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Solve Pairs of Prime Numbers using Python Language

Solve Pairs of Prime Numbers using Python to enhance your skills with python coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Pairs of Prime Numbers

Difficulty : Easy

Categories :

  • Mathematics

Given a positive integer n, find all pairs (sets) of prime numbers (p,q) such that p*q <= n. Return the pairs in ascending order.

Constraints:

  • 1 ≤ n ≤ 400

Examples:

Input: n = 4
Output: [2,2]
Explanation: Pair (2,2) has both prime numbers and satisfies 2*2 <= 4.
Input: n = 8
Output: [2,2,2,3,3,2]
Explanation: Pairs (2,2), (2,3), and (3,2) have prime numbers and satisfy p*q <= 8.

Follow-up:

Can you optimize your solution to achieve better than the expected time complexity of O(n2* sqrt(n))?

Problem Solving

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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.