Last Minute Lecture

Minimum Spanning Trees — Kruskal’s & Prim’s Algorithms Explained | Chapter 21 in Introduction to Algorithms Chapter 21 of Introduction to Algorithms (CLRS) dives deep into one of the most elegant and widely used topics in graph theory: the minimum spanning tree (MST). MST algorithms are essential in network design, clustering, and optimization problems. This chapter introduces the MST problem, explains the greedy strategy behind its solutions, and breaks down two classic algorithms—Kruskal’s and Prim’s—used to efficiently construct MSTs. 📺 Watch the video above for a podcast-style walkthrough, or read below for a complete written summary and key definitions you need to understand this foundational algorithmic concept. What Is a Minimum Spanning Tree? A minimum spanning tree is a subset of a graph’s edges that connects all the vertices together without forming cycles and with the least possible total edge weight. The MST of a connected, undirected, weighted graph ensur...

Heapsort & Priority Queues — Max-Heaps, Min-Heaps, and Efficient In-Place Sorting | Chapter 6 of Intro to Algorithms Sorting and managing dynamic data efficiently are critical tasks in computer science. Chapter 6 of Introduction to Algorithms introduces the heap data structure and the heapsort algorithm, demonstrating how heaps enable optimal in-place sorting and fast priority queue operations. Whether you’re preparing for coding interviews or building real-world systems, understanding heaps is essential for designing high-performance algorithms. Prefer to learn by listening? Watch the podcast summary below, and subscribe to Last Minute Lecture for comprehensive breakdowns of every chapter in introduction to algorithms . The Heap Data Structure A heap is a nearly complete binary tree stored efficiently in an array. Each node’s children and parent can be found using index arithmetic. There are two main types: Max-heap: Each parent node is greater than or equal ...