Best Time to Buy and Sell Stock III

Description

You are given an array prices where prices[i] is the price of a given stock on the ith day.

Find the maximum profit you can achieve. You may complete at most two transactions.

Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

Example 1:

Input: prices = [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: prices = [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: prices = [7,6,4,3,1] Output: 0 Explanation: In this case, no transaction is done, i.e. max profit = 0.

Constraints:

• 1 <= prices.length <= 105
• 0 <= prices[i] <= 105

Code

DP

Time Complexity: $O(n)$, Space Complexity: $O(n)$

一脈相承 Most consistent ways of dealing with the series of stock problems & Best Time to Buy and Sell Stock，程式碼的部分只改動了 int trades = 2;

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        int days = prices.size();
        int trades = 2;
        int T[days + 1][trades + 1][2];
 
        // On day 0, no way ending up with stock in hand
        for(int i = 0; i < trades + 1; i++) {
            T[0][i][0] = 0;
            T[0][i][1] = -1e4;
        }
 
        // no trade, no way ending up with stock in hand
        for(int i = 0; i < days + 1; i++) {
            T[i][0][0] = 0;
            T[i][0][1] = -1e4;
        }
 
        for(int k = 1; k < trades + 1; k++) {
            for(int i = 1; i < days + 1; i++) {
                T[i][k][0] = max(T[i - 1][k][0], T[i - 1][k][1] + prices[i - 1]);
                T[i][k][1] = max(T[i - 1][k][1], T[i - 1][k - 1][0] - prices[i - 1]);
            }
        }
        
        return T[days][trades][0];
    }
};
 

Source

• Best Time to Buy and Sell Stock III - LeetCode