6 articles
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.