Maximum Sum Score of Array Solution in Python

Problem Description

Welcome to the world of competitive programming! The “Maximum Sum Score of Array” problem is like trying to find the best way to split a pizza among friends without anyone getting upset. You have an array of integers, and your goal is to maximize the sum score by cleverly choosing how to split it.

Imagine you have a group of friends, and you want to impress them with your pizza-slicing skills. You can either take a slice from the left or the right, but you want to make sure you end up with the biggest slice possible. The challenge is to figure out how to do this without making a mess of the pizza (or the array, in this case).

Code Solution


import math

class Solution:
    def maximumSumScore(self, nums: list[int]) -> int:
        ans = -math.inf
        prefix = 0
        summ = sum(nums)

        for num in nums:
            prefix += num
            ans = max(ans, prefix, summ - prefix + num)

        return ans

Approach Explanation

The approach taken in this code is as straightforward as your last-minute decision to order pizza instead of cooking. The algorithm maintains a running total (prefix) of the sum of elements as it iterates through the array. It also keeps track of the total sum of the array (summ). For each element, it calculates the maximum score by considering both the current prefix and the remaining elements.

In simpler terms, it’s like checking how much pizza you’ve eaten so far and how much is left, then deciding if you want to keep going or take a slice from the other side.

Time and Space Complexity

Complexity Type	Complexity
Time Complexity	O(n), where n is the number of elements in the array. We traverse the array once.
Space Complexity	O(1), as we are using a constant amount of space for variables.

Real-World Example

Let’s say you’re at a party with a giant cake. You can either take a slice from the left or the right. The goal is to maximize the amount of cake you eat. If you keep track of how much cake you’ve eaten and how much is left, you can make a better decision on which slice to take next. This is essentially what the algorithm does with the array!