Salesforce·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Salesforce SWE interview, got a dynamic programming problem involving prime splitting on strings. The constraint about big numbers requiring Miller-Rabin was the part that really separated people who'd thought about this before from those who hadn't.

Questions Asked (1)

Given a string of digits, count the number of ways to split it into contiguous non-empty segments where every segment represents a prime number. Segments must preserve order, cover every character exactly once, have no leading zeros, and the answer should be returned modulo 1,000,000,007.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was just DP from left to right, define dp[i] as the number of valid splits for the first i characters, and for each position try all possible last segments.

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AI HintsAI Generated

Suggested Approach

Use dynamic programming where dp[i] represents the number of valid ways to split the prefix ending at index i. For each i, iterate over all possible start indices j < i, check if the substring s[j..i-1] is a prime number (no leading zeros, value prime), and if so, add dp[j] to dp[i]. Precompute primes up to the maximum possible value (length of string) using a sieve to allow O(1) primality checks.

Pro tip: Mention that you can optimize the inner loop by limiting the substring length to the number of digits of the maximum prime (e.g., 6 digits for 1e6), and discuss trade-offs between precomputing primes versus checking on the fly. Also, handle modulo operations carefully to avoid overflow.

1. Clarify constraints and edge cases

Ask about the maximum length of the string, whether the string can be empty, and confirm that segments cannot have leading zeros. This determines the feasible maximum prime value and the DP table size.

2. Define DP state and recurrence

Let dp[i] be the number of ways to split the prefix s[0..i-1]. Initialize dp[0] = 1. For each i from 1 to n, iterate j from 0 to i-1, and if s[j..i-1] is a valid prime, add dp[j] to dp[i] modulo 1e9+7.

3. Efficient primality checking

Precompute all primes up to the maximum possible value (e.g., 10^6 if string length ≤ 6) using the Sieve of Eratosthenes. Then, for each substring, convert to integer (avoiding leading zeros) and check primality in O(1).

4. Optimize the inner loop

Limit the substring length to the number of digits of the maximum prime (e.g., 6). Also, skip substrings with leading zeros. This reduces time complexity from O(n^2) to O(n * L) where L is max digits.

5. Return the result and discuss complexity

Return dp[n] modulo 1e9+7. Analyze time complexity: O(n * L) for DP plus O(M log log M) for sieve, where M is max prime value. Space complexity: O(n + M).

Key Points to Mention

Dynamic programming with state dp[i] representing ways to split prefix of length i.
Handling leading zeros: a segment cannot start with '0' unless the segment is exactly '0', but '0' is not prime, so any segment starting with '0' is invalid.
Precomputing primes using Sieve of Eratosthenes for O(1) primality checks.
Modulo arithmetic to prevent integer overflow and meet the requirement.
Time and space complexity analysis, including the optimization to limit substring length.
Edge cases: empty string, string with no valid splits, very long string (e.g., length 10^5) and how to handle if max prime exceeds memory.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.