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 from 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.
Input: list = [-2 10 3 -8 -4 -1 5 -2 -3 1]
The largest subsequence with the greatest sum is [-2 10 -1 5 -2 1] with length 6.
Input: list=[12 4 -5 7 -9]
The largest subsequence with greatest sum is [12 -5 7 -9] with length 4.
Approach: The solution can be reached by following approach:-
- For getting alternating subsequence with maximum length and 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 elements of 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 element of opposite sign we will simply add those elements to that list named large.
- Finally the list named large will have longest alternating subsequence with 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].
- 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.
- Now -2 and -5 have the same sign so we will append -2 to another List.
- Now, the sign of 1 and -7 are opposite, so we will append 1 to large.
large=[3, -2, 1]
- For -7, -1 signs are same, Hence append -1 to large.
large=[3, -2, 1, -1]
- Calculate the sum = 3 – 2 + 1 – 1 = 1
Below is Python implementation of the above approach:-
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- Longest alternating subsequence with maximum sum | Set 2
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- Maximum length subsequence such that adjacent elements in the subsequence have a common factor
- Rearrange a given list such that it consists of alternating minimum maximum elements
- Longest subsequence with first and last element greater than all other elements
- Maximize sum of all elements which are not a part of the Longest Increasing Subsequence
- Longest subsequence such that adjacent elements have at least one common digit
- Length of the longest subsequence such that xor of adjacent elements is non-decreasing
- Longest Increasing Subsequence using Longest Common Subsequence Algorithm
- Length of longest subsequence in an Array having all elements as Nude Numbers
- Maximum sum subsequence with at-least k distant elements
- Maximum subsequence sum such that all elements are K distance apart
- Maximum subsequence sum of at most K-distant adjacent elements
- Maximum subsequence sum with adjacent elements having atleast K difference in index
- Length of largest subsequence consisting of a pair of alternating digits
- Length of the longest alternating even odd subarray
- Length of the longest alternating subarray
- Minimal product subsequence where adjacent elements are separated by a maximum distance of K
- Cost of creating smallest subsequence with sum of difference between adjacent elements maximum
Improved By : bgangwar59