Master Two Sum and its variants — 3Sum, 4Sum, Two Sum II — using hashmap for O(N) and two pointers for sorted arrays. Amazon relies on this problem family to assess foundational array skills and generalization ability.
Return all possible sentence segmentations of a string using valid dictionary words via DP memoization and backtracking. Google tests this to evaluate recursive search pruning and memoization applied to NLP-style segmentation.
Merge accounts that share any email address using Union-Find on email nodes. Meta uses this to test graph connectivity thinking and identity resolution — directly applicable to Facebook account deduplication systems.
Compute trapped rain water in a 3D height map using a min-heap BFS that processes cells from the boundary inward. Google asks this as a hard follow-up to 1D trapping rain water, testing 3D spatial reasoning and heap-driven BFS.
Find the median of two sorted arrays in O(log(min(m,n))) using binary search on partition points. Amazon and Google use this hard problem to test binary search on abstract criteria and numerical reasoning under pressure.