large. so from 1, 2 and 4 we will append 4 to another list.
• If we have consecutive elements of opposite sign, we will simply add those elements to that list named large.
• Finally, the list named large will have the longest alternating subsequence with the largest elements.
• Now, we will have to calculate the sum of all elements from that list named large.

Lets take an example, we have a list [1, 2, 3, -2, -5, 1, -7, -1].

1. In traversing this list length-1 times, we are getting 1, 2, 3 with the same sign so we will append greatest of these (i.e 3) to another list named large here.
Hence large=[3]
2. Now -2 and -5 have the same sign so we will append -2 to another List.
large=[3, -2]
3. Now, the sign of 1 and -7 are opposite, so we will append 1 to large.
large=[3, -2, 1]
4. For -7, -1 signs are same, Hence append -1 to large.
large=[3, -2, 1, -1]
5. Calculate the sum = 3 – 2 + 1 – 1 = 1

Below is the implementation of the above approach:

## C++

 `// C++ implementation to find the``// longest alternating subsequence``// which has the maximum sum``#include``using` `namespace` `std;` `int` `calculateMaxSum(``int` `n, ``int` `li[])``{``    ` `    ``// Creating a temporary list ar to``    ``// every time store same sign element``    ``// to calculate maximum element from``    ``// that list ar``    ``vector<``int``> ar;``    ` `    ``// Appending 1st element of list li``    ``// to the ar``    ``ar.push_back(li[0]);``    ` `    ``// Creating list to store maximum``    ``// values``    ``vector<``int``> large;` `    ``for``(``int` `j = 0; j < n - 1; j++)``    ``{``       ` `       ``// If both number are positive``       ``// then append (j + 1)th element``       ``// to temporary list ar``       ``if``(li[j] > 0 and li[j + 1] > 0)``       ``{``           ``ar.push_back(li[j + 1]);``       ``}``       ``else` `if``(li[j] > 0 and li[j + 1] < 0)``       ``{``           ` `           ``// If opposite elements found``           ``// then append maximum element``           ``// to large list``           ``large.push_back(*max_element(ar.begin(),``                                        ``ar.end()));``                                        ` `           ``// Empty ar list to re-append``           ``// next elements``           ``ar.clear();``           ``ar.push_back(li[j + 1]);``       ``}``       ``else` `if``(li[j] < 0 and li[j + 1] > 0)``       ``{``           ` `           ``// If opposite elements found``           ``// then append maximum element``           ``// to large list``           ``large.push_back(*max_element(ar.begin(),``                                        ``ar.end()));``           ` `           ``// Empty ar list to re-append``           ``// next elements``           ``ar.clear();``           ``ar.push_back(li[j + 1]);``       ``}``       ``else``       ``{``           ``// If both number are negative``           ``// then append (j + 1)th element``           ``// to temporary list ar``           ``ar.push_back(li[j + 1]);``       ``}``    ``}``    ` `    ``// The final Maximum element in ar list``    ``// also needs to be appended to large list``    ``large.push_back(*max_element(ar.begin(),``                                 ``ar.end()));``    ` `    ``// Returning the sum of all elements``    ``// from largest elements list with``    ``// largest alternating subsequence size``    ``int` `sum = 0;``    ``for``(``int` `i = 0; i < large.size(); i++)``       ``sum += large[i];``    ``return` `sum;``}``    ` `// Driver code``int` `main()``{``    ``int` `list[] = { -2, 8, 3, 8, -4, -15,``                    ``5, -2, -3, 1 };``    ``int` `N = ``sizeof``(list) / ``sizeof``(list[0]);` `    ``cout << (calculateMaxSum(N, list));``}` `// This code is contributed by Bhupendra_Singh`

