Explanation of Calculating the Sum of a List Using Divide and Conquer

We will write a function to calculate the sum of all elements in a given list of integers using the divide and conquer method.

This approach is implemented using recursive functions.

Function Implementation

1. Main Function solution:

   • It receives the list and the start and end indices, passing them to the recursive_sum function.

2. Recursive Function recursive_sum:

   • Base Case Handling:

     • If the list is empty (start > end), it returns 0.

     • If there is only one element in the list (start == end), it returns that element.

   • Divide Step:

     • The list is split into two parts at the midpoint.

   • Conquer Step:

     • The sum for each part is calculated recursively.

   • Combine Step:

     • The sums of the two parts are added together and returned.

Sample Solution

def solution(numbers):
    # Main function
    return recursive_sum(numbers, 0, len(numbers) - 1)

def recursive_sum(numbers, start, end):
    # Base case handling
    if start > end:
        return 0
    if start == end:
        return numbers[start]

    # Divide step
    mid = (start + end) // 2

    # Conquer step
    left_sum = recursive_sum(numbers, start, mid)
    right_sum = recursive_sum(numbers, mid + 1, end)

    # Combine step
    return left_sum + right_sum

Usage Example

Input/Output Example

print(solution([1, 2, 3, 4, 5]))  # Output: 15

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