1. The problem is to find the Minimum Spanning Tree (MST) of a connected, weighted graph using Prim's algorithm. 2. Prim's algorithm starts with a single vertex and grows the MST by adding the smallest edge that connects a vertex in the MST to a vertex outside it. 3. Steps of Prim's algorithm: - Initialize the MST with any vertex. - Find the edge with the minimum weight that connects the MST to a vertex not yet in the MST. - Add that edge and vertex to the MST. - Repeat until all vertices are included. 4. Important rules: - The graph must be connected. - Always pick the minimum weight edge connecting MST to a new vertex. 5. Example intermediate work (assuming a graph is given): - Start with vertex A. - Edges from A: (A-B: 2), (A-C: 3). - Pick edge A-B (weight 2). - Now MST vertices: A, B. - Edges from MST to outside: (B-C: 1), (A-C: 3). - Pick edge B-C (weight 1). - MST vertices: A, B, C. - All vertices included, MST complete. 6. The final MST includes edges with weights 2 and 1, total weight 3. This process ensures the MST is found by always choosing the smallest connecting edge at each step.