121. Best Time to Buy and Sell Stock

DP

1
2
3
4
5
6
7
8
9
10
11
12
13
class Solution {
    public int maxProfit(int[] prices) {
        int maxProfit = 0, minPrice = prices[0];

        for (int i = 1; i < prices.length; i++) {
            int price = prices[i];
            maxProfit = Math.max(maxProfit, price - minPrice);
            minPrice = Math.min(minPrice, price);
        }

        return maxProfit;
    }
}

DP

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
class Solution {
    public int maxProfit(int[] prices) {
        int n = prices.length;

        // 定义 dp[i][j] 为第 i 天休市时处于 j 状态的最大利润，j = 0 为未持有股票，j = 1 为持有股票
        int[][] dp = new int[n][2];
        dp[0][0] = 0;
        dp[0][1] = -prices[0];

        for (int i = 1; i < n; i++) {
            dp[i][0] = Math.max(dp[i - 1][0], dp[i - 1][1] + prices[i]/*持有股票转换为未持有股票*/);
            dp[i][1] = Math.max(dp[i - 1][1], dp[0][0] - prices[i]/*未持有股票转换为持有股票，此处保证了只买入一次*/);
        }

        return dp[n - 1][0]; // 最后一天休市时不持有股票利润最大
    }
}

References

121. Best Time to Buy and Sell Stock
剑指 Offer 63. 股票的最大利润