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Solve Minimum Arithmetic Sequence Partition using Java Language

Solve Minimum Arithmetic Sequence Partition using Java to enhance your skills with java coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Minimum Arithmetic Sequence Partition

Difficulty : Hard

Categories :

  • Arrays

Given an array of integers arr, you need to create the minimum possible number of non-empty subarrays such that each array element belongs to exactly one subarray, and each subarray satisfies at least one of these conditions:

  • The subarray contains exactly one element
  • All elements in the subarray are equal
  • The elements in the subarray form an arithmetic sequence with a non-zero common difference

Return the minimum number of required subarrays.

An arithmetic sequence is a sequence where the difference between each consecutive element is constant.

Constraints:

  • 1 ≤ arr.length ≤ 10^5
  • -10^4 ≤ arr[i] ≤ 10^4

Examples:

Input: arr = [1,2,3,4,5,6]
Output: 1
Explanation: The entire array forms an arithmetic sequence with difference 1
Input: arr = [1,3,4,5,5,5,2]
Output: 4
Explanation: We can split into [1], [3,4,5], [5,5], [2]
[1] and [2] have one element, [3,4,5] is arithmetic with difference 1, [5,5] has equal elements. [1,3,4,5] is not arithmetic (differences 2, 1, 1), and no split into 3 subarrays is valid

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Choose from the following categories

Strings A sequence of characters used to represent text, with problems focused on manipulation, searching, and pattern matching.

Arrays A collection of elements stored in contiguous memory locations, allowing efficient random access and manipulation.

Linked Lists A linear data structure where each element (node) points to the next, offering dynamic memory allocation and efficient insertions/deletions.

Trees A hierarchical data structure with nodes connected by edges, used in applications like databases, file systems, and parsing.

Graphs A collection of nodes (vertices) connected by edges, representing relationships, widely used in networking, routing, and social networks.

Dynamic Programming An optimization technique that solves problems by breaking them into overlapping subproblems and storing their results.

Backtracking A problem-solving method that explores all possibilities recursively, backtracking when a solution is not feasible.

Sorting Algorithms Techniques for arranging elements in a specific order, such as quicksort, mergesort, and bubble sort, essential for data organization.

Searching Algorithms Methods for finding elements in a dataset, such as binary search, linear search, and graph traversal techniques.

Mathematics A field of study involving numbers, calculations, and logical reasoning, forming the foundation for algorithms and problem-solving.

Recursion A programming technique where a function calls itself to solve smaller instances of the same problem, often used in divide-and-conquer approaches.

Bit Manipulation Operations performed directly on binary representations of data, used for efficient computations and optimization tasks.