| ## Page 1 | |
| 299 | |
| Train Swapping | |
| At an old railway station, you may still encounter one of the last remaining “train swappers”. A train | |
| swapper is an employee of the railroad, whose sole job it is to rearrange the carriages of trains. | |
| Once the carriages are arranged in the optimal order, all the train driver has to do, is drop the | |
| carriages off, one by one, at the stations for which the load is meant. | |
| The title “train swapper” stems from the first person who performed this task, at a station close to | |
| a railway bridge. Instead of opening up vertically, the bridge rotated around a pillar in the center of | |
| the river. After rotating the bridge 90 degrees, boats could pass left or right. | |
| The first train swapper had discovered that the bridge could be operated with at most two carriages | |
| on it. By rotating the bridge 180 degrees, the carriages switched place, allowing him to rearrange the | |
| carriages (as a side effect, the carriages then faced the opposite direction, but train carriages can move | |
| either way, so who cares). | |
| Now that almost all train swappers have died out, the railway company would like to automate | |
| their operation. Part of the program to be developed, is a routine which decides for a given train the | |
| least number of swaps of two adjacent carriages necessary to order the train. Your assignment is to | |
| create that routine. | |
| Input | |
| The input contains on the first line the number of test cases (N). Each test case consists of two input | |
| lines. The first line of a test case contains an integer L, determining the length of the train (0 ≤L ≤50). | |
| The second line of a test case contains a permutation of the numbers 1 through L, indicating the current | |
| order of the carriages. The carriages should be ordered such that carriage 1 comes first, then 2, etc. | |
| with carriage L coming last. | |
| Output | |
| For each test case output the sentence: ‘Optimal train swapping takes S swaps.’ where S is an | |
| integer. | |
| Sample Input | |
| 3 | |
| 3 | |
| 1 3 2 | |
| 4 | |
| 4 3 2 1 | |
| 2 | |
| 2 1 | |
| Sample Output | |
| Optimal train swapping takes 1 swaps. | |
| Optimal train swapping takes 6 swaps. | |
| Optimal train swapping takes 1 swaps. |