Best Time To Buy And Sell Stock Iii Problem


Description

LeetCode Problem 123.

You are given an array prices where prices[i] is the price of a given stock on the i^th 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:

1
2
3
4
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:

1
2
3
4
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:

1
2
3
Input: prices = [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.

Example 4:

1
2
Input: prices = [1]
Output: 0

Constraints:

  • 1 <= prices.length <= 10^5
  • 0 <= prices[i] <= 10^5


Sample C++ Code

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
class Solution {
public:
    int MaxProfitDp(int[] prices) {
    	// DP formula:
    	// dp[k, i] = max(dp[k, i-1], prices[i] - prices[j] + dp[k-1, j-1]), j=[0..i-1]
        if (prices.Length == 0) return 0;
            var dp = new int[3, prices.Length];
        for (int k = 1; k <= 2; k++) {
            int min = prices[0];
            for (int i = 1; i < prices.Length; i++) {
                min = Math.Min(min, prices[i] - dp[k-1, i-1]);
                dp[k, i] = Math.Max(dp[k, i-1], prices[i] - min);
            }
        }

        return dp[2, prices.Length - 1];
    }
};




Related Posts

Valid Permutations For DI Sequence Problem

LeetCode 903. You are given a string s of length...

Tallest Billboard Problem

LeetCode 956. You are installing a billboard and want it...

Sum Of Subarray Minimums Problem

LeetCode 907. Given an array of integers arr, find the...

Stone Game Problem

LeetCode 877. Alice and Bob play a game with piles...

Split Array With Same Average Problem

LeetCode 805. You are given an integer array nums.

Soup Servings Problem

LeetCode 808. There are two types of soup, type A...