23 articles
The complete 2D Dynamic Programming roadmap for FAANG interviews — LCS, Edit Distance, grid path counting, interval DP, stock state machines, and 2D knapsack with Python and JavaScript templates.
LC 62 Unique Paths is the foundational 2D grid DP problem at Amazon, Google, and Meta. Learn the recurrence, space-optimize to 1D, and master the combinatorics shortcut interviewers love to ask about.
LC 63 Unique Paths II extends the classic grid DP with obstacle cells. Master the obstacle-zeroing pattern, handle blocked start/end edge cases, and space-optimize to O(n) — the exact follow-up interviewers throw immediately after Unique Paths.
LC 64 Minimum Path Sum is the essential cost-minimization variant of grid DP, asked heavily at Amazon and Google. Learn the 2D recurrence, space-optimize to O(n), and understand why bottom-up tabulation handles borders without special-casing.
LC 120 Triangle asks for the minimum-sum path from apex to base. The bottom-up DP approach eliminates border initialization complexity and achieves O(n) space — a classic 2D DP problem that tests your ability to work on non-rectangular structures.
LC 1143 Longest Common Subsequence is the foundational sequence DP problem at every FAANG company. Master the 2D recurrence, space-optimize to O(n), and learn how to reconstruct the actual LCS — skills that transfer directly to Edit Distance, Shortest Common Supersequence, and Diff algorithms.
LC 72 Edit Distance (Levenshtein Distance) is the hard-level sequence DP benchmark at Google, Amazon, and Meta. Master the 3-operation recurrence, space-optimize to O(n), and understand how this algorithm powers spell-checkers, DNA alignment, and autocomplete systems.
LC 1092 Shortest Common Supersequence combines LCS computation with DP table reconstruction to produce the actual shortest string containing both inputs as subsequences. A hard-level 2D DP problem asked at Google and Amazon that demands both algorithm depth and reconstruction skill.
LC 312 Burst Balloons is the classic hard-level interval DP problem asked at Google, Amazon, and Meta. The key insight is thinking in reverse — instead of choosing which balloon to burst first, choose which one to burst last in each interval. This transforms an impossible ordering problem into clean O(n^3) DP.
LC 121 Best Time to Buy and Sell Stock is the foundational stock DP problem at every FAANG company. While solvable with a one-pass greedy approach, understanding its state machine formulation (hold/not-hold states) unlocks the full stock problem series from LC 122 through LC 714.
LC 122 Best Time to Buy and Sell Stock II allows unlimited buy-sell transactions (hold at most 1 share at a time). Solvable with a greedy slope-collection approach, but the state machine DP extension reveals how unlimited transactions differ structurally from single-transaction stock problems.
LC 123 Best Time to Buy and Sell Stock III limits transactions to at most 2. The state machine tracks 4 explicit states — buy1, sell1, buy2, sell2 — evolving each day through clean transitions. This is the hardest single-interview stock variant and the direct precursor to the k-transactions generalization in LC 188.
LC 188 Best Time to Buy and Sell Stock IV generalizes the stock problem to at most k transactions using a 2D DP table where dp[t][i] tracks the maximum profit using t transactions through day i. This is the hardest stock variant in FAANG interviews and requires combining the k-transaction state machine with the unlimited-transaction shortcut for large k.
LC 309 Best Time to Buy and Sell Stock with Cooldown adds a 1-day cooldown after selling. The state machine expands to 3 states — holding, sold (cooldown), and resting — and the buy transition reads from 2 days ago instead of 1 day ago. This structural change is the cleanest example of how constraints reshape state machine DP.
LC 714 Best Time to Buy and Sell Stock with Transaction Fee extends unlimited transactions by subtracting a fee on each sell. The state machine is identical to Stock II with one modification: the sell transition subtracts the fee. This is the final stock series variant and the cleanest demonstration that state machine DP is a modular framework.
LC 97 Interleaving String asks whether s3 can be formed by interleaving s1 and s2 while preserving character order. The 2D DP table dp[i][j] checks whether s3[:i+j] can be formed from s1[:i] and s2[:j] — a classic Boolean 2D DP problem asked at Google and Amazon.
LC 10 Regular Expression Matching implements "." (any char) and "*" (zero or more of preceding) using 2D DP. It is a Hard-level problem and the most complex string DP asked at Google and Meta — the star (*) handling requires 3 separate cases that trip up even experienced candidates.
LeetCode 44 Wildcard Matching is the classic 2D string DP question Meta and Google ask to test recurrence design under tricky base cases. We derive the dp[i][j] transitions for ? and *, dry-run a full table, and finish with a two-pointer optimization that drops memory to O(1).
LeetCode 174 Dungeon Game is the textbook example of why DP direction matters. We derive why forward DP fails, build the backward dp[i][j] = max(1, ...) recurrence, dry-run the grid, and finish with a space-optimized 1D solution loved at FAANG.
LeetCode 474 Ones and Zeroes is the cleanest two-capacity 0/1 knapsack on the platform. We derive the dp[i][j] recurrence, walk a full 2D table, and ship a 1D-collapsed solution that handles the dual-resource constraint while staying interview-friendly.
LeetCode 931 Minimum Falling Path Sum is the cleanest grid DP with diagonal moves. We derive the dp[i][j] recurrence with three predecessors, walk a full table, and ship an O(1) extra-space in-place tabulation that interviewers love.
LeetCode 664 Strange Printer is the canonical O(n^3) interval DP every senior FAANG interviewer expects you to handle. We derive the dp[i][j] recurrence, walk through the merge-on-match optimization, dry-run a full table, and discuss where Strange Printer sits in the Burst Balloons / MCM family.
The full 2D Dynamic Programming cheatsheet for FAANG interviews — seven pattern transitions, stock state machine, interval DP template, LCS reconstruction, and the complete problem index.