How do you solve Maximum Sum of 3 Non-Overlapping Subarrays on LeetCode?

Maximum Sum of 3 Non-Overlapping Subarrays (LeetCode #689) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using prefix sums allows for quick calculation of subarray sums, reducing redundant calculations.

What is the brute force solution for Maximum Sum of 3 Non-Overlapping Subarrays?

The brute force approach for Maximum Sum of 3 Non-Overlapping Subarrays is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible combination of three non-overlapping subarrays of length k. This method guarantees finding the maximum sum but is inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Sum of 3 Non-Overlapping Subarrays?

Maximum Sum of 3 Non-Overlapping Subarrays uses the following concepts: Array, Dynamic Programming, Sliding Window, Prefix Sum. The recommended patterns to study are: Dynamic Programming, Prefix Sum, Sliding Window.

What are the interview tips for Maximum Sum of 3 Non-Overlapping Subarrays?

Always clarify the problem constraints and edge cases before diving into coding. Explain your thought process while coding to demonstrate your understanding. Practice writing both brute-force and optimal solutions to solidify your understanding of the problem.

What are common mistakes when solving Maximum Sum of 3 Non-Overlapping Subarrays?

Failing to account for overlapping subarrays, leading to incorrect indices. Not using prefix sums effectively, resulting in unnecessary repeated calculations.

#689

Maximum Sum of 3 Non-Overlapping Subarrays

Hard

ArrayDynamic ProgrammingSliding WindowPrefix SumDynamic ProgrammingPrefix SumSliding Window

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(n)

The optimal solution uses a combination of prefix sums and dynamic programming to efficiently calculate the maximum sum of three non-overlapping subarrays. This reduces the number of calculations significantly by leveraging previously computed results.

⚙️

Algorithm

4 steps

1Step 1: Calculate the prefix sums for the array to quickly get the sum of any subarray.
2Step 2: Create an array to store the maximum sums of subarrays of length k up to each index.
3Step 3: Iterate through the array to find the best starting indices for the second and third subarrays while ensuring they do not overlap with the first.
4Step 4: Keep track of the maximum sum and the corresponding starting indices.

solution.py17 lines

1def maxSumOfThreeSubarrays(nums, k):
2    n = len(nums)
3    prefix_sum = [0] * (n + 1)
4    for i in range(n):
5        prefix_sum[i + 1] = prefix_sum[i] + nums[i]
6    max_sum = [0] * (n + 1)
7    for i in range(n - k + 1):
8        max_sum[i + 1] = max(max_sum[i], prefix_sum[i + k] - prefix_sum[i])
9    max_total = 0
10    result = []
11    for j in range(2 * k, n + 1):
12        for i in range(j - k):
13            total = max_sum[i + 1] + (prefix_sum[j] - prefix_sum[j - k]) + (prefix_sum[n] - prefix_sum[n - k])
14            if total > max_total:
15                max_total = total
16                result = [i, j - k, n - k]
17    return result

ℹ

Complexity note: The time complexity is O(n) because we only iterate through the array a few times, and the space complexity is O(n) due to the prefix sum and max sum arrays.

1Using prefix sums allows for quick calculation of subarray sums, reducing redundant calculations.
2Dynamic programming helps in storing intermediate results, allowing for efficient retrieval.

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