1. Bin Packing and Sorting – Calculate a lower bound for containers, apply first-fit bin packing, perform quick sort on a list, and use binary search to locate a specific value in the sorted list.
2. Minimum Spanning Tree (Kruskal′s Algorithm) – Use Kruskal’s algorithm to determine the minimum spanning tree of a network and calculate its total weight.
3. Activity Network and Scheduling – Draw an activity network, determine early and late event times, and calculate the minimum number of workers needed for project completion.
4. Shortest Path Calculation – Apply Dijkstra’s algorithm to find the shortest path in a road network and determine the path′s total length.
5. Linear Programming – Formulate a linear programming problem with constraints and an objective function, then solve using graphical or algebraic methods.
6. Optimization in Network Problems – Solve network optimization problems using algorithms like Prim’s and Dijkstra’s to determine the minimal travel route and time.