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LC 53 Maximum Subarray is the foundational problem behind Kadane's Algorithm — a deceptively simple O(n) DP that asks: at each position, should I extend the current subarray or start fresh? Asked at Amazon, Google, and Microsoft and the basis for Maximum Product Subarray and other contiguous-subarray problems.
LC 152 Maximum Product Subarray extends Kadane's Algorithm by tracking both the running maximum and minimum products simultaneously. A negative number flips today's minimum into tomorrow's maximum. This dual-tracking insight is tested at Amazon, Google, and LinkedIn as a harder follow-up to Maximum Subarray.
Crack LeetCode 363 Max Sum of Rectangle No Larger Than K by fixing two row boundaries to collapse 2D into 1D, then using prefix sums plus a sorted set (or BIT/segment tree) to find the best subarray sum bounded above by K.