How do you solve Maximize Cyclic Partition Score on LeetCode?

Maximize Cyclic Partition Score (LeetCode #3743) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * k) time complexity and O(n * k) space complexity. Key insight: Cyclic nature of the array requires careful handling of indices.

What is the brute force solution for Maximize Cyclic Partition Score?

The brute force approach for Maximize Cyclic Partition Score is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try every possible partitioning of the array into up to k subarrays and calculate the score for each. This approach is straightforward but inefficient due to the exponential number of partitions. The optimal Optimal Solution approach improves this to O(n * k).

What algorithm or data structure is used to solve Maximize Cyclic Partition Score?

Maximize Cyclic Partition Score uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Sliding Window.

What are the interview tips for Maximize Cyclic Partition Score?

Clarify the cyclic nature of the array. Discuss potential edge cases upfront. Explain your thought process clearly while coding.

What are common mistakes when solving Maximize Cyclic Partition Score?

Not considering the cyclic nature of the array. Forgetting to handle edge cases with k = 1 or k = n.

#3743

Maximize Cyclic Partition Score

Hard

ArrayDynamic ProgrammingDynamic ProgrammingSliding Window

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * k)
Space	O(1)	O(n * k)

💡

Intuition

Time O(n * k)Space O(n * k)

We can use dynamic programming to efficiently calculate the maximum score by modeling the problem with extreme picks. We track contributions of maximum and minimum values in a cyclic manner.

⚙️

Algorithm

3 steps

1Step 1: Create an extended array by concatenating nums to itself to handle cyclic nature.
2Step 2: Use dynamic programming to calculate max contributions of selected elements as max or min.
3Step 3: Iterate through possible partitions and compute the score based on selected max and min contributions.

solution.py12 lines

1def maxScore(nums, k):
2    n = len(nums)
3    nums = nums + nums
4    dp = [[0] * (k + 1) for _ in range(2 * n)]
5    for i in range(2 * n):
6        max_val, min_val = nums[i], nums[i]
7        for j in range(i, min(i + n, 2 * n)):
8            max_val = max(max_val, nums[j])
9            min_val = min(min_val, nums[j])
10            for p in range(1, k + 1):
11                dp[j][p] = max(dp[j][p], dp[i - 1][p - 1] + (max_val - min_val))
12    return max(dp[n - 1])

ℹ

Complexity note: The complexity is driven by the nested loops iterating through the extended array and the number of partitions, making it linear with respect to the input size and k.

1Cyclic nature of the array requires careful handling of indices.
2Dynamic programming allows us to build solutions incrementally.

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