✅Day 56 | LeetCode 2709. Greatest Common Divisor Traversal
🌟 Welcome to the Algorithmic Adventure of Traversing All Pairs! 🚀
Embark on an intriguing journey through the intricacies of prime factorization and graph traversal as we tackle the challenge of traversing all pairs in a given array. Brace yourself for an adventure filled with algorithmic insights and graph theory mastery.
🎯 Problem Overview:
In this thrilling challenge, we are presented with an array of integers. Our mission is to determine whether it's possible to traverse all pairs of elements in the array, where traversal is only allowed between elements with a common prime factor. We aim to devise an efficient algorithm to solve this traversal problem and explore every pair of elements that share a common prime factor.
🚀 Algorithm Breakdown:
We begin by performing prime factorization for each element in the array. We build two maps:
prime2index: Maps each prime factor to the indices of array elements containing that prime factor.
index2prime: Maps each array index to the prime factors present in the corresponding element.
We implement a depth-first search (DFS) algorithm to traverse the pairs of elements. The DFS explores elements connected by common prime factors, ensuring that all pairs are visited.
During the DFS traversal, we mark visited indices and prime factors to avoid revisiting the same elements.
Finally, we check if all array indices have been visited during the DFS traversal. If any index remains unvisited, we conclude that it's not possible to traverse all pairs and return false; otherwise, we return true.
📊 Complexity Analysis:
Time Complexity: O(N * log(max_element)), where N is the number of elements in the array and max_element is the maximum value in the array. The complexity arises from prime factorization and DFS traversal.
Space Complexity: O(N), where N is the number of elements in the array. Additional space is used for storing prime factorization mappings and auxiliary data structures.
Prepare to delve into the depths of graph traversal and prime factorization as we unravel the solution together! Explore the intricacies of algorithmic strategies and deepen your understanding of traversing all pairs in an array based on common prime factors. 🔗✨
Tags: #algorithmicadventure #graphtraversal #primefactorization #codingchallenge #programminglogic #algorithmexplained #dfs #pairtraversal #graphtheory