How do you solve Best Time to Buy and Sell Stock IV on LeetCode?

Best Time to Buy and Sell Stock IV (LeetCode #188) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(nk) time complexity and O(nk) space complexity. Key insight: Understanding the difference between brute force and dynamic programming can help you choose the right approach.

What is the time complexity of Best Time to Buy and Sell Stock IV?

The optimal solution for Best Time to Buy and Sell Stock IV runs in O(nk) time and uses O(nk) space. The time complexity is O(nk) because we iterate through each day for each transaction, and the space complexity is O(nk) due to the 2D dp array.

What is the brute force solution for Best Time to Buy and Sell Stock IV?

The brute force approach for Best Time to Buy and Sell Stock IV is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible transactions and calculating the profit for each combination. This method is straightforward but inefficient, as it can lead to a large number of calculations. The optimal Optimal Solution approach improves this to O(nk).

What algorithm or data structure is used to solve Best Time to Buy and Sell Stock IV?

Best Time to Buy and Sell Stock IV uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Greedy Algorithm.

What are the interview tips for Best Time to Buy and Sell Stock IV?

Always clarify the constraints and edge cases before diving into coding. Explain your thought process as you work through the problem to demonstrate your understanding. Practice dynamic programming problems to build familiarity with state transitions and recursive relationships.

What are common mistakes when solving Best Time to Buy and Sell Stock IV?

Failing to handle edge cases, such as when prices are empty or when k is larger than the number of possible transactions. Not realizing that multiple transactions can be combined into one if k is large enough.

#188

Best Time to Buy and Sell Stock IV

Hard

ArrayDynamic ProgrammingDynamic ProgrammingGreedy Algorithm

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(nk)
Space	O(1)	O(nk)

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Intuition

Time O(nk)Space O(nk)

The optimal solution uses dynamic programming to keep track of profits for each transaction up to k. This reduces the number of calculations significantly by storing intermediate results.

⚙️

Algorithm

3 steps

1Step 1: Create a 2D array dp where dp[i][j] represents the maximum profit on day j with at most i transactions.
2Step 2: Iterate through the number of transactions (1 to k) and for each transaction, calculate the maximum profit for each day.
3Step 3: Use a variable to track the maximum profit achievable by considering the best buy price seen so far.

solution.py16 lines

1# Full working Python code
2
3def maxProfit(prices, k):
4    if not prices:
5        return 0
6    n = len(prices)
7    if k >= n // 2:
8        return sum(max(prices[i + 1] - prices[i], 0) for i in range(n - 1))
9    dp = [[0] * n for _ in range(k + 1)]
10    for i in range(1, k + 1):
11        max_diff = -prices[0]
12        for j in range(1, n):
13            dp[i][j] = max(dp[i][j - 1], prices[j] + max_diff)
14            max_diff = max(max_diff, dp[i - 1][j] - prices[j])
15    return dp[k][n - 1]
16

ℹ

Complexity note: The time complexity is O(nk) because we iterate through each day for each transaction, and the space complexity is O(nk) due to the 2D dp array.

1Understanding the difference between brute force and dynamic programming can help you choose the right approach.
2Recognizing when to use a greedy approach (when k is large) can simplify the problem significantly.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.