Best Time to Buy and Sell Stock III 解答

Question

Say you have an array for which the ith 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 (ie, you must sell the stock before you buy again).

Solution

This problem can be solved by "divide and conquer". We can use left[i] array to track maximum profit for transactions before i (including i), and right[i + 1] to track maximum profit for transcations after i.

Prices: 1 4 5 7 6 3 2 9
left = [0, 3, 4, 6, 6, 6, 6, 8]
right= [8, 7, 7, 7, 7, 7, 7, 0]

Time complexity O(n), space cost O(n).

 1 public class Solution {
 2     public int maxProfit(int[] prices) {
 3         if (prices == null || prices.length < 2)
 4             return 0;
 5         int length = prices.length, min = prices[0], max = prices[length - 1], tmpProfit = 0;
 6         int[] leftProfits = new int[length];
 7         leftProfits[0] = 0;
 8         int[] rightProfits = new int[length];
 9         rightProfits[length - 1] = 0;
10         // Calculat left side profits
11         for (int i = 1; i < length; i++) {
12             if (prices[i] > min)
13                 tmpProfit = Math.max(tmpProfit, prices[i] - min);
14             else
15                 min = prices[i];
16             leftProfits[i] = tmpProfit;
17         }
18         // Calculate right side profits
19         tmpProfit = 0;
20         for (int j = length - 2; j >= 0; j--) {
21             if (prices[j] < max)
22                 tmpProfit = Math.max(tmpProfit, max - prices[j]);
23             else
24                 max = prices[j];
25             rightProfits[j] = tmpProfit;
26         }
27         // Sum up
28         int result = Integer.MIN_VALUE;
29         for (int i = 0; i < length - 1; i++)
30             result = Math.max(result, leftProfits[i] + rightProfits[i + 1]);
31         result = Math.max(result, leftProfits[length - 1]);
32         return result;
33     }
34 }