My first instinct was just brute force DP, loop over every valid jump from each position.
Model the problem as a dynamic programming problem where dp[i] represents the maximum sum to reach index i. For each index, consider jumps of +1 and +k for all prime k ending in 3, and take the maximum. Optimize by precomputing valid k values and using efficient data structures if needed.
Pro tip: Clarify edge cases upfront (e.g., array length, negative values, unreachable indices) and discuss time/space complexity trade-offs, showing you think about scalability and real-world constraints.
Restate the problem, confirm jump rules, and ask about array size, value ranges, and whether all indices must be reachable. Identify that k must be prime and end with digit 3.
Let dp[i] be the maximum sum to reach index i. Initialize dp[0] = arr[0]. For i > 0, dp[i] = arr[i] + max(dp[i-1], max over valid k of dp[i-k] if i-k >= 0).
Generate all primes ending in 3 up to n-1 using a sieve or trial division. Store them in a list for quick access during DP transitions.
Iterate i from 1 to n-1, compute dp[i] using the recurrence. If the number of valid k is large, consider optimizing by grouping or using a sliding window maximum, but analyze complexity first.
Time complexity: O(n * P) where P is number of valid primes, or O(n log log n + n * P) with sieve. Space: O(n). Handle cases where no valid jump exists (dp[i] = -infinity) and negative values.
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