Derailleur gears by 13 drive-train. Most road bicycles have two chainrings, and touring bicycles commonly have three. The rear derailleur serves double duty: moving the chain between rear sprockets and taking up chain slack caused by moving to a smaller sprocket at the rear or a smaller chainring by the front derailleur. In order to accomplish this second task, it is positioned in the path of the bottom, slack portion of chain. Sometimes the rear-derailleurs are re-purposed as chain tensioners for single-speed bicycles that cannot adjust chain tension by a different method. Although variations exist, as noted below, most rear derailleurs have
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