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Best Time to Buy and Sell Stock III

HARD

52 upvotes

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Problem

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Best Time to Buy and Sell Stock III

Contributed by

Himanshu Tanwar

Hard

0/120

52 upvotes

Problem Statement

You are Harshad Mehta’s friend. He told you the price of a particular stock for the next ‘N’ days. You can either buy or sell a stock. Also, you can only complete at most 2-transactions. Find the maximum profit that you can earn from these transactions. You can take help from Mr. Mehta as well.

Note

1. Buying a stock and then selling it is called one transaction. 
2. You are not allowed to do multiple transactions at the same time. This means you have to sell the stock before buying it again.

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input Format:

The first line contains a single integer 'T' representing the number of test cases.      
Then 'T' test cases follow:

The first line of each test case contains an integer 'N' denoting the number of days. 

The second line of each test case contains 'N' space-separated integers, where the 'i-th' element is the price of the particular stock on the 'i-th' day.

Output Format :

For each test case, the first and only line of output contains an integer denoting the maximum profit. 

The output of every test case is printed in a separate line.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10
1 <= N <= 5 * 10^4
0 <= price <= 10^3

Where ‘price’ is the price of the stock on each day. 

Time Limit: 1 sec

Sample Input 1:

1
7
3 3 5 0 3 1 4

Sample output 1:

Explanation of Sample output 1:

The maximum profit can be earned by:
Transaction 1: Buying the stock on day 4 ( price 0 ) and then selling it on day 5 ( price 3 ). 
Transaction 2: Buying the stock on day 6 ( price 1 ) and then selling it on day 6 ( price 4 ).
Total profit earned will be (3 - 0) + ( 4 - 1) = 6.

Sample Input2:

1 
5
5 4 3 2 1

Sample Output2:

Explanation of Sample output 2

It's better to not do any transaction as the prices of the stock are decreasing.

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