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

Maximum Sum of Two Non-Overlapping Subarrays (LeetCode #1031) 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 calculations of subarray sums, making the solution efficient.

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

The brute force approach for Maximum Sum of Two Non-Overlapping Subarrays is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible pairs of non-overlapping subarrays of the specified lengths. This means we will calculate the sum for every possible combination, which is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

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

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

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

Always consider edge cases, such as the smallest possible arrays. Discuss your thought process clearly; explain why you're choosing a specific approach. Practice recognizing patterns in problems, such as when to use prefix sums or dynamic programming.

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

Forgetting to check for non-overlapping conditions when selecting subarrays. Not using prefix sums effectively, leading to unnecessary recalculations.

#1031

Maximum Sum of Two Non-Overlapping Subarrays

Medium

ArrayDynamic ProgrammingSliding WindowPrefix SumsDynamic ProgrammingSliding 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 approach uses prefix sums to efficiently calculate the maximum sums of the two non-overlapping subarrays. By maintaining the maximum sum of one subarray while iterating through the array, we can find the best combination without redundant calculations.

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Algorithm

3 steps

1Step 1: Create a prefix sum array to quickly calculate the sum of any subarray.
2Step 2: Iterate through the array, maintaining the maximum sum of the first subarray seen so far while calculating the sum of the second subarray.
3Step 3: For each position, calculate the maximum possible sum of the two subarrays considering their lengths and update the result.

solution.py14 lines

1# Full working Python code
2
3def maxSumTwoNoOverlap(nums, firstLen, secondLen):
4    n = len(nums)
5    prefix = [0] * (n + 1)
6    for i in range(n):
7        prefix[i + 1] = prefix[i] + nums[i]
8    max_first = 0
9    max_sum = 0
10    for i in range(firstLen + secondLen - 1, n):
11        max_first = max(max_first, prefix[i - secondLen + 1] - prefix[i - secondLen + 1 - firstLen])
12        current_sum = prefix[i + 1] - prefix[i + 1 - secondLen]
13        max_sum = max(max_sum, max_first + current_sum)
14    return max_sum

ℹ

Complexity note: The time complexity is O(n) because we traverse the array a constant number of times (once for prefix sums and once for calculating the maximum sums), making it efficient.

1Using prefix sums allows for quick calculations of subarray sums, making the solution efficient.
2Maintaining a running maximum of one subarray while iterating for the other prevents redundant calculations.

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