## Java

 `// Java implementation to find the``// longest alternating subsequence``// which has the maximum sum``import` `java.util.*;` `class` `GFG{` `static` `int` `calculateMaxSum(``int` `n, ``int` `li[])``{``    ` `    ``// Creating a temporary list ar to``    ``// every time store same sign element``    ``// to calculate maximum element from``    ``// that list ar``    ``Vector ar = ``new` `Vector<>();``    ` `    ``// Appending 1st element of list li``    ``// to the ar``    ``ar.add(li[``0``]);``    ` `    ``// Creating list to store maximum``    ``// values``    ``Vector large = ``new` `Vector<>();` `    ``for``(``int` `j = ``0``; j < n - ``1``; j++)``    ``{``        ` `        ``// If both number are positive``        ``// then append (j + 1)th element``        ``// to temporary list ar``        ``if``(li[j] > ``0` `&& li[j + ``1``] > ``0``)``        ``{``            ``ar.add(li[j + ``1``]);``        ``}``        ``else` `if``(li[j] > ``0` `&& li[j + ``1``] < ``0``)``        ``{``                ` `            ``// If opposite elements found``            ``// then append maximum element``            ``// to large list``            ``large.add(Collections.max(ar));``                                            ` `            ``// Empty ar list to re-append``            ``// next elements``            ``ar.clear();``            ``ar.add(li[j + ``1``]);``        ``}``        ``else` `if``(li[j] < ``0` `&& li[j + ``1``] > ``0``)``        ``{``                ` `            ``// If opposite elements found``            ``// then append maximum element``            ``// to large list``            ``large.add(Collections.max(ar));``                ` `            ``// Empty ar list to re-append``            ``// next elements``            ``ar.clear();``            ``ar.add(li[j + ``1``]);``        ``}``        ``else``        ``{``            ``// If both number are negative``            ``// then append (j + 1)th element``            ``// to temporary list ar``            ``ar.add(li[j + ``1``]);``        ``}``    ``}``    ` `    ``// The final Maximum element in ar list``    ``// also needs to be appended to large list``    ``large.add(Collections.max(ar));``    ` `    ``// Returning the sum of all elements``    ``// from largest elements list with``    ``// largest alternating subsequence size``    ``int` `sum = ``0``;``    ``for``(``int` `i = ``0``; i < large.size(); i++)``        ``sum += (``int``)large.get(i);``        ` `    ``return` `sum;``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``int` `list[] = { -``2``, ``8``, ``3``, ``8``, -``4``, -``15``,``                    ``5``, -``2``, -``3``, ``1` `};``    ``int` `N = (list.length);``    ` `    ``System.out.print(calculateMaxSum(N, list));``}``}` `// This code is contributed by Stream_Cipher`

## Python3

 `# Python3 implementation to find the``# longest alternating subsequence``# which has the maximum sum` `def` `calculateMaxSum(n, li):``    ``# Creating a temporary list ar to every``    ``# time store same sign element to``    ``# calculate maximum element from``    ``# that list ar``    ``ar ``=``[]``    ` `    ``# Appending 1st element of list li``    ``# to the ar``    ``ar.append(li[``0``])``    ` `    ``# Creating list to store maximum``    ``# values``    ``large ``=``[]``    ` `    ``for` `j ``in` `range``(``0``, n``-``1``):``        ` `        ``# If both number are positive``        ``# then append (j + 1)th element``        ``# to temporary list ar``        ``if``(li[j]>``0` `and` `li[j ``+` `1``]>``0``):``            ``ar.append(li[j ``+` `1``])``        ``elif``(li[j]>``0` `and` `li[j ``+` `1``]<``0``):``            ` `            ``# If opposite elements found``            ``# then append maximum element``            ``# to large list``            ``large.append(``max``(ar))``            ` `            ``# Empty ar list to re-append``            ``# next elements ``            ``ar ``=``[]``            ``ar.append(li[j ``+` `1``])``        ``elif``(li[j]<``0` `and` `li[j ``+` `1``]>``0``):``            ` `            ``# If opposite elements found``            ``# then append maximum element``            ``# to large list``            ``large.append(``max``(ar))``            ` `            ``# Empty ar list to re-append``            ``# next elements``            ``ar ``=``[]``            ``ar.append(li[j ``+` `1``])``        ``else``:``            ``# If both number are negative``            ``# then append (j + 1)th element``            ``# to temporary list ar``            ``ar.append(li[j ``+` `1``])``            ` `    ``# The final Maximum element in ar list``    ``# also needs to be appended to large list``    ``large.append(``max``(ar))``    ` `    ``# returning the sum of all elements``    ``# from largest elements list with``    ``# largest alternating subsequence size``    ``return` `sum``(large)`  `# Driver code``list` `=``[``-``2``, ``8``, ``3``, ``8``, ``-``4``, ``-``15``, ``5``, ``-``2``, ``-``3``, ``1``]``N ``=` `len``(``list``)` `print``(calculateMaxSum(N, ``list``))`

