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Run Dijkstra's algorithm on the following graph, starting from vertex A. Whenever there are multiple choices of vertex at the same time, choose the one that is alphabetically first. You are expected to show how you initialize the graph, how you picked a vertex and update the d values at the each, and what is final shortest distance of each vertex from A. B A F E

Run Dijkstra's algorithm on the following graph, starting from vertex A. Whenever there are multiple choices of vertex at the same time, choose the one that is alphabetically first. You are expected to show how you initialize the graph, how you picked a vertex and update the d values at the each, and what is final shortest distance of each vertex from A. B A F E

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Title: Running Dijkstra's Algorithm on a Sample Graph** **Instructions:** Run Dijkstra’s algorithm on the graph displayed, starting from vertex A. When there are multiple vertex choices simultaneously, select the one that is alphabetically first. You should demonstrate how you initialize the graph, how you select a vertex, update the distance (d) values at each step, and determine the final shortest distance of each vertex from A. **Graph Description:** - **Vertices:** A, B, C, D, E, F - **Edges and Weights:** - A to B: weight 2 - A to C: weight 6 - B to C: weight 1 - B to D: weight 9 - B to F: weight 11 - C to E: weight 3 - D to E: weight 2 - E to D: weight 2 - E to F: weight 2 **Step-by-Step Algorithm Execution:** 1. **Initialization:** - Start from vertex A. Set initial distances: d(A) = 0, d(B) = ∞, d(C) = ∞, d(D) = ∞, d(E) = ∞, d(F) = ∞. 2. **Iteration Steps:** - Choose the vertex with the smallest tentative distance. - Update the distances of its adjacent vertices. - If a smaller path to a vertex is found, update the vertex's distance. 3. **Final Calculation:** - Upon completing the algorithm, display the shortest path distances from vertex A to all other vertices. **Objective:** Utilize the algorithm to determine the shortest path from vertex A to all other vertices in the graph, ensuring that for any choices, the alphabetical priority is followed.
Transcribed Image Text:**Title: Running Dijkstra's Algorithm on a Sample Graph** **Instructions:** Run Dijkstra’s algorithm on the graph displayed, starting from vertex A. When there are multiple vertex choices simultaneously, select the one that is alphabetically first. You should demonstrate how you initialize the graph, how you select a vertex, update the distance (d) values at each step, and determine the final shortest distance of each vertex from A. **Graph Description:** - **Vertices:** A, B, C, D, E, F - **Edges and Weights:** - A to B: weight 2 - A to C: weight 6 - B to C: weight 1 - B to D: weight 9 - B to F: weight 11 - C to E: weight 3 - D to E: weight 2 - E to D: weight 2 - E to F: weight 2 **Step-by-Step Algorithm Execution:** 1. **Initialization:** - Start from vertex A. Set initial distances: d(A) = 0, d(B) = ∞, d(C) = ∞, d(D) = ∞, d(E) = ∞, d(F) = ∞. 2. **Iteration Steps:** - Choose the vertex with the smallest tentative distance. - Update the distances of its adjacent vertices. - If a smaller path to a vertex is found, update the vertex's distance. 3. **Final Calculation:** - Upon completing the algorithm, display the shortest path distances from vertex A to all other vertices. **Objective:** Utilize the algorithm to determine the shortest path from vertex A to all other vertices in the graph, ensuring that for any choices, the alphabetical priority is followed.
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