Best Time to Buy and Sell Stock with Cooldown

mediumTests passed 2026-11-11v1.0.0
TC: O(N)|SC: O(1)
2D DPOriginal Statement (leetcode).md

1. Core Invariant / The Trick

Three-state machine on day `i`: `hold` (currently holding share), `sold` (just sold today -> enters cooldown tomorrow), `rest` (not holding, cooled off). Transitions: `hold = max(hold, rest - p)`, `rest = max(rest, sold)`, `sold = prev_hold + p`.

2. Complexity Bounds & Proof

State-machine FSM reduces 2D `(day, state)` DP table into 3 rolling integer registers.

3. Minimal Idiomatic Code

def maxProfit(prices: list[int]) -> int:
    hold, sold, rest = float('-inf'), 0, 0
    for p in prices:
        prev_hold = hold
        hold = max(hold, rest - p)
        rest = max(rest, sold)
        sold = prev_hold + p
    return max(sold, rest)

4. Failure Modes & Interview Follow-ups

Pitfalls:- Allowing `rest - p` to transition directly from `sold` skips the mandatory 1-day cooldown. - Initialize `hold = -inf, sold = 0, rest = 0` so selling before buying is impossible.
Follow-ups:- Stock with Transaction Fee drops `sold` state and subtracts `fee` on sell; Stock IV limits to `k` transactions (`O(N * k)` states).

Personal Notes & Scratchpad (Local-First Yjs CRDT)

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Related Invariants

Best Time to Buy and Sell Stock (O(N))House Robber (O(N))
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