## C#

 `// C# implementation to find the``// longest alternating subsequence``// which has the maximum sum``using` `System;``using` `System.Collections.Generic;` `class` `GFG{` `static` `int` `find_max(List<``int``> ar)``{``    ``int` `mx = -1000000;``    ``foreach``(``var` `i ``in` `ar)``    ``{``        ``if``(i > mx)``           ``mx = i;``    ``}``    ``return` `mx;``}` `static` `int` `calculateMaxSum(``int` `n, ``int` `[]li)``{``    ` `    ``// Creating a temporary list ar to``    ``// every time store same sign element``    ``// to calculate maximum element from``    ``// that list ar``    ``List<``int``> ar = ``new` `List<``int``>();``    ` `    ``// Appending 1st element of list li``    ``// to the ar``    ``ar.Add(li[0]);``    ` `    ``// Creating list to store maximum``    ``// values``    ``List<``int``> large = ``new` `List<``int``>();` `    ``for``(``int` `j = 0; j < n - 1; j++)``    ``{``        ` `        ``// If both number are positive``        ``// then append (j + 1)th element``        ``// to temporary list ar``        ``if``(li[j] > 0 && li[j + 1] > 0)``        ``{``            ``ar.Add(li[j + 1]);``        ``}``        ``else` `if``(li[j] > 0 && li[j + 1] < 0)``        ``{``                ` `            ``// If opposite elements found``            ``// then append maximum element``            ``// to large list``            ``large.Add(find_max(ar));``                                            ` `            ``// Empty ar list to re-append``            ``// next elements``            ``ar.Clear();``            ``ar.Add(li[j + 1]);``        ``}``        ``else` `if``(li[j] < 0 && li[j + 1] > 0)``        ``{``                ` `            ``// If opposite elements found``            ``// then append maximum element``            ``// to large list``            ``large.Add(find_max(ar));``                ` `            ``// Empty ar list to re-append``            ``// next elements``            ``ar.Clear();``            ``ar.Add(li[j + 1]);``        ``}``        ``else``        ``{``            ` `            ``// If both number are negative``            ``// then append (j + 1)th element``            ``// to temporary list ar``            ``ar.Add(li[j + 1]);``        ``}``    ``}``    ` `    ``// The final Maximum element in ar list``    ``// also needs to be appended to large list``    ``large.Add(find_max(ar));``    ` `    ``// Returning the sum of all elements``    ``// from largest elements list with``    ``// largest alternating subsequence size``    ``int` `sum = 0;``    ``foreach``(``var` `i ``in` `large)``    ``{``        ``sum += i;``    ``}``    ``return` `sum;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `[]list = { -2, 8, 3, 8, -4, -15,``                    ``5, -2, -3, 1 };``    ``int` `N = (list.Length);``    ` `    ``Console.WriteLine(calculateMaxSum(N, list));``}``}` `// This code is contributed by Stream_Cipher   `

## Javascript

 ``

Output:

`6`

Time Complexity:O(N2)
Auxiliary Space: O(N)

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