LeetCode 309: Best Time to Buy and Sell Stock with Cooldown Solution

Master LeetCode problem 309 (Best Time to Buy and Sell Stock with Cooldown), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

309. Best Time to Buy and Sell Stock with Cooldown

Medium

Array Dynamic Programming

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming with state machines. We can define three states: buy, sell, and cooldown. At each day, we can be in one of these states. We need to keep track of the maximum profit we can achieve at each state.

sell[i]: Maximum profit on day i if we sell on day i.
buy[i]: Maximum profit on day i if we buy on day i.
cooldown[i]: Maximum profit on day i if we are in cooldown on day i.

We can update these states based on the following conditions:

sell[i] = buy[i-1] + prices[i]
buy[i] = max(cooldown[i-1] - prices[i], buy[i-1])
cooldown[i] = max(sell[i-1], cooldown[i-1])

The final answer will be the maximum of sell[n-1] and cooldown[n-1], where n is the number of days.

Time complexity: O(n)
Space complexity: O(1)

Solution Code

class Solution {
    public int maxProfit(int[] prices) {
        if (prices == null || prices.length <= 1) {
            return 0;
        }
        
        int sell = 0, buy = -prices[0], cooldown = 0;
        
        for (int i = 1; i < prices.length; i++) {
            int prevSell = sell;
            sell = buy + prices[i];
            buy = Math.max(cooldown - prices[i], buy);
            cooldown = Math.max(prevSell, cooldown);
        }
        
        return Math.max(sell, cooldown);
    }
}

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