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 (i.e., you must sell the stock before you buy again).

Example 1:

題目

和之前一樣，這次你至多能買賣兩次。

思路

1. Split the array into two parts, one trade each.

2. Say that f(i) stands for max profit in [0,i] , g(i) stands for max profix in [i, n-1] , then update and finally return max(f(i) + g(i))

程式碼

 1 // Best Time to Buy and Sell Stock III
 
 2 // 時間複雜度O(n)，空間複雜度O(n)
 3 public class Solution {
 4     public int maxProfit(int[] prices) {
 5         if (prices.length < 2) return 0;
 6 
 7         final int n = prices.length;
 8         int[] f = new int[n];
 9         int[] g = new int[n];
10 
11         for (int i = 1, valley = prices[0]; i < n; ++i) {
 
12             valley = Math.min(valley, prices[i]);
13             f[i] = Math.max(f[i - 1], prices[i] - valley);
14         }
15 
16         for (int i = n - 2, peak = prices[n - 1]; i >= 0; --i) {
17             peak = Math.max(peak, prices[i]);
18             g[i] = Math.max(g[i], peak - prices[i]);
19         }
20 
21         int max_profit = 0;
22         for (int i = 0; i < n; ++i)
23             max_profit = Math.max(max_profit, f[i] + g[i]);
24 
25         return max_profit;
26     }
27 }