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Sorting. contents. 3 kinds of sorting methods Selection, exchange , and insertion O(n 2 ) sorts – VERY inefficient, but OK for ≈ 10 elements Simple selection, bubble (exchange), and insertion sorts heaps , for efficient selection sort heapsort priority queues using heaps
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contents • 3 kinds of sorting methods • Selection, exchange, and insertion • O(n2) sorts – VERY inefficient, but OK for ≈ 10 elements • Simple selection, bubble (exchange), and insertion sorts • heaps, for efficient selection sort • heapsort • priority queues using heaps • quicksort - example of divide-and-conquer strategy for efficient exchange sort • mergesort - for sequential files • radix sort - a non-comparison-based sort • no such thing as a universally good sorting scheme • Results may depend just how bad (out of order) the list is
Selection Sort Algorithm • Set i=0 • Start at element i • Search for smallest item < current item • Swap them • Advance i to i+1 • Repeat from step 2 until done
Selection sort • Make passes through a list • Each time correctly reposition one element • Restart at current (new) element and try again • Always moves the smallest item toward 0 5, 1, 12, -5, 16, 2, 12, 14 No smaller items so -5 gets swapped 5, 1, 12, -5, 16, 2, 12, 14
Selection Sort Results (red="to be swapped") • 5, 1,12,-5,16,2,12,14 (original array) • -5,1,12,5,16,2,12,14, • -5,1,2,5,16,12,12,14, • -5,1,2,5,12,16,12,14, • -5,1,2,5,12,12,16,14, • -5,1,2,5,12,12,14,16 done swapping, but not done • -5,1,2,5,12,12,14,16 done!! • 5 swaps
Selection sort code n=sizeof(myarray)/sizeof(*myarray); // #elements in array for(i = 0; i < n - 1; i++) // n is size of array (NOT max subs) { minloc= i; for (j = i + 1; j < n; j++) if (myarray[j] < myarray[minloc]) // smaller value? minloc= j; // if yes, new minloc if(minloc!= i) // if not itself { // swap the 2 elements temp = myarray[i]; // save new smaller one array[i] = myarray[minloc]; // move bigger one myarray[minloc] = temp; // insert smaller one } }
Exchange Sort Algorithm • n=#elements of the array • start at item n • Search for FIRST smaller item • Swap as soon as one is found • Repeat from step 3 until end of array • // above 2 steps move largest item toward end • Increase n • Repeat from step 2
Exchange sort results (red="to be swapped") • 5,1,12,-5,16,2,12,14 (original array) • 1,5,12,-5,16,2,12,14, • -5,5,12,1,16,2,12,14 • -5,1,12,5,16,2,12,14, • -5,1,5,12,16,2,12,14, • -5,1,2,12,16,5,12,14, • -5,1,2,5,16,12,12,14, • -5,1,2,5,12,16,12,14, • -5,1,2,5,12,12,16,14, • -5,1,2,5,12,12,14,16 done! • Nine swaps!
Exchange Sort code n=sizeof(myarray)/sizeof(*myarray); for (i=0; i<n-1; i++) for (j=i+1; j<n; j++) if (myarray[i] > myarray[j]) { //swap values temp = myarray[i]; // save new smaller one array[i] = myarray[j]; // move bigger one myarray[j] = temp; // insert smaller one }
Bubble Sort Algorithm (an exchange sort) • Repeat • hasChanged := false • decrementitemCount • repeat (index from 1 toitemCount) • if(item at index) > (item at (index + 1)) swap (item at index) with (item at (index + 1)) • hasChanged := true • untilhasChanged = false • A swap occurs at every value of itemcount
Bubble Sort Results (red="to be swapped") • 5, 1,12,-5,16,2,12,14 (original array) • 1,5,12,-5,16,2,12,14, • 1,5,-5,12,16,2,12,14, • 1,5,-5,12,2,16,12,14, • 1,5,-5,12,2,12,16,14, • 1,5,-5,12,2,12,14,16, • 1,-5,5,12,2,12,14,16, • 1,-5,5,2,12,12,14,16, • -5,1,5,2,12,12,14,16, • -5,1,2,5,12,12,14,16, done!! • 9 swaps!!
Bubble Sort Code asize=sizeof(myarray)/sizeof(*myarray); for(x=0; x<asize; x++) // start with one item {for(y=0; y<asize-1; y++) // for all following pairs in array {if(myarray[y]>myarray[y+1]) {// swap a pair as needed temp = myarray[y+1]; myarray[y+1] = myarray[y]; myarray[y] = temp; printarray(); } } // end y loop. Start again. 2nd item is part of a pair } // end x loop
Insertion Sort • Repeatedly insert a new element into an already sorted list • Great for a linked list
Algorithm for Linear Insertion Sort • Consider array as having 2 parts: • Sorted: 1st element (even if not in right place) • Unsorted: remaining elements • Look at first item in the UNsorted part • Move it to left or right of sorted part • Copy it to a temp • Locate where to put the item • Starting there, shift all elements, to the "right" • Makes a hole for the item • Insert the item • Define new beginning of Unsorted part • Repeat all of above until done
Re-stating the Algorithm for Linear Insertion Sort //similar to selection sort • Get a list of unsorted numbers • Set a "marker" for the sorted section after the first number in the list • Repeat steps 4 through 6 until the unsorted section is empty • Select the first unsorted number • Swap this number to the left until it arrives at the correct sorted position • Advance the marker to the right by one position • Stop
Insertion Sort Results (red ="to be moved") • 5, 1, 12, -5, 16, 2, 12, 14 original array • Remove the 1 & slide the 5 to the right • ---, 5, 12, -5, 16, 2, 12, 14 now insert the 1 • 1, 5, 12, -5, 16, 2, 12, 14 the 12 is OK, move the -5 • -5, 1, 5, 12, 16, 2, 12, 14 need to move the 2 • -5, 1, ---, 5, 12, 16, 12, 14 • -5, 1, 2, 5, 12, 16, 12, 14 now swap 2,-5, 1 • -5, 1, 2, 5, 12, 16, 12, 14 insert the 2nd 12 • -5, 1, 2, 5, 12, 12, 16, 14 insert the 14 • -5, 1, 2, 5, 12, 12, 14, 16
Insertion Sort Code asize=sizeof(myarray)/sizeof(*myarray); for (i = 1; i < asize; i++) { j = i; while (j > 0 && myarray [j - 1] > myarray [j]) { tmp= myarray[j]; myarray [j] = myarray[j - 1]; myarray[j - 1] = tmp; j--; } }
