C++ Program for Size of The Subarray With Maximum Sum

An array is given, find length of the subarray having maximum sum.

Examples : 

Input : a[] = {1, -2, 1, 1, -2, 1}
Output : Length of the subarray is 2
Explanation: Subarray with consecutive elements 
and maximum sum will be {1, 1}. So length is 2

Input : ar[] = { -2, -3, 4, -1, -2, 1, 5, -3 }
Output : Length of the subarray is 5
Explanation: Subarray with consecutive elements 
and maximum sum will be {4, -1, -2, 1, 5}. 

This problem is mainly a variation of Largest Sum Contiguous Subarray Problem.
The idea is to update starting index whenever sum ending here becomes less than 0.

5

Time Complexity: O(N) where N is size of the input array. This is because a for loop is executing from 1 to size of the array.

Space Complexity: O(1) as no extra space has been taken.

Approach#2: Using Kadane’s algorithm

This approach implements the Kadane’s algorithm to find the maximum subarray sum and returns the size of the subarray with maximum sum.

Algorithm:

1. Initialize max_sum, current_sum, start, end, max_start, and max_end to the first element of the array.
2. Iterate through the array from the second element.
3. If the current element is greater than the sum of the current element and current_sum, update start to the current index.
4. Update current_sum as the maximum of the current element and the sum of current element and current_sum.
5. If current_sum is greater than max_sum, update max_sum, end to the current index, and max_start and max_end to start and end  respectively.
6. Return max_end – max_start + 1 as the size of the subarray with maximum sum.

Below is the implementation of the approach:

5

Time Complexity: O(n), where n is length of array
Auxiliary Space: O(1)

Note: The above code assumes that there is at least one positive element in the array. If all the elements are negative, the code needs to be modified to return the maximum element in the array.

Please refer complete article on Size of The Subarray With Maximum Sum for more details!