Classic combinatorics-meets-string-manipulation type problem.
First, clarify the splitting criteria and constraints, as the problem is underspecified. Then, propose a dynamic programming solution where dp[i] represents the number of ways to split the prefix ending at i, and transition by checking all valid previous split points. Optimize with precomputation or sliding window if the criteria allow.
Pro tip: Always discuss time and space complexity trade-offs and mention edge cases like empty string or no valid splits. This shows you think about robustness and efficiency, which is crucial at Google.
Ask questions to understand the splitting criteria, constraints, and expected output. For example, what defines a valid part? Are parts contiguous? Can they be empty?
Let dp[i] be the number of ways to split the substring s[0..i-1] (or up to index i). Initialize dp[0] = 1 for the empty prefix.
For each i, iterate over possible previous split points j < i, and if the substring s[j..i-1] satisfies the criteria, add dp[j] to dp[i]. This yields O(n^2) time, which can be optimized.
If the criteria allow, use precomputation (e.g., prefix sums, hashing) or sliding window to reduce time complexity to O(n) or O(n log n). Discuss the trade-offs.
State the time and space complexity of your solution. Walk through examples, including edge cases like empty string, no valid splits, or all valid splits.
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