GATE-CS-2002 Question 3

This is a programming question that tests your understanding of basic data structures and algorithms. In this question, you will be asked to write a Python program that takes a list of integers as input and returns the maximum sum of consecutive numbers in the list.

Algorithm

To solve this problem, we can use a modified version of the Kadane's algorithm. The Kadane's algorithm is an optimization of the brute-force approach where we find all possible subarrays and return the maximum sum. In Kadane's algorithm, we assume that the maximum sum is the sum of the subarray ending at the current index or the current element itself. We update the maximum sum and the current sum at each step.

For this problem, we can modify Kadane's algorithm to handle negative numbers as well. We can keep track of two variables, max_sum and current_sum, where max_sum is the maximum sum seen so far and current_sum is the sum of the current subarray. If current_sum becomes negative, we reset it to 0 since a negative subarray cannot add to the maximum sum. We update max_sum at each step and return it as the final result.

Solution

Here's the Python program to solve this problem:

def max_sum_subarray(arr):
    max_sum = arr[0]
    current_sum = 0
    for i in arr:
        current_sum += i
        if current_sum > max_sum:
            max_sum = current_sum
        if current_sum < 0:
            current_sum = 0
    return max_sum

This program takes a list of integers as input and returns the maximum sum of consecutive numbers in the list. We initialize max_sum to the first element of the list and current_sum to 0. We iterate over the list, adding each element to current_sum. If current_sum becomes greater than max_sum, we update max_sum. If current_sum becomes negative, we reset it to 0. We return max_sum as the final result.

Conclusion

In this question, we learned how to find the maximum sum of consecutive numbers in a list using a modified version of the Kadane's algorithm. We also implemented the solution using Python. This problem is a good practice exercise for learning basic data structures and algorithms.