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: dp. max profit = max { l2r[0...i] + r2l[i+1...N-1] }. 0 <= i <= N-1
1 class Solution {
2 public:
3 // max_profit = max {l2r[0,1,...,i], r2l[i+1,...,N-1]}
4 int maxProfit(vector<int> &prices) {
5 if (prices.size() <= 1) {
6 return 0;
7 }
8 int N = prices.size();
9 vector<int> l2r(N,0);
10 vector<int> r2l(N,0);
11
12 int minv = prices[0];
13 for(int i = 1; i < N; i++) {
14 minv = min(minv, prices[i]);
15 l2r[i] = max(l2r[i-1], prices[i]-minv);
16 }
17
18 int maxv = prices[N-1];
19 for(int i = N-2; i >= 0; i--) {
20 maxv = max(maxv, prices[i]);
21 r2l[i] = max(r2l[i+1], maxv-prices[i]);
22 }
23
24 int res = l2r[N-1];
25 for(int i = 0; i < N-1; i++) {
26 res = max(res, l2r[i]+r2l[i+1]);
27 }
28 return res;
29 }
30 };