The Amazon framing about 'major vs minor actions' threw me off for a second because I kept trying to make the business context mean something for the solution.
Clarify the problem constraints and edge cases, then propose an efficient algorithm using prefix sums and hashing to count valid substrings in O(n) time. Explain the transformation of the condition into a prefix sum equation and how to handle the square relationship.
Pro tip: Discuss the time and space complexity trade-offs and mention how you would test the solution with edge cases like empty string or all zeros. This shows you consider production quality and not just correctness.
Restate the problem in your own words and ask clarifying questions about input size, character set, and expected output. Confirm that substrings are contiguous and that we count all occurrences.
Mention that a naive O(n^2) solution checks all substrings and counts zeros and ones, but it's inefficient for large n. This sets the stage for optimization.
Define prefix counts of zeros and ones. For a substring from i to j, the condition is (Z_j - Z_i) = (O_j - O_i)^2. Rearrange to find a relationship between prefix sums that can be checked efficiently.
Iterate through the string, maintaining counts of zeros and ones. For each position, compute the required value based on the equation and use a hash map to count how many previous prefixes satisfy it.
State that the algorithm runs in O(n) time and O(n) space. Discuss edge cases: empty string, no valid substrings, all zeros, all ones, and large inputs.
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