Is Divide Array Into Increasing Sequences easy or hard?

LeetCode classifies it as Hard because the key insight is not obvious. Many candidates initially try to construct subsequences using greedy structures, but the intended solution reduces the problem to a simple counting constraint with O(n) complexity.

Divide Array Into Increasing Sequences Python/Java solution

In Python or Java, iterate through the sorted array, track consecutive equal values, and maintain the maximum frequency. After the pass, check whether nums.length ≥ maxFreq × k. If the condition holds return true, otherwise return false.

How to solve Divide Array Into Increasing Sequences in O(n)?

Iterate through the sorted array and track the length of each run of equal numbers to compute the maximum frequency. Let maxFreq be the largest count of a single value. Since duplicates cannot appear in the same increasing subsequence, you need at least maxFreq subsequences. The array can be divided only if n ≥ maxFreq × k.

What is the best approach for Divide Array Into Increasing Sequences?

The optimal approach uses a counting observation. Because the array is non-decreasing, duplicate values must belong to different subsequences. If the maximum frequency of any number is maxFreq, at least maxFreq subsequences are required. Each subsequence must have length ≥ k, so the condition n ≥ maxFreq × k determines whether the division is possible.

Is Divide Array Into Increasing Sequences asked at Google/Amazon/Meta?

This problem represents a common interview pattern around frequency counting and greedy reasoning on sorted arrays. Variants of the same idea appear in interviews at large tech companies where candidates must derive constraints from duplicates and sequence requirements.

What data structure is used in Divide Array Into Increasing Sequences?

The optimal solution relies mainly on counting frequencies while scanning the array, so it uses constant extra space. A more explicit greedy simulation may use a priority queue or heap to track subsequence lengths during construction.

What is the time complexity of Divide Array Into Increasing Sequences?

The optimal solution runs in O(n) time and O(1) space. You scan the array once to compute the maximum frequency of any value and check whether n ≥ maxFreq × k. A simulation-based greedy approach using heaps would take O(n log n) time.

Description Hints 5 Solution Video 7:38

1121. Divide Array Into Increasing Sequences

Hard65.4% acceptance1 companyPremium elsewhere, free here

Given an integer array nums sorted in non-decreasing order and an integer k, return true if this array can be divided into one or more disjoint increasing subsequences of length at least k, or false otherwise.

Example 1:

Input: nums = [1,2,2,3,3,4,4], k = 3
Output: true
Explanation: The array can be divided into two subsequences [1,2,3,4] and [2,3,4] with lengths at least 3 each.

Example 2:

Input: nums = [5,6,6,7,8], k = 3
Output: false
Explanation: There is no way to divide the array using the conditions required.

Constraints:

1 <= k <= nums.length <= 10⁵
1 <= nums[i] <= 10⁵
nums is sorted in non-decreasing order.

Asked at 1 company

Google

Topics

Array Counting

Hints open one at a time

Hint 1

Think in the frequency of the numbers and how this affects the number of sequences needed.

Hint 2

What is the minimum number of sequences we need to form? Considering frequency of the numbers.

Hint 3

Think about the least number of sequences to maximize the lengths.

Hint 4

The number of sequences needed is equal to the maximum frequency of an element.

Hint 5

How to put the other elements into sequences ? Think in a greedy approach.

7:38

Still stuck?Read 2 approaches, or watch a walkthrough.

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1class Solution:
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Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[1,2,2,3,3,4,4]
3

Input

[5,6,6,7,8]
3

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