Python Coding Practice

Solve Sieve of Eratosthenes using Python Language

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

Sieve of Eratosthenes

Difficulty : Easy

Categories :

  • Searching algorithms
  • Mathematics

Given a number N, calculate all prime numbers up to N using the Sieve of Eratosthenes algorithm. Return the list of prime numbers less than or equal to N in ascending order.

Constraints:

  • 1 ≤ N ≤ 104

Examples:

Input: N = 10
Output: [2,3,5,7]
Explanation: The prime numbers less than or equal to 10 are 2, 3, 5, and 7.
Input: N = 35
Output: [2,3,5,7,11,13,17,19,23,29,31]
Explanation: The prime numbers less than or equal to 35 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

Follow-up:

The Sieve of Eratosthenes algorithm has a time complexity of O(NloglogN). Can you implement it efficiently using the optimal space complexity of O(N)?

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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.