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insertion sorting

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- 1. The Insertion Sort Mr. Dave ClausenLa Cañada High School
- 2. Insertion Sort DescriptionThe insertion sort uses a vectors partial ordering. Onthe kth pass, the kth item should be inserted into itsplace among the first k items in the vector.After the kth pass (k starting at 1), the first k items ofthe vector should be in sorted order.This is like the way that people pick up playing cardsand order them in their hands. When holding the first(k - 1) cards in order, a person will pick up the kthcard and compare it with cards already held until itssorted spot is found. Mr. Dave Clausen 2
- 3. Insertion Sort AlgorithmFor each k from 1 to n - 1 (k is the index of vector element to insert) Set item_to_insert to v[k] Set j to k - 1 (j starts at k - 1 and is decremented until insertion position is found) While (insertion position not found) and (not beginning of vector) If item_to_insert < v[j] Move v[j] to index position j + 1 Decrement j by 1 Else The insertion position has been found Mr. Dave Clausen 3 item_to_insert should be positioned at index
- 4. C + + Code For Insertion Sort void Insertion_Sort(apvector<int> &v) { int item_to_insert, j; // On the kth pass, insert item k into its correct bool still_looking; // position among the first k entries in vector. for (int k = 1; k < v.length(); ++k) { // Walk backwards through list, looking for slot to insert v[k] item_to_insert = v[k]; j = k - 1; still_looking = true; while ((j >= 0) && still_looking ) if (item_to_insert < v[j]) { v[j + 1] = v[j]; --j; } else Dave Clausen Mr. 4 still_looking = false; // Upon
- 5. Insertion Sort Example The Unsorted Vector: 80 40For each pass, the index j begins at 32the (k - 1)st item and moves that 84item to position j + 1 until we findthe insertion point for what was 61originally the kth item.We start with k = 1and set j = k-1 or 0 (zero) Mr. Dave Clausen 5
- 6. The First Pass K=280 Insert 40, 80 Insert 40 4040 compare 80 80 & move32 32 3284 84 8461 61 61 item_to_insert 40 Mr. Dave Clausen 6
- 7. The Second Pass K=340 40 Compare 40 Insert 32 32 & move80 Insert 32, 80 40 4032 compare 80 80 80 & move84 84 84 8461 61 61 61 item_to_insert 32 Mr. Dave Clausen 7
- 8. The Third PassK=4 324080 Insert 84?84 compare & stop61 item_to_insert 84 Mr. Dave Clausen 8
- 9. The Fourth Pass K=532 32 32 3240 Compare 40 40 40 & stop80 80 Compare 80 Insert 61 61 & move84 Insert 61, 84 80 8061 compare 84 84 84 & move item_to_insert 61 Mr. Dave Clausen 9
- 10. What “Moving” Meansitem_to_insert 80 40 40 32Place the second element 84into the variable 61item_to_insert. Mr. Dave Clausen 10
- 11. What “Moving” Meansitem_to_insert 80 80 40 32Replace the second element 84with the value of the first 61element. Mr. Dave Clausen 11
- 12. What “Moving” Meansitem_to_insert 40 80 40 32Replace the first element 84(in this example) with the 61variable item_to_insert. Mr. Dave Clausen 12
- 13. C + + Examples of The Insertion SortOn the Net:http://compsci.exeter.edu/Winter99/CS320/Resources/sortDemo.htmlhttp://www.aist.go.jp/ETL/~suzaki/AlgorithmAnimation/index.html Mr. Dave Clausen 13
- 14. Big - O NotationBig - O notation is used to describe the efficiencyof a search or sort. The actual time necessary tocomplete the sort varies according to the speed ofyour system. Big - O notation is an approximatemathematical formula to determine how manyoperations are necessary to perform the search orsort. The Big - O notation for the Insertion Sort isO(n2), because it takes approximately n2 passes tosort the “n” elements. Mr. Dave Clausen 14

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