Maximum Sum Subsequence

Given an array arr[] of size N, the task is to find the maximum sum non-empty subsequence present in the given array.

Examples:

Input: arr[] = { 2, 3, 7, 1, 9 } 
Output: 22 
Explanation: 
Sum of the subsequence { arr[0], arr[1], arr[2], arr[3], arr[4] } is equal to 22, which is the maximum possible sum of any subsequence of the array. 
Therefore, the required output is 22.

Input: arr[] = { -2, 11, -4, 2, -3, -10 } 
Output: 13 
Explanation: 
Sum of the subsequence { arr[1], arr[3] } is equal to 13, which is the maximum possible sum of any subsequence of the array. 
Therefore, the required output is 13.

Naive Approach: The simplest approach to solve this problem is to generate all possible non-empty subsequences of the array and calculate the sum of each subsequence of the array. Finally, print the maximum sum obtained from the subsequence.

 Time Complexity: O(N * 2^N) 
Auxiliary Space: O(N)

Efficient Approach: The idea is to traverse the array and calculate the sum of positive elements of the array and print the sum obtained. Follow the steps below to solve the problem:

• Check if the largest element of the array is greater than 0 or not. If found to be true, then traverse the array and print the sum of all positive elements of the array.
• Otherwise, print the largest element present in the array.

Below is the implementation of the above approach:

13

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