Find the Score of All Prefixes of an Array

Problem Description

Given a 0-indexed integer array nums of length n, return an array ans of length n where ans[i] is the score of the prefix nums[0..i]. The score is defined as the sum of the conversion array conver, where conver[i] = nums[i] + max(nums[0..i]).

Key Insights

• The conversion array for each prefix is dependent on the maximum value found in that prefix.
• We can maintain a running maximum as we iterate through the array, which eliminates the need to recompute the maximum for each prefix.
• The score for each prefix can be computed incrementally by adding the current conversion value to a running total.

Space and Time Complexity

Time Complexity: O(n) - We traverse the array once.
Space Complexity: O(n) - We store the result in an output array of the same length.

Solution

To solve the problem, we will:

1. Initialize a variable to keep track of the current maximum value in the array.
2. Iterate through the input array, updating the maximum and calculating the conversion value for each prefix.
3. Maintain a running sum to keep track of the total score for the prefixes.

The main data structures used are an array to store the result and a variable to hold the maximum value.

Code Solutions