dynamic programming

DP feels like pattern-matching magic until you have a method. The signal is a repeatable drill: spot overlapping subproblems and optimal substructure, define the state and recurrence, then memoize or tabulate. Here is that method applied to a worked example.

Edit distance is the archetypal 2D string DP, powering spell-check, diff, and fuzzy matching. What interviewers watch for: naming the subproblem and the insert/delete/replace recurrence. Here is the answer.

Maximum subarray is the entry-point 1D DP problem, and Kadane's is the O(n) one-liner. What interviewers watch for: the 'extend or restart' call at each element and the all-negative edge case most people fumble. Here is the answer.

Word Break is the classic 1D string DP that snags people who reach for greedy or naive recursion. What interviewers watch for: the dp[i] = 'is the prefix of length i segmentable' recurrence, plus why a locally valid split can doom the rest. Here is the answer.

The DP that reveals why greedy quietly fails on non-standard denominations, and how a single bottom-up table fixes it. What interviewers watch for: the dp[amount] recurrence and the unbounded-reuse insight.

LCS is the template 2D-sequence DP behind diff tools and bioinformatics. Interviewers look for rebuilding the match/mismatch recurrence from memory and not mixing up subsequence (gaps allowed) with substring (contiguous). The answer follows.

LIS has an obvious O(n²) DP and a clever O(n log n) solution that catches people off guard. Interviewers look for the patience-sorting/binary-search approach that maintains 'tails'. Both appear below.

House Robber is the tidiest choose-with-a-constraint 1D DP, and it reduces to O(1) space. Interviewers look for the take-this-or-skip recurrence and the two-variable rolling optimization.

The textbook grid DP where each cell depends on three neighbors at once. What interviewers want is the min-of-three recurrence, plus the reason it has to be min. The answer follows.

Decode Ways is a 1D DP whose difficulty sits entirely in the edge cases: zeros and the valid 1-26 range. Interviewers look for the take-one-digit-or-two recurrence plus disciplined validity checks. The answer follows.

Negative subtrees, a path that bends through any node, and a return value distinct from the answer you track: this problem stuffs three traps into one DFS. Here is the clean O(n) solution and the reasoning that holds up under follow-ups.

Floyd-Warshall computes shortest paths between every pair of nodes in O(V cubed) with a compact three-line triple loop. The signal is the intermediate-node DP order and why k has to be the outer loop. Here is the answer.

HMMs are the classic probabilistic sequence model behind speech and tagging, and Viterbi is how you decode them. What matters is the hidden-states plus transitions/emissions structure, and that Viterbi is dynamic programming for the single best state path, not a probability.