VISUALIZATION OF THE ALGORITHM FOR FINDING THE OPTIMAL PATH BETWEEN TWO POINTS IN A GRID MAZE WITH DYNAMICALLY CHANGING OBSTACLES

<ns0:p>This paper investigates the current problem of finding the optimal path in dynamic environments modeled as cellular labyrinths with obstacles. The problem of finding the optimal path between two points of a cellular labyrinth is relevant due to its versatility, applied value and fundamental importance for the development of modern technologies. The main attention is paid to the development and software implementation of a system for visualizing algorithms on graphs, which allows real-time observation of the decision-making process of an autonomous agent. The paper provides a detailed comparative analysis of classical methods, such as Dijkstra's algorithm and A*, as well as specialized incremental approaches, in particular D* Lite. The advantages of using graph theory for solving problems in environmental management, logistics and robotics, where the environment can change unpredictably, are substantiated. The purpose of the presented work is to develop a program for visualizing the algorithm for finding the optimal path on a field, which can be represented as a labyrinth with surmountable and insurmountable obstacles. The task is to find the optimal path between two points on the field and display it. The practical part of the research includes the development of software in C#, which demonstrates the process of rerouting the route when new obstacles arise without the need for a complete recalculation of the entire network. This is critically important for minimizing computational costs in complex information and analytical systems. A special emphasis is placed on the educational aspect: the developed visualization is integrated into the educational process for teaching the disciplines "Algorithms and Data Structures" and "Object-Oriented Programming", which significantly improves the assimilation of complex mathematical concepts by students. The results of the work confirm that the combination of theoretical methods of pathfinding with interactive visualization provides high reliability and transparency of the functioning of modern navigation and environmental monitoring systems. The program for visualizing the algorithm for finding the optimal path in a maze has great practical importance and can be used in robotics and autonomous systems for robot navigation in a real environment, in networks and telecommunications it searches for the optimal data transmission route. Visualizing the algorithm for finding the optimal path in a cellular maze with dynamic obstacles allows for a deeper understanding of the principles of operation of algorithms, to assess their effectiveness in real time, and to experiment with different strategies for rerouting the route.Received 2026-02-23Accepted 2026-04-01</ns0:p>