Problem Statement
Stock Trader with K Transactions
You are a stock trader who wants to maximize profit by buying and selling stocks. You are given an integer k and 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 k transactions.
Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).
Examples
Example 1:
Input: k = 2, prices = [2, 4, 1]
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4 - 2 = 2.
Example 2:
Input: k = 2, prices = [3, 2, 6, 5, 0, 3]
Output: 7
Explanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6 - 2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3 - 0 = 3. Total profit is 4 + 3 = 7.
Constraints
- 0 <= k <= 100
- 0 <= prices.length <= 1000
- 0 <= prices[i] <= 1000
Problem Breakdown
To solve this problem, we need to:
- The key insight is to use dynamic programming to track the maximum profit after different states of transactions.
- We need to consider 2k states: after buying the 1st stock, after selling the 1st stock, ..., after buying the kth stock, after selling the kth stock.
- For each day, we have the option to either do nothing or perform a transaction (buy or sell), and we want to maximize our profit.
- When k is large (k >= n/2), the problem reduces to the Best Time to Buy and Sell Stock II problem, where we can make as many transactions as we want.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Stock Trader with K Transactions
You are a stock trader who wants to maximize profit by buying and selling stocks. You are given an integer k and 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 k transactions.
Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).
Examples
Example 1:
Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4 - 2 = 2.
Example 2:
Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6 - 2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3 - 0 = 3. Total profit is 4 + 3 = 7.
Problem Breakdown
Constraints:
- 0 <= k <= 100
- 0 <= prices.length <= 1000
- 0 <= prices[i] <= 1000
Key Insights:
The key insight is to use dynamic programming to track the maximum profit after different states of transactions.
We need to consider 2k states: after buying the 1st stock, after selling the 1st stock, ..., after buying the kth stock, after selling the kth stock.
For each day, we have the option to either do nothing or perform a transaction (buy or sell), and we want to maximize our profit.
When k is large (k >= n/2), the problem reduces to the Best Time to Buy and Sell Stock II problem, where we can make as many transactions as we want.
Real-World Application
This problem has several practical applications:
Stock Trading
Optimizing trading strategies with a limited number of transactions.
Transaction Planning
Planning financial transactions with constraints on the number of operations.
Portfolio Optimization
Optimizing investment portfolios with limited rebalancing opportunities.