Math Problem Statement

answer question b

P4: (a) State the Dijkstra's algorithm for an undirected weighted graph with all positive integer edge weights. (b) The below Figure represents a network of roads. The number on each arc is the length, in km, of the corresponding road. (i) Use Dijkstra’s algorithm to find the shortest route from A to J. State the shortest route and its length. (ii) Explain how you determined the shortest route from your labelled diagram. (iii) Find the shortest route from A to J via E and state its length.

Solution

To address question (b) for part (i), (ii), and (iii), I'll need to analyze the graph structure provided in the image. I will extract the necessary information and solve each part systematically. Let me process this image first. PIL import Image import pytesseract

Load the uploaded image

image_path = '/mnt/data/1733301478541hpi6zly0.jpg' image = Image.open(image_path)

Extract text from the image

extracted_text = pytesseract.image_to_string(image) extracted_textThe extracted text outlines the problem description but doesn't capture the diagram, which is essential for solving the problem. To proceed, I will need to recreate or interpret the graph structure (nodes and edges with weights) based on your input. Please provide details of the graph's structure (e.g., node connections and their respective weights) so I can compute the solutions.

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Math Problem Analysis

Mathematical Concepts

Graph Theory
Shortest Path Algorithms

Formulas

Dijkstra's Algorithm for shortest paths

Theorems

Triangle inequality property in graphs

Suitable Grade Level

Undergraduate level or advanced high school