computing the quartet distance between general trees

7.2. IMPLEMENTATION 57ble sort, will, in spite of a quadratic worst-case running time, perform in linear time oninput that is nearly sorted, indeed giving a wrong impression of the algorithm. My implementationmakes a depth-first numbering of the leaves in T and then numbers theleaves in T ′ according to this. This numbering determines in which order we processdifferent parts of the tree. If we shuffle the leaves in both trees and redo the experimentthe topologies of the trees remain the same, but the algorithm will process each tree in adifferent order.Repeating the experiment 25 times with different permutations of the leaves result inthe plot displayed in Fig. 7.13. The difference in performance is difficult to observe andit is evident that the order of the leaves is not a decisive factor; the running time is onlydependent on the structure of the tree. These results will hopefully heighten the level ofconfidence.time in seconds - t(n)10001001010.1Performance of the C++ implementation if leaves are shuffled before execution.bin, best exp= 2.06ran, best exp= 2.07sqrt, best exp= 1.79star, best exp= 2.04wc, best exp= 2.02nn 2n 30.0150 100 200 500 800number of leaves - nFigure 7.13: Shuffling the leaves does not yield a different running time.