biparty graph

This slide is about formally defining “bipartite graph”. Here’s how you can explain it, avoiding repetition from the previous page: 🎓 Formal Definition of Bipartite Graph Core task of this page: From intuitive model → abstract definition. We just saw an example of a bipartite graph: one side is classrooms, the other is exams, and an edge … Read more

Deep Dive into Hash Tables_ Python vs C++ vs Java

A hash table is an efficient data structure used to implement associative arrays or sets. Its core idea is to use a hash function to map keys to indices in an array, enabling fast lookup, insertion, and deletion operations. However, different languages and standard libraries have variations in their specific implementations, particularly in handling hash … Read more

greedy algorithm proofs

Activity Selection Problem Proof of Optimality for the Greedy Algorithm in the Activity Selection Problem We prove that the greedy strategy of always selecting the activity with the earliest finish time yields an optimal solution to the activity selection problem. The proof relies on two key properties: 1. Greedy-Choice Property Claim: There exists an optimal … Read more

Learning AWK From Patterns to Programs

AWK Program Structure AWK scripts are organized into three main blocks: BEGIN block Body block (pattern-action block) END block BEGIN { awk-commands } /pattern/ { awk-commands } END { awk-commands } 1. BEGIN Block The BEGIN block is executed once and only once, before any input line is read. It’s typically used for initialization, such … Read more

Binary Search Explained in Detail with Three Templates

In its simplest form, binary search works on a contiguous sequence with specified left and right indices, also known as the search space. It continuously narrows down the search range to eventually locate the target value or determine that it does not exist. Basic Concept Binary search maintains three pointers: left, right, and mid At … Read more

c++ learning resources

the most clear modern C++ course for free. cs106L at stanford CS 106L: Standard C++ Programming videos CS 106L Fall 2019 – Lecture 0: Introduction (Screencast) cs106l/cs106l-assignments: Course assignments for CS106L C++ template debugging tool: https://cppinsights.io/ C/C++ to assembly tool: https://godbolt.org/ macro debugger: notfoundry/ppstep: Interactive C/C++ preprocessor macro debugger

combinational motion planing

roadmap The slide you’ve provided discusses the concept of a "roadmap" in the context of combinatorial motion planning. Here’s an explanation of the key elements: Topological Graph G: A graph $G$ is considered, where: Vertices represent different configurations $q$ that belong to a free configuration space, denoted as $C_{free}$. Edges represent paths $\Pi$ that connect … Read more