Analysis of recursive algorithms by the contraction method

Several examples of the asymptotic analysis of recursive algorithms are investigated by the contraction method. The examples concern random permutations and binary search trees. In these examples it is demonstrated that the contraction method can be applied successfully to problems with contraction constants converging to one and with nonregular normalizations as logarithmic normalizations, which are typical in search type algorithms. An advantage of this approach is its generality and the possibility to obtain quantitative approximation results.