How do you solve Longest Non-decreasing Subarray From Two Arrays on LeetCode?

Longest Non-decreasing Subarray From Two Arrays (LeetCode #2771) 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: Choosing the optimal value from two arrays can maximize the length of non-decreasing subarrays.

What is the time complexity of Longest Non-decreasing Subarray From Two Arrays?

The optimal solution for Longest Non-decreasing Subarray From Two Arrays runs in O(n) time and uses O(n) space. The time complexity is O(n) because we only make a single pass through the arrays, and the space complexity is O(n) due to the storage of the dp arrays.

What is the brute force solution for Longest Non-decreasing Subarray From Two Arrays?

The brute force approach for Longest Non-decreasing Subarray From Two Arrays is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks every possible combination of values from nums1 and nums2 to form nums3 and then finds the longest non-decreasing subarray. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Longest Non-decreasing Subarray From Two Arrays?

Longest Non-decreasing Subarray From Two Arrays uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Array.

What are the interview tips for Longest Non-decreasing Subarray From Two Arrays?

Always start with a brute-force solution to understand the problem better. Explain your thought process clearly, especially when transitioning to a more optimal solution. Practice recognizing patterns in problems, such as dynamic programming or greedy approaches.

What are common mistakes when solving Longest Non-decreasing Subarray From Two Arrays?

Not considering all possible combinations when using brute force. Failing to update the dp arrays correctly in the optimal approach.

#2771

Longest Non-decreasing Subarray From Two Arrays

Medium

ArrayDynamic ProgrammingDynamic ProgrammingArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses dynamic programming to keep track of the longest non-decreasing subarray ending at each index for both nums1 and nums2. This reduces the number of checks needed significantly.

⚙️

Algorithm

4 steps

1Step 1: Initialize two arrays dp1 and dp2 of length n to store the lengths of the longest non-decreasing subarrays ending with nums1[i] and nums2[i].
2Step 2: Iterate through the arrays from index 0 to n-1, updating dp1 and dp2 based on the previous values and the current elements from nums1 and nums2.
3Step 3: For each index, check if the current element can extend the previous non-decreasing subarray, updating the dp arrays accordingly.
4Step 4: The result is the maximum value found in dp1 and dp2.

solution.py18 lines

1def longest_non_decreasing_subarray(nums1, nums2):
2    n = len(nums1)
3    dp1 = [1] * n
4    dp2 = [1] * n
5    max_length = 1
6
7    for i in range(1, n):
8        if nums1[i] >= nums1[i - 1]:
9            dp1[i] = dp1[i - 1] + 1
10        if nums2[i] >= nums2[i - 1]:
11            dp2[i] = dp2[i - 1] + 1
12        if nums1[i] >= nums2[i - 1]:
13            dp1[i] = max(dp1[i], dp2[i - 1] + 1)
14        if nums2[i] >= nums1[i - 1]:
15            dp2[i] = max(dp2[i], dp1[i - 1] + 1)
16        max_length = max(max_length, dp1[i], dp2[i])
17
18    return max_length

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the arrays, and the space complexity is O(n) due to the storage of the dp arrays.

1Choosing the optimal value from two arrays can maximize the length of non-decreasing subarrays.
2Dynamic programming allows us to build solutions incrementally, reducing redundant calculations.

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