Solutions for Introduction to algorithms second edition
Merelya vaguesuggestiontoa solutiontosomeoftheexercisesposedinthebo okIntroductiontoalgo-rithmsbyCormen, is youhavefoundanerror, havea bettersolutionorwishtocontributeinsomeco nstructivewaypleasesenda is lastresortortocheckif yourinstructorgotit underconstructionandis updatedonlysporadically. ,PhilipBilleLastupdate:December9, 20021:2-2Insertionsortbeatsmergesortwhen 8n2< 64nlgn,)n < 8lgn,)2n=8< n. Thisis truefor26n643(foundbyusinga calculator). 107236 1082864 10822592 109294608 1010294608 1012pn101236 10141296 1016746496 10166718464 10188950673664 10208950673664 1024n1066 10736 108864 1082592 10994608 101094608 1012nlgn627462801417??????????n2103244948976 104293938160996830758413307584134n31023911532442013736981694556612n19253136414956n!911121315171822:1-2Inline5ofINSERTION-SORTalterA[i]> keytoA[i]< :1-3Algorithm1LINEAR-SEARCH(A; v)Input:A=ha1; a2; : : : anianda :Anindexisuchthatv=A[i]ornilifv62Afori 1tondoifA[i] =vthenreturniend ifend forreturnnilAsa loopinvariantwesaythatnoneoftheelementsa tindexA[1; : : : ; i-1] , allpropertiesarefull :2-1n3=1000-100n2-100n+3= (n3).
2:1-2 In line 5 of INSERTION-SORT alter A[i] > key to A[i] < key in order to sort the elements in nonincreasing order. 2:1-3 Algorithm 1 LINEAR-SEARCH(A;v) Input: A = ha1;a2;:::ani and a value v. Output: An index i such that v = A[i] or nil if v 62A for i 1 to n do if A[i] = v then return i end if end for return nil As a loop invariant we say that none of the elements at index A[1;:::;i - 1 ...
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