GATE-CS-2017(Set 1) Problem 23 Introduction

This question is from Computer Science GATE 2017 (Set 1), Problem 23. It is a programming question that involves writing code to perform a specific task. The task involves finding the maximum sum of a subarray in a given array.

Problem Details

The problem statement for this question is as follows:

Given an array of integers, find the maximum sum of any contiguous subarray of the array.

We need to write a function with the following signature:

def maximum_sum_subarray(numbers: List[int]) -> int:
    pass

where numbers is a list of integers, and the function should return the maximum sum of any contiguous subarray of the input list.

Solution Approach

The basic idea behind solving this problem is to make use of Kadane's algorithm. The algorithm is based on the principle that any subarray A[i:j] can be written as A[j] - A[i-1]. If we use this principle, we can subtract the minimum prefix sum from the current sum at every index, and find the maximum difference possible. This difference is the maximum sum of any contiguous subarray in the given array.

The main steps involved in the solution approach are as follows:

1. Initialize two variables, max_sum and current_sum, to 0.
2. Iterate through the given input numbers list.
3. At every element, add it to the current_sum.
4. If the current_sum is less than 0, reset it to 0.
5. If the current_sum is greater than max_sum, set max_sum to current_sum.
6. Return the max_sum.

The code for this solution approach is as follows:

from typing import List

def maximum_sum_subarray(numbers: List[int]) -> int:
    max_sum = 0
    current_sum = 0
    
    for i in range(len(numbers)):
        current_sum += numbers[i]
        if current_sum < 0:
            current_sum = 0
        if current_sum > max_sum:
            max_sum = current_sum
            
    return max_sum

Conclusion

This question requires us to write a function that finds the maximum sum of any contiguous subarray in a given array of integers. We can solve this problem using Kadane's algorithm, which involves finding the maximum difference between the current sum and the minimum prefix sum at every index. The main steps involved in the solution approach are initializing variables, iterating through the input list, adding elements to the current sum, resetting the current sum if it is less than 0, and updating the max sum if required. The output is the maximum sum of any contiguous subarray in the given array.