algorithms fourth edition

Quick sort, tail recursion. Worst case stack depth θ (LGN)1 ImportRandom2 defpatition (A, L, R):3j =L4Key =A[r]5 forIinchRange (L, r+1):6 ifA[i] Key:7temp =A[j]8A[J] =A[i]9A[i] =TempTenJ + = 1 OneA[R] =A[j] AA[J] =Key - returnJ - the defquicksort (A, L, R): - ifL r: -p =patition (A, L, R) -Recusive_tail_quicksort (A, L, p-1) +Recusive_tail_quicksort (A, p+1, R) - + defRecusive_tail_quicksort (A, L, R): A whileL r: atp =patition (A, L, R) - if(p-l) p): -Recusiv

1counting-SORT2 (a,k)2 Let C[0..K] is a new array3 fori =0 to K4c[i]=05 fori = 1To A.length6C[a[i]] = c[a[i]]+17 fori = 1to K8C[i] = C[i] + c[i-1]9 fori = a.length Downto 1Ten whileI C[a[i]) One Exchagnge A[i] with A[j] AC[A[J]] = c[a[j]]-1#include 　　Introduction to Algorithms third Edition study questions 8-2.E

is n, the loop is invariant, that is, either the subscript I (a[i] = = v) is taken in the array n, or it is not found (v = NIL). Then add an element, make the scale of n+1, easy to know, the size of n since the establishment (can get a useful nature, conclusion), scale n+1 at most one time equal judgment (that is, in the original array does not take the case of I), and finally can obtain useful conclusions. The iteration (in this case, size + 1) will keep the loop invariant.Termination: Finall

[] arr = {2, 5, 8, 3, 6}; Selectionsort (arr); } Public Static voidSelectionsort (int[] arr) { for(inti=0;i//The outer loop controls which position the number is compared to the number in the back for(intj=i+1;j//the inner loop controls how many times this number needs to be compared to the subsequent number. if(Arr[i]>arr[j]) {// //This condition is guaranteed to be arranged from small to large, and vice versa from large to small intt

Requirements:As written, each loop iteration in the List-search ' procedure requires the tests:One for X≠l.nil and one for x.key≠k. Show How to eliminate the test forX≠l.nil in each iteration.Solution:The key is to set Sentinel Sentinel's key value to K prior to the start of the while loop, so that the while loop will terminate if the query succeeds in the listPseudo codeList-search ' (L, K)1 L.nil.key = k2 x = L.nil.next3 while X.key≠k4 x = X.next5 if x = = L.nil6 L.nil.key = Nil7 return XIntro

Binary Lookup Pseudo-code: IterationBinary-search (a,low,high,x)while (LowBinary-search (a,low,high,x) if (Low>high) return nullmid= (Low+high)/2if (a[mid]==x) return Midelse if (a[mid]>x) Return Binary-search (a,low,mid-1,x) Else return Binary-search (a,mid+1,high,x) proves simple enough to draw a tree. T (n) =t (N/2) +o (1)Introduction to Algorithms third Edition exercise 2.3-5

this optimal step size of the smaller array109 //var Steparr = [1031612713, 217378076, 45806244, 9651787, 2034035, 428481, 90358, 19001, 4025, 836, 182, 34, 9, 1]//for large The step selection of an array the vari = 0;111 varSteparrlength =steparr.length; the varLen =Array.Length;113 varLen2 = parseint (LEN/2); the the for(; i ) { the if(Steparr[i] >len2) {117 Continue;118 }119 - Stepsort (Steparr[i]);121 }122 123 //Sort a step124