Rearranging Trains

1. Engine Train cars Track B A D C Sorted order D C B A Stub or lead B A D C B A D C Stub or lead Stub or lead C A B D C A B D Siding Rearranging Trains Stack or LIFO data structure in CE Question: Is there an ordering that cannot be sorted using a stub? Devising a sorting algorithm Queue or FIFO Sorting Networks

2. 2 C B A D 3 1 Delivering Train Cars in a Specific Order Cars in the train below have been sorted according to their delivery points. However, it is still nontrivial to deposit car A in stub 1, car B in stub 2, and car C in siding 3. Cars can be pulled or pushed by the engine. 2 3 1 2 3 1 Is there a better initial ordering of the cars for the deliveries in this puzzle? Sorting Networks

3. B A 1 2 Train Passing Puzzle The trains below must pass each other using a siding that can hold only one car or one engine. Show how this can be done. Sorting Networks

4. 5 10 8 12 5 8 10 12 2 5 6 7 0 1 2 3 2 6 7 14 8 10 12 14 6 14 2 7 4 5 6 7 4 15 9 1 1 4 9 15 0 1 3 4 8 9 10 11 9 11 13 15 0 3 11 13 11 13 3 0 12 13 14 15 4-sorter tests (4, 4)-merger tests (8, 8)-merger tests A 16-Input Sorting Network Use 4-input sorters, follow by (4, 4)-mergers, and end with an (8, 8)-merger Using the 0-1 principle, we can validate this network via 16 + 25 + 81 tests Sorting Networks