Recommended
More Related Content
What's hot
What's hot (18)
Similar to Algorithm and Data Structure - Binary Search
Similar to Algorithm and Data Structure - Binary Search (20)
More from AndiNurkholis1
More from AndiNurkholis1 (20)
Recently uploaded
Recently uploaded (20)
Algorithm and Data Structure - Binary Search
- 1. Algorithm and Data Structure Andi Nurkholis, S.Kom, M.Kom Study Program of Informatics Faculty of Engineering and Computer Science SY. 2020-2021 May 10, 2021
- 3. 3 What is Searching? Searching for data stored in different data structures is a crucial part of pretty much every single application. There are many different algorithms available to utilize when searching, and each have different implementations and rely on different data structures to get the job done.
- 4. 4 Searching Algorithm 1) Linear Search 2) Binary Search Being able to choose a specific algorithm for a given task is a key skill for developers and can mean the difference between a fast, reliable and stable application and an application that crumbles from a simple request.
- 6. 6 Binary Search Binary Search is a searching algorithm for finding an element's position in a sorted array. In this approach, the element is always searched in the middle of a portion of an array. Binary search can be implemented only on a sorted array of items. If the elements are not sorted already, we need to sort them first.
- 7. Steps of Binary Search 1. Start with the middle element: a. If the target value is equal to the middle element of the array, then return the index of the middle element. b. If not, then compare the middle element with the target value, • If the target value is greater than the number in the middle index, then pick the elements to the right of the middle index, and start with Step 1. • If the target value is less than the number in the middle index, then pick the elements to the left of the middle index, and start with Step 1. 7
- 8. Steps of Binary Search (cont.) 2. When a match is found, return the index of the element matched. 3. If no match is found, then return -1 8
- 9. Example 9 data_1 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21} Find value 15 in array data_1 data_2 = {1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31} Find value 4 in array data_2 data_3 = {1, 5, 9, 13, 17, 21, 25, 29, 33, 37} Find value 33 in array data_3
- 10. Answer 1 10 Low 1 3 5 7 9 11 13 15 17 19 21 Value searched for 15 Value in middle-index array is 11 Is value 15 = 11? FALSE Is value 15 > 11? TRUE Then Algorithm is CONTINUE If value searched greater than value in middle-index array, then searching continue to the right High Mid Step 1
- 11. 11 At each step, the middle-index changes according to the direction of the search At next step, low-index [1] changes to the previous middle-index [11]. That is because searching continues to the right What is the meaning? The next high-index [11] that changes will also cause the next middle-index [15] to change
- 12. Answer 1 (cont.) 12 1 3 5 7 9 11 13 15 17 19 21 Step 2 Value searched for 15 Value in middle-index array is 15 Is value 15 = 15? TRUE Then Algorithm is STOP Low High Mid
- 13. 13 Final Result Value searched for 15 is FOUND in step 2
- 14. Answer 2 14 Step 1 1 4 7 10 13 16 19 22 25 28 31 Value searched for 4 Value in middle-index array is 16 Is value 4 = 16? FALSE Is value 4 > 11? FALSE Then Algorithm is CONTINUE If value searched less than value in middle-index array, then searching continue to the left Low High Mid
- 15. 15 At each step, the middle-index changes according to the direction of the search At next step, low-index [31] changes to the previous middle-index [16]. That is because searching continues to the left What is the meaning? The next high-index [16] that changes will also cause the next middle-index [7] to change
- 16. Answer 2 (cont.) 16 1 4 7 10 13 16 19 22 25 28 31 Step 2 Value searched for 4 Value in middle-index array is 7 Is value 4 = 7? FALSE Is value 4 > 7? FALSE Then Algorithm is CONTINUE Low High Mid If value searched less than value in middle-index array, then searching continue to the left
- 17. 17 At each step, the middle-index changes according to the direction of the search At next step, low-index [16] changes to the previous middle-index [7]. That is because searching continues to the left What is the meaning? The next high-index [7] that changes will also cause the next middle-index [4] to change
- 18. Answer 2 (cont.) 18 1 4 7 10 13 16 19 22 25 28 31 Step 3 Value searched for 4 Value in middle-index array is 13 Is value 4 = 13? FALSE Is value 4 > 11? FALSE Then Algorithm is STOP Low High Mid If value searched less than value in middle-index array, then searching continue to the left
- 19. 19 Final Result Value searched for 4 is FOUND in step 3
- 20. Answer 3 20 Step 1 1 5 9 13 17 21 25 29 33 37 Value searched for 33 Value in middle-index array is 17 Is value 33 = 17? FALSE Is value 33 > 17? TRUE Then Algorithm is CONTINUE If value searched greater than value in middle-index array, then searching continue to the right For an even-number array, done N/2, then N-1. For this case, 10/2 = 5, then 5-1 = 4. Therefore, middle-index array is 4-index. Low High Mid
- 21. 21 At each step, the middle-index changes according to the direction of the search At next step, low-index [1] changes to the previous middle-index [17]. That is because searching continues to the right What is the meaning? The next high-index [17] that changes will also cause the next middle-index [25] to change
- 22. Answer 3 (cont.) 22 1 5 9 13 17 21 25 29 33 37 Step 2 Value searched for 33 Value in middle-index array is 25 Is value 33 = 25? FALSE Is value 33 > 25? TRUE Then Algorithm is CONTINUE If value searched greater than value in middle-index array, then searching continue to the right Low High Mid
- 23. 23 At each step, the middle-index changes according to the direction of the search At next step, low-index [17] changes to the previous middle-index [25]. That is because searching continues to the right What is the meaning? The next high-index [25] that changes will also cause the next middle-index [29] to change
- 24. Answer 3 (cont.) 24 1 5 9 13 17 21 25 29 33 37 Step 3 Value searched for 33 Value in middle-index array is 29 Is value 33 = 29? FALSE Is value 33 > 29? TRUE Then Algorithm is CONTINUE If value searched greater than value in middle-index array, then searching continue to the right Low High Mid
- 25. 25 At each step, the middle-index changes according to the direction of the search At next step, low-index [25] changes to the previous middle-index [29]. That is because searching continues to the right What is the meaning? The next high-index [29] that changes will also cause the next middle-index [33] to change
- 26. Answer 3 (cont.) 26 1 5 9 13 17 21 25 29 33 37 Step 4 Value searched for 33 Value in middle-index array is 33 Is value 33 = 33? TRUE Then Algorithm is STOP If value searched greater than value in middle-index array, then searching continue to the right Low High Mid
- 27. 27 Final Result Value searched for 33 is FOUND in step 4
- 28. Advantage of Linear Search 1. It eliminates half of the list from further searching by using the result of each comparison. 2. For large array of data, it works significantly better than linear search. 28
- 29. Disadvantage of Linear Search 1. The algorithm requires the array to be sorted first 2. In implementing, the algorithm more difficult than linear search 29
- 30. Thank You, Next … Sorting May 10, 2021 Andi Nurkholis, S.Kom, M.Kom Study Program of Informatics Faculty of Engineering and Computer Science SY. 2020-2021