On tree-growing search strategies

. . algorithms S s S a search strategy. Doberkat 1982 and Panny 1986 i is1 have studied the moments of the number of comparisons required for inser- . tion sort with one particular linear search strategy. In this paper, we show that if the values in a data array have been randomly selected from a continuous distribution, the number of comparisons needed to sort the values by most practical search strategies has asymptotically normal behavior. Thus we investigate properties of search strategies in general, with insertion sort serving as a conspicuous application. In order to insert a new key in a sorted data array, an implementation of insertion sort selects a sequence of probes: keys in the sorted array to which the algorithm compares the new key. If the new key is larger than a given probe, the algorithm selects a larger probe; if the probe's value exceeds that of the new key, the search continues in the segment of the data array contain- ing keys smaller than the probe. In general, the search algorithms applied for different keys in an insertion sort may be independent of each other. One 4 '