#graph
Dijkstra's Algorithm
Introduction Dijkstra’s Algorithm finds the shortest path from a source vertex to all other vertices in a weighted graph with non-negative edge weights. It’s the algorithm behind GPS navigation, network routing, and any system that needs to find the cheapest path between two points. The core idea: greedily pick the unvisited vertex with the smallest known distance, then update its neighbors’ distances. This is essentially BFS with a priority queue instead of a regular queue — the priority queue ensures we always process the closest vertex next. Read more →
March 31, 2026
Graph Representation
Introduction Before you can run BFS, DFS, or any other graph algorithm, you need to decide how to store the graph in memory. That choice affects the time and space complexity of every operation you perform on it. There are two standard representations: the adjacency list and the adjacency matrix. This tutorial covers both, when to use each, and how to handle directed, undirected, and weighted graphs. You should be familiar with Graphs Introduction and Arrays before reading this. Read more →
March 31, 2026
Depth-First Search (DFS)
Introduction Depth-First Search (DFS) is a fundamental graph traversal algorithm that explores as far as possible along each branch before backtracking. Think of it like exploring a maze by always taking the first path you see, going as deep as possible, then backtracking when you hit a dead end. DFS is essential for detecting cycles, topological sorting, finding connected components, and solving maze/puzzle problems. Unlike BFS which uses a queue, DFS uses a stack (or recursion, which implicitly uses the call stack). Read more →
November 19, 2025
Breadth-First Search (BFS)
Introduction Breadth-First Search (BFS) is a fundamental graph traversal algorithm that explores vertices level by level, visiting all neighbors of a vertex before moving to the next level. Think of it like ripples spreading out in water—you explore all vertices at distance 1, then distance 2, and so on. BFS is essential for finding shortest paths in unweighted graphs, level-order traversal of trees, and solving maze/puzzle problems. It uses a queue to maintain the order of exploration. Read more →
November 19, 2025
Graphs - Introduction
Introduction A graph is a non-linear data structure consisting of vertices (nodes) connected by edges. Unlike trees, graphs can have cycles, multiple paths between nodes, and connections in any direction. Graphs model relationships and networks, making them fundamental to solving real-world problems in social networks, maps, computer networks, and more. Graphs are one of the most versatile and powerful data structures in computer science. By the end of this tutorial, you’ll understand graph terminology, types of graphs, representation methods, and when to use them. Read more →
November 19, 2025