CCO '96 P1 - Train Swapping

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Points: 5
Time limit: 2.0s
Memory limit: 64M

Problem type
Canadian Computing Competition: 1996 Stage 2, Day 1, Problem 1

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 directions, 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 a routine that computes the minimal number of swaps.

Input Specification

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 \le L \le 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 Specification

For each test case output the sentence: Optimal train swapping takes S swaps. where S is an integer representing the minimal number of swaps to order the train.

Sample Input

1 3 2
4 3 2 1
2 1

Sample Output

Optimal train swapping takes 1 swaps.
Optimal train swapping takes 6 swaps.
Optimal train swapping takes 1 swaps.


  • 3
    bariumlanthanum  commented on June 3, 2020, 5:12 p.m. edited

    isnt this kind of like bubble sort? every time bubble sort switches 2 elements, it is a swap, and there are 2 whole seconds, so there is time for it

  • 5
    Plasmatic  commented on Feb. 22, 2019, 5:11 p.m.

    Is counting inversions only 5 points?

    • 8
      kingW3  commented on Feb. 22, 2019, 8:11 p.m. edited

      Counting inversions is straightforward with \mathcal{O}(n^2), if you had to do it in \mathcal{O}(n \log n) then I'd agree that it deserves more points.

    • 1
      magicalsoup  commented on Feb. 22, 2019, 7:31 p.m.

      Are you implying it should be more than 5pts? I believe 5pts is the right amount, its a very easy cco question after all