Say 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
思路: 188的简化版，参考188即可
class Solution {
public int maxProfit(int[] prices) {
if (prices == null || prices.length == 0) {
return 0;
}
int k = 2;
int[][] dp = new int[k + 1][prices.length];
for (int i = 1; i <= k; i++) {
int maxDiff = -prices[0];
for (int j = 1; j < prices.length; j++) {
dp[i][j] = Math.max(dp[i][j - 1], prices[j] + maxDiff);
maxDiff = Math.max(maxDiff, dp[i - 1][j] - prices[j]);
}
}
return dp[k][prices.length - 1];
}
}