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Longest Non-decreasing Subarray From Two Arrays

Difficulty: Medium

Problem Description

You are given two 0-indexed integer arrays nums1 and nums2 of length n. For each index i in the range [0, n - 1], you can assign either nums1[i] or nums2[i] to nums3[i]. Your task is to maximize the length of the longest non-decreasing subarray in nums3 by choosing its values optimally. Return an integer representing the length of the longest non-decreasing subarray in nums3.

Key Insights

  • You can choose elements from either of the two arrays for each index.
  • The goal is to construct the longest contiguous non-decreasing subarray.
  • A greedy approach can be utilized by iterating through the arrays and keeping track of the longest valid subarray.
  • The problem can be approached similarly to finding the longest increasing subsequence by leveraging the properties of non-decreasing sequences.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use a greedy algorithm that keeps track of the maximum length of a non-decreasing subarray as we iterate through the given arrays. We will maintain a current length of the non-decreasing subarray and update it based on the elements chosen from either nums1 or nums2. If the current element can continue the non-decreasing sequence, we increment the current length; otherwise, we reset it. We also keep track of the maximum length encountered during the iteration.

Code Solutions

def longestNonDecreasingSubarray(nums1, nums2):
    n = len(nums1)
    max_length = 0
    current_length = 1  # Start with the first element

    for i in range(1, n):
        # Check if we can extend the current non-decreasing subarray
        if (nums1[i] >= nums1[i - 1]) or (nums1[i] >= nums2[i - 1]) or (nums2[i] >= nums1[i - 1]) or (nums2[i] >= nums2[i - 1]):
            current_length += 1
        else:
            current_length = 1  # Reset the length
        
        max_length = max(max_length, current_length)
    
    return max_length
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