A Practical Introduction to Data Structures and Algorithm Analysis

436 Chap. 12 Lists and Arrays Revisitedremainder of size 50. Best fit has the disadvantage that it requires that the entire listbe searched. Another problem is that the remaining portion of the best-fit block islikely to be small, and thus useless for future requests. In other words, best fit tendsto maximize problems of external fragmentation while it minimizes the chance ofnot being able to service an occasional large request.A strategy contrary to best fit might make sense because it tends to minimize theeffects of external fragmentation. This is called worst fit, which always allocatesthe largest block on the list hoping that the remainder of the block will be usefulfor servicing a future request. In our example, the worst fit is the block of size900, leaving a remainder of size 300. If there are a few unusually large requests,this approach will have less chance of servicing them. If requests generally tendto be of the same size, then this might be an effective strategy. Like best fit, worstfit requires searching the entire freelist at each memory request to find the largestblock. Alternatively, the freelist can be ordered from largest to smallest free block,possibly by using a priority queue implementation.Which strategy is best? It depends on the expected types of memory requests.If the requests are of widely ranging size, best fit might work well. If the requeststend to be of similar size, with rare large and small requests, first or worst fit mightwork well. Unfortunately, there are always request patterns that one of the threesequential fit methods will service, but which the other two will not be able toservice. For example, if the series of requests 600, 650, 900, 500, 100 is made toa freelist containing blocks 500, 700, 650, 900 (in that order), the requests can allbe serviced by first fit, but not by best fit. Alternatively, the series of requests 600,500, 700, 900 can be serviced by best fit but not by first fit on this same freelist.Buddy MethodsSequential-fit methods rely on a linked list of free blocks, which must be searchedfor a suitable block at each memory request. Thus, the time to find a suitable freeblock would be Θ(n) in the worst case for a freelist containing n blocks. Mergingadjacent free blocks is somewhat complicated. Finally, we must either use additionalspace for the linked list, or use space within the memory pool to support thememory manager operations. In the second option, both free and reserved blocksrequire tag and size fields. Fields in free blocks do not cost any space (because theyare stored in memory that is not otherwise being used), but fields in reserved blockscreate additional overhead.The buddy system solves most of these problems. Searching for a block ofthe proper size is efficient, merging adjacent free blocks is simple, and no tag orother information fields need be stored within reserved blocks. The buddy system