Find the Score of All Prefixes of an Array

Find the Score of All Prefixes of an Array

1. What is this problem about?

The Find the Score of All Prefixes of an Array interview question involves a two-step transformation of an array. First, you define a conversion array conver where conver[i] = nums[i] + max(nums[0...i]). Then, the "score" of each prefix is the sum of all elements in the conver array up to that index. You need to return the array of these prefix scores.

2. Why is this asked in interviews?

TikTok asks the Find the Score of All Prefixes coding problem to test a candidate's ability to implement multi-step array processing efficiently. It evaluates your skills in Prefix Sum interview patterns and maintaining a "Running Maximum." It checks if you can perform both transformations in a single pass to achieve $O(N)$ time complexity.

3. Algorithmic pattern used

This problem follows the Running Maximum and Prefix Sum pattern.

• Maintain State: Keep track of the max_seen_so_far.
• Maintain Running Total: Keep track of the sum of the conver values calculated so far.
• Linear Scan: For each element:
  1. Update max_seen = max(max_seen, nums[i]).
  2. Calculate conver_val = nums[i] + max_seen.
  3. Add conver_val to the current_score_sum.
  4. Store current_score_sum in the result array.

4. Example explanation

Array: [2, 3, 7, 5, 10]

• $i=0$: max=2, conver=2+2=4. Score: 4.
• $i=1$: max=3, conver=3+3=6. Score: $4+6=10$.
• $i=2$: max=7, conver=7+7=14. Score: $10+14=24$. Result: [4, 10, 24, ...]

5. Common mistakes candidates make

• $O(N^2)$ Max search: Searching for the maximum of the prefix from scratch at every index.
• $O(N^2)$ Summation: Calculating the sum of the conversion array from the beginning for every index.
• Integer Overflow: The scores can grow very large, especially with 100,000 elements. Use long (64-bit integers) for the summation and result array.

6. Interview preparation tip

Be attentive to the "cumulative" nature of the operations. If a step depends on the "max of prefix" or "sum of prefix," you can always update the previous answer in $O(1)$ rather than re-calculating. This is the essence of the Array interview pattern.