{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:25:41Z","timestamp":1750307141558,"version":"3.41.0"},"reference-count":7,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2011,12,1]],"date-time":"2011-12-01T00:00:00Z","timestamp":1322697600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Inroads"],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:p>\n            This article examines the recurrence obtained for Catalan numbers based on their description of the number of unique binary search tree structures possible with\n            <jats:italic>n<\/jats:italic>\n            distinct keys. The straightforward recurrence obtained, when transformed into a recursive method, obtains the solution in 3\n            <jats:sup>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sup>\n            method invocations. With a small change based on symmetry, this can be changed to obtain the solution in 2\n            <jats:sup>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sup>\n            method invocations. Of course, one can obtain the solution in massively fewer operations (O(\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            )) in a dynamic programming\/memoized solution.\n          <\/jats:p>","DOI":"10.1145\/2038876.2038889","type":"journal-article","created":{"date-parts":[[2012,10,15]],"date-time":"2012-10-15T19:22:23Z","timestamp":1350328943000},"page":"33-37","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Exponential base change based on symmetry"],"prefix":"10.1145","volume":"2","author":[{"given":"Timothy","family":"Rolfe","sequence":"first","affiliation":[{"name":"Eastern Washington University, Washington"}]}],"member":"320","published-online":{"date-parts":[[2011,12]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Nick Parlante \"Binary Trees\" http:\/\/cslibrary.stanford.edu\/110\/BinaryTrees.html accessed 2011 Aug 15.  Nick Parlante \"Binary Trees\" http:\/\/cslibrary.stanford.edu\/110\/BinaryTrees.html accessed 2011 Aug 15."},{"key":"e_1_2_1_2_1","unstructured":"\"Catalan Number\" http:\/\/en.wikipedia.org\/wiki\/Catalan_number accessed 2011 Aug 15.  \"Catalan Number\" http:\/\/en.wikipedia.org\/wiki\/Catalan_number accessed 2011 Aug 15."},{"key":"e_1_2_1_3_1","unstructured":"Nick Parlante loc. cit.  Nick Parlante loc. cit."},{"key":"e_1_2_1_4_1","unstructured":"For {EQUATION} reflecting a loop that executes zero times.  For {EQUATION} reflecting a loop that executes zero times."},{"key":"e_1_2_1_5_1","unstructured":"{EQUATION}  {EQUATION}"},{"key":"e_1_2_1_6_1","unstructured":"http:\/\/penguin.ewu.edu\/~trolfe\/BaseChange\/  http:\/\/penguin.ewu.edu\/~trolfe\/BaseChange\/"},{"key":"e_1_2_1_7_1","unstructured":"Stanley Richard and Weisstein Eric W. \"Catalan Number.\" From MathWorld--A Wolfram Web Resource. http:\/\/mathworld.wolfram.com\/CatalanNumber.html. Accessed 2011 Aug 15.  Stanley Richard and Weisstein Eric W. \"Catalan Number.\" From MathWorld--A Wolfram Web Resource. http:\/\/mathworld.wolfram.com\/CatalanNumber.html. Accessed 2011 Aug 15."}],"container-title":["ACM Inroads"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2038876.2038889","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2038876.2038889","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T09:48:53Z","timestamp":1750240133000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2038876.2038889"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["10.1145\/2038876.2038889"],"URL":"https:\/\/doi.org\/10.1145\/2038876.2038889","relation":{},"ISSN":["2153-2184","2153-2192"],"issn-type":[{"type":"print","value":"2153-2184"},{"type":"electronic","value":"2153-2192"}],"subject":[],"published":{"date-parts":[[2011,12]]},"assertion":[{"value":"2011-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}