Recognize this as a dynamic programming problem where dp[i] represents the maximum sum to reach index i. For each index, consider all valid moves (1 step right or prime jumps ending in 3) and take the maximum. Precompute the valid prime jumps up to the array length to optimize.
Pro tip: Clarify with the interviewer whether you can land on the same cell multiple times or if each cell can be collected only once; this affects whether the problem is a simple DP or requires tracking visited cells. Also, mention that you'd precompute primes ending in 3 using a sieve to avoid repeated checks.
Confirm the rules: start at index 0, moves are +1 or +p where p is a prime ending in 3, and you collect the value at each landed cell. Ask about array size, value ranges, and whether cells can be revisited.
Let dp[i] be the maximum sum to reach index i. Initialize dp[0] = arr[0]. For each i from 1 to n-1, dp[i] = arr[i] + max(dp[i-1], max over valid primes p ≤ i of dp[i-p]).
Use the Sieve of Eratosthenes up to n to find all primes, then filter those whose last digit is 3. Store them in a list for quick access during DP.
Iterate through the array, and for each index, check all valid prime jumps. If the number of such primes is large, consider optimizing by grouping or using a sliding window, but typically O(n * number_of_primes) is acceptable.
Time complexity: O(n * P) where P is the number of primes ending in 3 up to n; space O(n). Handle edge cases: n=1, no valid jumps, negative values (though problem implies positive? clarify).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.