Say you have an array for which the *i*^{th} element 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:6Explanation: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:4Explanation: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:0Explanation:In this case, no transaction is done, i.e. max profit = 0.

class Solution { public int maxProfit(int[] prices) { int dp_i10 = 0, dp_i11 = Integer.MIN_VALUE; int dp_i20 = 0, dp_i21 = Integer.MIN_VALUE; for(int price:prices){ dp_i20 = Math.max(dp_i20,dp_i21+price); dp_i21 = Math.max(dp_i21,dp_i10-price); dp_i10 = Math.max(dp_i10,dp_i11+price); dp_i11 = Math.max(dp_i11,-price); } return dp_i20; } }

Runtime: 1 ms, faster than 99.83% of Java online submissions for Best Time to Buy and Sell Stock III.

Memory Usage: 37.3 MB, less than 100.00% of Java online submissions for Best Time to Buy and Sell Stock III.