Consider how Kadane's algorithm maintains a running sum and decides when to reset it, leveraging the optimal substructure property of the problem.

Prove correctness by induction: show that the algorithm's invariant (max sum ending at index i) holds for all i, and that the global maximum is correctly tracked.

Analyze edge cases (all negative numbers, single-element array) and explain why Kadane's algorithm handles them without additional modifications, using the recurrence relation `dp[i] = max(nums[i], dp[i-1] + nums[i])`.