How do you solve Find the Score of All Prefixes of an Array on LeetCode?

Find the Score of All Prefixes of an Array (LeetCode #2640) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Keep track of the maximum value seen so far to optimize calculations.

What is the time complexity of Find the Score of All Prefixes of an Array?

The optimal solution for Find the Score of All Prefixes of an Array runs in O(n) time and uses O(n) space. This complexity is linear because we only traverse the input array once, maintaining the maximum and calculating scores incrementally.

What is the brute force solution for Find the Score of All Prefixes of an Array?

The brute force approach for Find the Score of All Prefixes of an Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach calculates the conversion array for each prefix by finding the maximum value in the prefix repeatedly. This is straightforward but inefficient, as it recalculates the maximum for overlapping parts of the array. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Score of All Prefixes of an Array?

Find the Score of All Prefixes of an Array uses the following concepts: Array, Prefix Sum. The recommended patterns to study are: Prefix Sum, Dynamic Programming.

What are the interview tips for Find the Score of All Prefixes of an Array?

Always think about how you can reduce the number of calculations by storing intermediate results. Explain your thought process clearly; interviewers appreciate understanding your reasoning. Practice dry-running your code with examples to ensure you understand the flow and logic.

What are common mistakes when solving Find the Score of All Prefixes of an Array?

Not maintaining the maximum value efficiently, leading to unnecessary recalculations. Confusing the conversion array with the score array; they are related but distinct.

#2640

Find the Score of All Prefixes of an Array

Medium

ArrayPrefix SumPrefix SumDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

By maintaining a running maximum and using it to compute scores incrementally, we can avoid redundant calculations and achieve a linear time complexity.

⚙️

Algorithm

3 steps

1Step 1: Initialize an empty result array 'ans' and a variable 'max_so_far' to track the maximum value seen so far.
2Step 2: Iterate through the nums array, updating 'max_so_far' with the maximum value at each index.
3Step 3: For each index 'i', calculate ans[i] as ans[i-1] + nums[i] + max_so_far, handling the first index separately.

solution.py10 lines

1# Full working Python code
2
3def findPrefixScores(nums):
4    n = len(nums)
5    ans = [0] * n
6    max_so_far = 0
7    for i in range(n):
8        max_so_far = max(max_so_far, nums[i])
9        ans[i] = (ans[i - 1] + nums[i] + max_so_far) if i > 0 else (nums[i] + max_so_far)
10    return ans

ℹ

Complexity note: This complexity is linear because we only traverse the input array once, maintaining the maximum and calculating scores incrementally.

1Keep track of the maximum value seen so far to optimize calculations.
2Use cumulative sums to build results incrementally instead of recalculating.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.