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Elementary Sorting

This guide explores Selection and Insertion sorting, explaining how to implement them from scratch. Detailed examples, code snippets, efficiency analysis, and comparison of other sorting techniques are included.

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Elementary Sorting

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  1. Elementary Sorting • Have talked about using “built-in” sorting • Arrays.sort • Collections.sort • These are “heavy-duty”, “industrial” sorts that are for general use. With the appropriate Compator, they can meet most of your needs. • However, you should know how to write a simple sort routine from scratch.

  2. Selection Sort Example • N items in an array named Data [ 2 | 4 | 7 | 3 | 1 | 8 | 5 ] • Find smallest of elements 1 thru N of Data • Interchange this with 1st element of array Data [ 1 | 4 | 7 | 3 | 2 | 8 | 5 ] • Find smallest of elements 2 thru N of Data • Interchange this with 2nd element of array Data [ 1 | 2 | 7 | 3 | 4 | 8 | 5 ] • ... • Find smallest of elements K thru N of Data • Interchange this with Kth element of array Data [ 1 | 2 | 3 | 7 | 4 | 8 | 5 ] [ 1 | 2 | 3 | 4 | 7 | 8 | 5 ] [ 1 | 2 | 3 | 4 | 5 | 8 | 7 ] • Done when K = N [ 1 | 2 | 3 | 4 | 5 | 7 | 8 ]

  3. Selecton Sort Code publicint locMin(int[] nums, int start){ int loc = start; for (int k = start + 1; k < nums.length; k++){ if (nums[k] < nums[loc]) loc = k; } return loc; } publicvoid SelectSort(int[]nums){ for (int k = 0; k < nums.length; k++) { int minloc = locMin(nums, k); int temp = nums[k]; nums[k] = nums[minloc]; nums[minloc] = temp; } }

  4. Selection Sort • Think about Selection Sort • Loop Invariant • What can we say about our partially sorted list that is true each time around? • How efficient is it? • Develop measure of efficiency • We say it’s performance is proportional to N2

  5. More Sorting • Other Simple Sorts • Simple results in order N2 performance • Bubble Sort? (XXX) • Worst of the N2 sorts • Insertion Sort • Develop Algorithm • (steps often used when updating a sorted list, one item at a time) • More complicated to program than selection sort • But, has some very nice properties

  6. [ 5| 4 | 6 | 9 | 3 | 8 | 1 ] 4 [ 5| 4 | 6 | 9 | 3 | 8 | 1 ] 4 [ 5| 5 | 6 | 9 | 3 | 8 | 1 ] 4 [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] 6 [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] 6 [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] 9 [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] 9 [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] 3 [ 4| 5 | 6 | 9 | 3 | 8 | 1 ] 3 [ 4| 5 | 6 | 9 | 9 | 8 | 1 ] 3 [ 4| 5 | 6 | 6 | 9 | 8 | 1 ] 3 [ 4| 5 | 5 | 6 | 9 | 8 | 1 ] 3 [ 4| 4 | 5 | 6 | 9 | 8 | 1 ] 3 [ 3 | 4 | 5 | 6 | 9 | 8 | 1 ] [ 3| 4 | 5 | 6 | 9 | 8 | 1 ] 8 [ 3| 4 | 5 | 6 | 9 | 8 | 1 ] 8 [ 3| 4 | 5 | 6 | 9 | 9 | 1 ] 8 [ 3| 4 | 5 | 6 | 8 | 9 | 1 ] [ 3| 4 | 5 | 6 | 8 | 9 | 1 ] 1 [ 3| 4 | 5 | 6 | 8 | 9 | 1 ] 1 [ 3| 4 | 5 | 6 | 8 | 9 | 9 ] 1 [ 3| 4 | 5 | 6 | 8 | 8 | 9 ] 1 [ 3| 4 | 5 | 6 | 6 | 8 | 9 ] 1 [ 3| 4 | 5 | 5 | 6 | 8 | 9 ] 1 [ 3| 4 | 4 | 5 | 6 | 8 | 9 ] 1 [ 3| 3 | 4 | 5 | 6 | 8 | 9 ] 1 [ 1 | 3 | 4 | 5 | 6 | 8 | 9 ] Example

  7. Insertion Sort Code publicvoid insertSort(int[]nums){ int j, k, temp; for (k = 1; k < nums.length; k++) { temp = nums[k]; for (j = k; j > 0; j--){ // decrement! if (temp<nums[j-1]) nums[j] = nums[j-1]; else break; } nums[j] = temp; } }

  8. Insertion Sort • Loop Invariant? • How efficient? • For almost sorted? • Is stable! • What does that mean?

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