The i+1 movement is obvious but the 'jump to any index ending in 3' rule threw me off at first.
Clarify the problem constraints (array size, score definition, jump rule) and then propose a dynamic programming solution. Define dp[i] as the maximum score to reach index i, and compute it using transitions from i-1 and from all indices j where j ends in 3 and j < i. Optimize by precomputing the best jump source among indices ending in 3.
Pro tip: Mention that you can maintain a running maximum of dp[j] for all j ending in 3 to achieve O(n) time, and discuss edge cases like when the last index is not reachable or when the array has only one element.
Ask about the definition of score (e.g., sum of values at visited indices, including start and end), constraints on array size and values, and whether jumps to indices ending in 3 are allowed only from certain positions or from any position.
Let dp[i] be the maximum score to reach index i. Then dp[i] = value[i] + max(dp[i-1], max_{j < i, j ends in 3} dp[j]). Base case: dp[0] = value[0].
Maintain a variable best_jump that stores the maximum dp[j] for all j ending in 3 seen so far. Update it when i ends in 3, and use it for the jump transition.
Check if the last index is reachable (e.g., if n=1, answer is value[0]). Time complexity O(n), space O(1) if only dp[i-1] and best_jump are kept, or O(n) if full dp array is used.
Walk through a small example to verify the recurrence and edge cases, such as [1,2,3,4] where jumps to index 3 are allowed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.