Is Non-decreasing Subsequences easy or hard?

Non-decreasing Subsequences is considered a medium-level problem. Generating subsequences is straightforward, but handling duplicates while preserving order introduces additional complexity. The difficulty mainly comes from managing recursion state and pruning duplicate branches efficiently.

How to solve Non-decreasing Subsequences in O(n)?

An O(n) algorithm is not possible because the number of valid subsequences can grow exponentially with the input size. Any correct algorithm must potentially enumerate up to 2^n subsequences. Efficient solutions focus on pruning invalid branches early using backtracking and hash sets to avoid generating duplicates.

What is the best approach for Non-decreasing Subsequences?

Recursive backtracking with a per-level hash set is the most efficient and commonly accepted solution. The algorithm builds subsequences incrementally while ensuring each next value keeps the sequence non-decreasing. A set at each recursion depth prevents duplicate subsequences when the input array contains repeated numbers. The overall complexity is O(2^n) time with O(n) recursion space.

Is Non-decreasing Subsequences asked at Google/Amazon/Meta?

Non-decreasing subsequence generation problems appear in interviews at companies like Amazon, Meta, and Google as variations of backtracking and subset generation. The problem tests recursion, duplicate pruning, and sequence validation—skills commonly evaluated in medium-level algorithm interviews.

What data structure is used in Non-decreasing Subsequences?

The main data structures include arrays for traversal, recursion stacks for backtracking, and hash sets to prevent duplicate subsequences. The set is typically used at each recursion level to ensure the same value is not chosen multiple times from the same depth of the search tree.

What is the time complexity of Non-decreasing Subsequences?

The typical backtracking solution runs in O(2^n) time because each element can either be included or skipped when generating subsequences. Additional checks ensure the subsequence remains non-decreasing and duplicates are avoided. Space complexity is O(n) for the recursion stack, excluding the space required to store resulting subsequences.

Non-decreasing Subsequences Python or Java solution approach?

Python and Java implementations usually rely on recursive backtracking. The algorithm maintains a current path list, checks if the next number keeps the sequence non-decreasing, and uses a set at each recursion depth to skip duplicates. JavaScript and Java variants sometimes demonstrate a bitmask enumeration approach as an alternative.

Description Solution Video 29:42

491. Non-decreasing Subsequences

Medium63.1% acceptance3 companies

Given an integer array nums, return all the different possible non-decreasing subsequences of the given array with at least two elements. You may return the answer in any order.

Example 1:

Input: nums = [4,6,7,7]
Output: [[4,6],[4,6,7],[4,6,7,7],[4,7],[4,7,7],[6,7],[6,7,7],[7,7]]

Example 2:

Input: nums = [4,4,3,2,1]
Output: [[4,4]]

Constraints:

1 <= nums.length <= 15
-100 <= nums[i] <= 100

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491. Non-decreasing Subsequences

Asked at 3 companies

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