Is Longest Non-decreasing Subarray From Two Arrays easy or hard?

This problem is generally classified as Medium difficulty. The challenge comes from modeling the two choices at every index and handling transitions correctly. Once the dynamic programming states are identified, the implementation becomes straightforward.

Longest Non-decreasing Subarray From Two Arrays Python/Java solution

Python and Java implementations typically use two integer variables representing the sequence length if the current element is chosen from nums1 or nums2. Update these values at each step based on comparisons with the previous elements. Both implementations run in O(n) time and O(1) space.

How to solve Longest Non-decreasing Subarray From Two Arrays in O(n)?

Iterate through both arrays and maintain two DP values: the longest subarray ending at index i when choosing nums1[i] and when choosing nums2[i]. Compare each candidate with nums1[i-1] and nums2[i-1] to determine valid transitions. Update the lengths and keep a global maximum. This single pass gives O(n) time and constant space.

What is the best approach for Longest Non-decreasing Subarray From Two Arrays?

Dynamic Programming with two running states is the most reliable approach. Track the longest non-decreasing subarray ending at index i if you pick nums1[i] or nums2[i]. Each step compares the current values with both previous choices. This yields an O(n) time and O(1) space solution.

Is Longest Non-decreasing Subarray From Two Arrays asked at Google/Amazon/Meta?

Problems involving dynamic programming over arrays and sequence transitions frequently appear in interviews at companies like Google, Amazon, and Meta. Variants that require maintaining multiple state choices or comparing previous selections are common in mid-level algorithm rounds.

What data structure is used in Longest Non-decreasing Subarray From Two Arrays?

The solution mainly uses arrays and constant variables to track dynamic programming states. No complex data structures like heaps or trees are required. The key idea is maintaining two running sequence lengths while iterating through the arrays.

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

The optimal solution runs in O(n) time because the arrays are scanned once while maintaining two state values. Each index performs a constant number of comparisons. Space complexity is O(1) since only the previous state lengths are stored.

Description Hints 3 Solution Video 13:09

2771. Longest Non-decreasing Subarray From Two Arrays

Medium31.0% acceptance6 companies

You are given two 0-indexed integer arrays nums1 and nums2 of length n.

Let's define another 0-indexed integer array, nums3, 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.

Note: A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums1 = [2,3,1], nums2 = [1,2,1]
Output: 2
Explanation: One way to construct nums3 is: 
nums3 = [nums1[0], nums2[1], nums2[2]] => [2,2,1]. 
The subarray starting from index 0 and ending at index 1, [2,2], forms a non-decreasing subarray of length 2. 
We can show that 2 is the maximum achievable length.

Example 2:

Input: nums1 = [1,3,2,1], nums2 = [2,2,3,4]
Output: 4
Explanation: One way to construct nums3 is: 
nums3 = [nums1[0], nums2[1], nums2[2], nums2[3]] => [1,2,3,4]. 
The entire array forms a non-decreasing subarray of length 4, making it the maximum achievable length.

Example 3:

Input: nums1 = [1,1], nums2 = [2,2]
Output: 2
Explanation: One way to construct nums3 is: 
nums3 = [nums1[0], nums1[1]] => [1,1]. 
The entire array forms a non-decreasing subarray of length 2, making it the maximum achievable length.

Constraints:

1 <= nums1.length == nums2.length == n <= 10⁵
1 <= nums1[i], nums2[i] <= 10⁹

Asked at 6 companies

Polar Squarepoint Capital Visa Meesho

Google Amazon

Topics

Array Dynamic Programming

Hints open one at a time

Hint 1

Consider using dynamic programming.

Hint 2

Let dp[i][0] (dp[i][1]) be the length of the longest non-decreasing ending with nums1[i] (nums2[i]).

Hint 3

Initialize dp[i][0] to 1. If nums1[i] >= nums1[i - 1] then dp[i][0] may be dp[i - 1][0] + 1. If nums1[i] >= nums2[i - 1] then dp[i][0] may be dp[i - 1][1] + 1. Perform a similar calculation for nums2[i] and dp[i][1].

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