An algorithm is presented which finds all occurrences of one. given string within another, in running time proportional to the sum of the lengths of the strings. The constant of proportionality is low enough to make this algorithm of practical use, and the procedure can also be extended to deal with some more general pattern-matching problems. A theoretical application of the algorithm shows that the set of concatenations of even palindromes, i.e., the language {can}*, can be recognized in linear time. Other algorithms which run even faster on the average are also considered. Key words, pattern, string, text-editing, pattern-matching, trie memory, searching, period of a string, palindrome, optimum algorithm, Fibonacci string, regular expression Text-editing programs are often required to search through a string of characters looking for instances of a given "pattern" string; we wish to find all positions, or perhaps only the leftmost position, in which the pattern occurs as a contiguous substring of the text. For example, c a e n a r y contains the pattern e n, but we do not regard c a n a r y as a substring. The obvious way to search for a matching pattern is to try searching at every starting position of the text, abandoning the search as soon as an incorrect character is found. But this approach can be very inefficient, for example when we are looking for an occurrence of aaaaaaab in aaaaaaaaaaaaaab. When the pattern is a"b and the text is a2"b, we will find ourselves making (n + 1) *
Objectives-To better define the neuropathology of vascular dementia. Methods-The neuropathological findings in 18 elderly, undemented subjects free of cerebrovascular disease were compared with 19 elderly undemented subjects who had cerebrovascular disease (many of whom had had a "stroke") and 24 elderly demented subjects who had cerebrovascular disease, but no other pathology to account for dementia. Cases in all groups were selected for absence or no more than very mild Alzheimer type pathology. Results-Microvascular brain damage in the form of severe cribriform change and associated subcortical white matter damage and microinfarction were correlated with a history of dementia. Severe cribriform change was much more common and microinfarction somewhat more common in the demented group with vascular disease than the undemented group with vascular disease (P=0.0006 and P=0.031 respectively). Other findings of note were that congophilic angiopathy had a greater prevalence in the vascular dementia group than the control group, single cerebral infarcts were more common in the group who were undemented with vascular disease than in the group with dementia and vascular disease (P=0.0028), and the last group lacked evidence of macroscopic infarction more often than the first (P=0.034). There was a non-significant trend for the ratio of infarcted:uninfarcted tissue in one cerebral hemisphere to be higher in the group with dementia and vascular disease than in the group with vascular disease but no dementia. Conclusions-Microvascular disease, not macroscopic infarction, was the chief substrate of vascular dementia in this series of cases.
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