Spent way too long trying to think of this as a pure greedy problem and kept failing the example mentally.
Clarify the problem constraints and define the state for dynamic programming. Use DP where the state tracks the last operation and how many times it has been consecutively chosen, then optimize transitions with prefix maxima or sliding window to achieve O(n) time.
Pro tip: After presenting the DP, mention that you can optimize space to O(k) or even O(1) by keeping running maxima, and discuss how the solution scales if k is large or if operations have dependencies.
Ask clarifying questions about input format, constraints (n, k, reward range), and whether operations are independent. Restate the goal: select a subsequence with no more than k consecutive identical operations to maximize sum of rewards.
Define dp[i][op][c] as max reward considering first i operations, ending with operation op repeated c times consecutively. Recurrence: either skip operation i, or take it if it's different from previous op (c=1) or same and c<k (c+1).
Naive transition is O(n * distinct_ops * k). Optimize by maintaining for each operation the best value for each count c, and for switching operations, keep the global best and second-best to avoid O(distinct_ops) per step. This yields O(n * k) or O(n) with further optimization.
Consider cases where k=0 (no operations allowed), k>=n (no restriction), all operations identical, or negative rewards (skip all). Analyze time and space complexity and discuss possible space optimization.
Walk through a small example to verify the DP transitions and edge cases. If time permits, mention alternative approaches like greedy with priority queue or segment tree, but emphasize DP as the robust solution.
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