Derailleur gears chain slack. Cage length determines the total capacity of the derailleur, that is the size difference between the largest and smallest chainrings, and the size difference between the largest and smallest sprockets on the cogset added together. A larger sum requires a longer cage length. Typical cross country mountain bikes with three front chainrings will use a long cage rear derailleur. A road bike with only two front chainrings and close ratio sprockets can operate with either a short or long cage derailleur, but will work better with a short cage. Manufacturer stated derailleur capacities are as follows: Shimano long
Library sort sort it is based on, library sort is a stable comparison sort and can be run as an online algorithm; however, it was shown to have a high probability of running in O(n log n) time (comparable to quicksort), rather than an insertion sort's O(n). The mechanism used for this improvement is very similar to that of a skip list. There is no full implementation given in the paper, nor the exact algorithms of important parts, such as insertion and rebalancing. Further information would be needed to discuss how the efficiency of library sort compares to that of other sorting