algorithms 4th 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

import Java.util.arraylist;import java.util.List; Public classStrtest { Public Static voidMain (string[] args) {//simulation generates a large integerLong n=Shengcheng (); //split this big integer to see what 's made of it.listsplitnumber (n); for(intI=0; I) {System. out. println (list.Get(i)); } } /** function: Calculates 2 of the whole number of times * Yellow Sea * Time: 2016-01-20 * @param n * @return*/ Private Static LongGetnumberbyid (intN) {return(Long) Math.pow (2, N); }

))intHornerintA[],intXintN) { intI, sum=a[n-1]; for(i=n-2; i>=0; i--) sum = a[i] + x *sum; returnsum;}intPolynominal (intA[],intXintN) { intI, Xarray[n], sum=0; xarray[0] =1; for(i=1; i1]; for(i=0; iXarray[i]; returnsum;}View Code2.4: Calculating the inverse θ of the series (NLGN)intMergecount (intA[],intLintR) { intm; if(L r) {m= (L + r)/2; returnMergecount (A, L, m) + Mergecount (A, m+1, R) +merge (A, L, M, R); } return 0;}intMergeintA[],intLintMintR) { intI, J, K, cnt=0; int

- * 8000 35.7 8.0 + * ... - * + ******************************************************************************/ A at /** - * The - * The running time of a method using a doubling ratio test. - * - * For additional documentation, see http://algs4.cs.princeton.edu/14analysis">section 1.4 - * of in * - * @authorRobert Sedgewick to * @authorKevin Wayne + */ - Public classDoublingratio { the Private Static Final intMaximum_integer = 1000000; * $ //This is class should not bei

improvement)Algorithm: asks if a set of n numbers contains and is 2 elements of X (need to support C99 standard)BOOLSumX (intA[],intNintx) { intlength, complement[n]; MergeSort (A,0, N-1); Length=deduplication (A, n); Xcomplement (A, complement, length, x); returnMergesearch (A, complement, length);}BOOLMergesearch (intA[],intB[],intN) { intI, J; for(i=0, j=n-1; I0 a[i]!=B[j];) if(A[i] ; Elsej--; returnI0;}voidXcomplement (intA[],intAcomplement[],intNintx) { inti; for(i=0; ia[i];}

its specified element.9, Mulitmap and mulitset elements of the same key, stored in the adjacent location, the traversal can be guaranteed to return the same key elements. So count (key) returns the number of elements of the key, and find (key) returns the first function of the key.Here is a simple example of applying a map container: Reading a file, recording the number of occurrences of each word in the file, and outputting the occurrences of the word and the number of occurrences in dictionar