123. Best Time to Buy and Sell Stock III 

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class Solution {
    public int maxProfit(int[] prices) {
        int n = prices.length;

        // 定义 dp[i][j] 表示第 i 天休市时处于 j 状态的最大利润
        // j = 0: 未购买过
        // j = 1: 买入一次
        // j = 2: 买入、卖出
        // j = 3: 买入、卖出、买入
        // j = 4: 买入、卖出、买入、卖出
        int[][] dp = new int[n][5];
        dp[0][0] = 0;
        dp[0][1] = -prices[0];
        dp[0][2] = 0;
        dp[0][3] = -prices[0];
        dp[0][4] = 0;

        for (int i = 1; i < n; i++) {
            dp[i][0] = dp[i - 1][0];
            dp[i][1] = Math.max(dp[i - 1][1], dp[i - 1][0] - prices[i]);
            dp[i][2] = Math.max(dp[i - 1][2], dp[i - 1][1] + prices[i]);
            dp[i][3] = Math.max(dp[i - 1][3], dp[i - 1][2] - prices[i]);
            dp[i][4] = Math.max(dp[i - 1][4], dp[i - 1][3] + prices[i]);
        }

        return dp[n - 1][4]; // 因为同一天可以买卖多次，所以最大值一定能转移到该状态
    }
}

References

123. Best Time to Buy and Sell Stock III