Sorting and Searching Searching List of numbers 5

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 What is the algorithm? 1. 2. 3. 4. 5. 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

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

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

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?

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

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?

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

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

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

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

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