Best Time to Buy And Sell Stock With Cooldown: the idea to remember.

The core insight

Choose between skipping, buying, or selling; after a sale advance past the cooldown day.

Why it works

Day and holding state determine every legal future action, allowing repeated subproblems to share one best result.

The mistake to avoid

A sale advances two days before the next buy opportunity, while holding through a day advances one.

Commented Java solution

Use java.util.* imports and a surrounding solution class. Tree snippets assume the standard TreeNode definition; linked lists use ListNode and Clone Graph uses a Node with val and neighbors; Copy Random List uses Node with val, next and random. Read the input assumptions above.

// Java reference adapted from neetcode-gh/leetcode (MIT).
// Choose between skipping, buying, or selling; after a sale advance past the cooldown day.
public int maxProfit(int[] prices) {
    Map<String, Integer> cache = new HashMap<>();
    return dfs(prices, cache, 0, true);
}

public int dfs(
    int[] prices,
    Map<String, Integer> cache,
    int index,
    boolean buying
) {
    if (index >= prices.length) {
        return 0;
    }
    String key = index + "-" + buying;

    if (cache.containsKey(key)) {
        return cache.get(key);
    }

    int cooldown = dfs(prices, cache, index + 1, buying);
    int buyOsell = Integer.MIN_VALUE;

    if (buying) {
        buyOsell = dfs(prices, cache, index + 1, !buying) - prices[index];
    } else {
        buyOsell = dfs(prices, cache, index + 2, !buying) + prices[index];
    }

    cache.put(key, Math.max(buyOsell, cooldown));
    return cache.get(key);
}

Java reference adapted from neetcode-gh/leetcode · MIT license

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