Took me longer than I'd like to admit to even figure out what the prime condition was changing about the state transitions.
Clarify the problem constraints and define the state as the maximum sum achievable at each index. Precompute primes up to n and use dynamic programming to transition from previous indices with prime differences, optimizing with a sliding window or prefix maxima if possible.
Pro tip: Discuss the trade-offs between a straightforward O(n * number of primes) DP and a more optimized approach using a sliding window maximum over prime gaps, showing awareness of time complexity for large inputs.
Ask about constraints: array size, value ranges, whether jumps can be forward only or both directions, and if the starting point is fixed. Confirm that the goal is to maximize the sum of visited elements.
Let dp[i] be the maximum sum achievable ending at index i. Initialize dp[0] = arr[0] if starting at index 0, and dp[i] = -infinity for others. The answer is the maximum dp[i] over all i.
Use the Sieve of Eratosthenes to generate all prime numbers up to n-1, where n is the array length. This allows O(1) prime checks during transitions.
For each index i from 1 to n-1, iterate over all primes p such that i-p >= 0, and update dp[i] = max(dp[i], dp[i-p] + arr[i]). This yields O(n * π(n)) time, where π(n) is the number of primes up to n.
If n is large, consider optimizing by maintaining a sliding window maximum over prime gaps or using a segment tree to query the maximum dp value among indices at prime distances. Discuss the trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.