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Sorting and Searching

Sorting and Searching. Searching. List of numbers (5, 9, 2, 6, 3, 4, 8) Find 3 and tell me where it was. Linear Search. Start at the beginning and search until you find the item What is the algorithm?. Linear Search. Start at the beginning and search until you find the item

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Sorting and Searching

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  1. Sorting and Searching

  2. Searching • List of numbers (5, 9, 2, 6, 3, 4, 8) • Find 3 and tell me where it was

  3. Linear Search • Start at the beginning and search until you find the item • What is the algorithm?

  4. Linear Search • Start at the beginning and search until you find the item • What is the algorithm? • Set current element to first element • Compare target and current element • if found – success! • else – set current element to be next element • go back to step 2

  5. Linear Search • In the worst case, how many comparisons will you perform?

  6. Linear Search • In the worst case, how many comparisons will you perform? • N where N is the number of items in the list

  7. Binary Search • If the list is sorted, can we find a better algorithm? (5, 9, 2, 6, 3, 4, 8) (2, 3, 4, 5, 6, 8, 9) • What is the algorithm?

  8. Binary Search (2, 3, 4, 5, 6, 8, 9) • compare item to middle element • if no match, divide list in half • if item is less than middle • search first half of list • else • search second half of list • go back to 1

  9. Binary Search • In the worst case, how many comparisons will you perform? • log N where N is the number of items in the list • Which is better, linear or binary search? • Why?

  10. Sorting • How would you sort a list of numbers? (5, 9, 1, 6, 3, 4, 8)

  11. Sorting • How would you sort a list of numbers? (5, 9, 1, 6, 3, 4, 8) • cur_index = 0 • for each element in list • linear search for smallest element in list starting at cur_index • if smallest element found is less than element at cur_index – swap • increment cur_index

  12. Sorting (5, 9, 1, 6, 3, 4, 8) cur_index = 0 min_index = 2 (element 1) swap 0th element and 2nd element (1, 9, 5, 6, 3, 4, 8) cur_index = 1

  13. Sorting (1, 9, 5, 6, 3, 4, 8) cur_index = 1 swap 1st and 4th (1, 3, 5, 6, 9, 4, 8) cur_index = 2 swap 2nd and 5th (1, 3, 4, 6, 9, 5, 8) cur_index = 3 swap 3rd and 5th (1, 3, 4, 5, 9, 6, 8) cur_index = 4 swap 4th and 5th (1, 3, 4, 5, 6, 9, 8) cur_index = 5 swap 5th and 6th (1, 3, 4, 5, 6, 8, 9) cur_index = 6

  14. Complexity of Selection Sort • How many comparisons were necessary for selection sort?

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