Download
1 / 3
40 likes | 175 Vues
This problem set presents various mathematical and algorithmic challenges. Firstly, it addresses the classic water jug problem, where two jugs of 3 and 5 quarts are used to measure exactly one quart of water. Next, it explores the nearest-neighbor algorithm to find a Hamiltonian circuit starting from specified vertices in a given graph. Additionally, it uses mathematical induction to demonstrate that any postage of at least 12 cents can be formed using 3-cent and 7-cent stamps. Finally, it involves finding Euler's path or circuit in several graphs.
E N D
Problem Set 1 Two jugs A and B have capacities of 3 quarts and 5 quarts, respectively. Use the jugs to measure exactly one quart of water. Take into account the following considerations: You may fill either jug to capacity from a water tap; you may empty the contents of either jug into a drain; you may pour water from each jug into the other. 2. Use nearest-neighbor algorithm to find a Hamiltonian circuit in the following graph.
Use nearest-neighbor method to find a Hamiltonian circuit in the following graph. • Start at vertex A. • Start at vertex D. • Determine a minimum Hamiltonian circuit for the graph. 4. Use mathematical induction to show that any postage of at least 12-cents can be obtained using 3-cents and 7-cents stamps.
