CS2223 Recitation Pointer sort -- an Adaptation of Quick Sort

1. CS2223 RecitationPointer sort--an Adaptation of Quick Sort by Song Wang

2. Motivation • Be familiar with the quick sort algorithm • Indexed data sorting • Calling stack minimization for recursive function call

3. Problem Definition • Given an array has a key field and data field, return the array sorted by the key value. • Eg. Note: Key value is unique in the whole column

4. Pointer Sort (or Index Sort) • Instead of moving large records, we build an array of pointers (an index) to do the swap. • Eg. • Frequently used for huge table sorting, e.g. for relational database table. Sorted Initial

5. Code--by Gonnet and Baeza-Yates #include <sys/types.h> #include <sys/wait.h> #include <limits.h> #include <stdio.h> #include <stdlib.h> #include <sys/time.h> #include <sys/resource.h> #define TIMEBASE 699940000.0 struct timeval tp; struct timezone tzp; #define N 100 double sec1, sec2; int depth = 0, m=5, ip, ip1;

6. Code (Cond.)--by Gonnet and Baeza-Yates main() { int *r, *pr, b=0, e=N-1, s,t, i; //prepare array if ( (r=(int *)malloc( 4*(N+1))) == NULL) {printf("allocation failed\n"); exit(2); } if ( (pr=(int *)malloc( 4*(N+1))) == NULL) {printf("allocation failed\n"); exit(2); } srandom(2934); for (s=0;s<N;s++) {pr[s]=s; r[s] = random()%1000;} Size of int Initialize all pointers Each key value is [0,1000) Easy to read the printouts

7. Code (Cond.)--by Gonnet and Baeza-Yates //calling quick sort pointer function gettimeofday(&tp, &tzp); sec1 = tp.tv_sec + tp.tv_usec/1000000.0; qsp(r, pr, &b, &e); gettimeofday(&tp, &tzp); sec2 = tp.tv_sec + tp.tv_usec/1000000.0; printf("qs time %f\n", sec2-sec1); //calling insertion sort pinsort(r,pr, N); gettimeofday(&tp, &tzp); sec1 = tp.tv_sec + tp.tv_usec/1000000.0; printf("insort time %f\n", sec1-sec2); Begin index &end index

8. Code (Cond.)--by Gonnet and Baeza-Yates //checking sorted array for (i=0; i<N-1;i++) if (r[pr[i]] > r[pr[i+1]]) printf("out of order at %d\n",i); } Note: Checking the order is of course only needed until the code is accepted as correct,

9. Code (Cond.)--by Gonnet and Baeza-Yates threshhold int qsp(int *r, int *pr, int *b, int *e){ int i ,j ,p, pb, t, ab, ae; while ( (*e)- (*b)>m ) { //find the pivot i = *b; j = *e; pb = pr[(*b)]; p = r[pr[(*b)]]; while (i<j) {while (r[pr[j]] > p) j--; pr[i] = pr[j]; while ( (i<j) && (r[pr[i]] <= p) ) i++; pr[j] = pr[i]; } pr[i] = pb; pb,p used for swap later Pivot at i

10. Code (Cond.)--by Gonnet and Baeza-Yates //recursive call qsp() for both portions if (i-*b < *e -i) { ae = i-1; qsp(r,pr,b,&ae); *b = i+1;} else { ab = i+1; qsp(r,pr,&ab,e); *e = i-1;} }//for while (i<j) }//for qsp Discussed later: Call stack minimization

11. Code (Cond.)--by Gonnet and Baeza-Yates // perform once a straight insertion sort pinsort(int *a, int *pr, int n) { int i,j, tj; int t; if (n <= 1) return; for (j=1; j<n; j++) { tj = pr[j]; t = a[pr[j]]; for (i=j-1; i>=0; i--) if(t < a[pr[i]]) pr[i+1] = pr[i]; else break; pr[i+1] = tj; } }

12. A Running Example r N=9 0 1 2 3 4 5 6 7 8 pr Initialize qsp(r, pr, 0, 8); j i pb = 0; p =13 j i

13. A Running Example (Cond.) r N=9 0 1 2 3 4 5 6 7 8 j i j i i Recursive call Recursive call

14. Call Stack Minimization if (i-*b < *e -i) { ae = i-1; qsp(r,pr,b,&ae); *b = i+1;} else { ab = i+1; qsp(r,pr,&ab,e); *e = i-1;} • First recursively qsp() shorter partition. • Why? • The worst case: the pivot is always the biggest element • Call left partition first will need O(n) call stack depth