三種快速排序算法的實現(xiàn)(遞歸算法、非遞歸算法、三路劃分快速排序)

1、三種快速排序算法的實現(xiàn)（遞歸算法、非遞歸算法、三路劃分快速排序） 快速排序的三個步驟：1、分解：將數(shù)組r劃分成兩個(可能空)子數(shù)組和 Ap+l.r,使得A1L.P-L中的每個元素都小于等于A(p),而且，小于等于 Ap+1. r中的元素。下標p也在這個劃分過程中計算。2、解決：通過遞歸調用快速排序，對數(shù)組AL.p-l和Ap+L.r排序。3、合并：因為兩個子數(shù)組時就地排序，將它們的合并并不需要操作，整個數(shù)組 已經排序。1 .快速排序的基礎實現(xiàn)：QUICKSORT(A, 1, r)if 1 < rthen q = PART I ON (A, 1, r)QUICKSORT(A, 1, p-1)

2、QUICKSORT(A, p+1, r)兩路PARTION算法主要思想：move from left to find an element that is not lessmove from right to find an element that is not greaterstop if pointers have crossedexchange實現(xiàn)代碼：cpp view plaincopy1. int partition(double* a, int left, int right)2. (3. double x = a right;4. inti =left-1, j = right

3、;5. for(;)6. (7. while(a+i < x) 118.while(a-j >x) if(j=left) break;9. if(i < j)10. swap (a i, aj);11. else break;12. )13. swap (a Ei, a right);14. return i;15. )16.17. void quicksort1(double* a, int left, int right)18. 19.if (left20. (21. int p = partition (a, left, right);22.23. quickSortl

4、 (a, left, p-1);24. quickSortl (a, p+1,right);25. 26. 2,非遞歸算法：其實就是手動利用棧來存儲每次分塊快排的起始點，棧非空時循環(huán)獲取中軸入棧。實現(xiàn)代碼：cpp view plaincopy1. void quickSort2(double* a, int left, int right)2. (3. stack<int> t;4. if ( p = partition(a, left, right);6.17.18.if (p-l>left)(t.pu

5、sh(left);t. push (p-1);)if (p+1(t. push (p+1);t. push(right);)1.32.33.while(!t. empty ()(int r = t. top();t. pop();int 1 = t. top();t. pop();p = partition (a,1, r);if (p-l>l)(t. push(l);t. push(p-1);if (P+134.35.t. push (p+1);36. t. push(r);37. )38.39. )40. )4

6、1. )3.三路劃分快速排序算法：Bentley-McIlroy 3-way partitioningPartitioning invariant equal lessgreater equal move from left to find an element that is not less o move from right to find an element that is not greater o stop if pointers have crossed o exchange o if left element equal, exchange to left end if ri

7、ght element equal, exchange to right endSwap equals to center after partition lessequalgreater實現(xiàn)代碼:cpp view plaincopy1. void quickSort3Way(double a, int left, int right)2. 3. if(left < right)4. (5. double x = aright;6. int i = left-1, j = right, p = left-1, q = right;7.8.9. while (a+i < x) 10.

8、 while (a-jJ > x)if(j=left) break;4.if(i < J)swap(ali, ajj);if (ai = x) p+;swaP(ap,ai) ;15. if (aj = x) q-一；swap (aq,aj) ;16. 17. else break;18. 19. swap(a Ei, a fright); j = i-1； i=i+l；20. for (int k=left; k<=p; k+,j-一)swap(ak, aj);21.for (int k=right-l; k>=q; k-i+) swap (aEi,

9、 ak);22.23. quickSort3Way (a, left, j);24. quickSort3Way (a, i, right);25. 26. 4.測試代碼：cpp view plaincopy1.itinclude2. itinclude3. ftinclude4. using namespacestd;5.6. /產生(a,b)范圍內的num個隨機數(shù)7. double* CreateRand(double a, double b, int num)8. (9. double *c;10. c = new doublenum;11. srand(unsigned int)tim

10、e(NULL);12. for (int i=0; i13. ci = (b-a)*(double)rand()/RAND_MAX + a;14. return c;15. 16.17. /兩路劃分，獲取中軸，軸左邊數(shù)小于軸，軸右邊數(shù)大于軸18. double partition(double* a, int left, int right)19. (20.21. 22.23. / 1.遞歸快速排序，利用兩路劃分24. void quicksort1(double* a, int left, int right)25. (26.27. 28.29. / 2,非遞歸快速排序，手動利用棧來存儲每次

11、分塊快排的起始點,棧非空時循環(huán)獲取中軸入棧30. void quickSort2(double* a, int left, int right)31. (32.33. 34.35. / 3.利用三路劃分實現(xiàn)遞歸快速排序36. void quickSort3Way(double a, int left, int right)37. (38.39. 40.41. void main()42. (43. double *a, *b, *c;44. int k=10000000;45. time_t start, end;46.47. a=CreateRand(0, 1, k);48. b=Creat

12、eRand (0, 1, k);49. c=CreateRand (0, 1, k);50.51. start = clock ();52. quickSortl (a, 0, kT);53. end = clock();54. cout«，zl. recursive ，z«l. 0*(end-start)/CLOCKS_PER_SEC<< seconds'155.56. start = clock();57. quickSort2 (b, 0, kT);58. end = clock();59. cout«，z2. non-recursive ，z«l. 0* (end-start) /CLOCKS_PER_SEC« seconds160.61. start = clock();62. quickSort3Way (c, 0, kT);63. end = clock();64. cout«z，3. 3 way z，«l.0* (endstart) /CLOCKS_PER_SEC« seconds"<65.66. cout<67