Leetcode
Dynamic Programming
123 Best Time to Buy and Sell Stock III

1. Question

ay you have an array for which thei_thelement is the price of a given stock on day_i.
Design an algorithm to find the maximum profit. You may complete at most_two_transactions.
Note: You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).
Example 1:
Input: [3,3,5,0,0,3,1,4]
Output: 6
Explanation:
Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.
Example 2:
Input: [1,2,3,4,5]
Output: 4
Explanation:
Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
engaging multiple transactions at the same time. You must sell before buying again.
Example 3:
Input: [7,6,4,3,1]
Output: 0
Explanation:
In this case, no transaction is done, i.e. max profit = 0.

2. Implementation

(1) DP
class Solution {
public int maxProfit(int[] prices) {
if (prices == null || prices.length == 0) {
return 0;
}
int[][] dp = new int[3][prices.length];
for (int i = 1; i <= 2; i++) {
int holding = -prices[0];
for (int j = 1; j < prices.length; j++) {
dp[i][j] = Math.max(dp[i][j - 1], holding + prices[j]);
holding = Math.max(holding, dp[i - 1][j - 1] - prices[j]);
}
}
return dp[2][prices.length - 1];
}
}

3. Time & Space Complexity

DP: 时间复杂度O(2n), 空间复杂度O(2n)