1. Minimum Spanning Tree – Apply Kruskal’s algorithm to find the minimum spanning tree for a given network of cities and calculate its total weight.
2. Bubble Sort – Perform a bubble sort on a given list, calculate the maximum number of passes, and apply first-fit bin packing to allocate items.
3. Shortest Path – Use Dijkstra’s algorithm to find the shortest route in a network, including the specific route and its length.
4. Route Length Bounds – Use the nearest neighbour algorithm and shortcut methods to find upper and lower bounds for the length of a travel route.
5. Activity Networks – Construct an activity network, calculate early/late event times, identify critical paths, and handle changes in project durations.
6. Linear Programming – Formulate and solve linear programming problems with constraints to minimize costs, and solve using algebra or graphical methods.