1. ITEC 2620M Introduction to Data Structures Instructor: Prof. Z. Yang Course Website: http://people.math.yorku.ca/~zyang/it ec2620m.htm Office: TEL 3049

2. Linked List

3. 3 Key Points of this Lecture Maintaining data records Inserting into sorted arrays Dynamic data structures Linked-lists

4. 4 Inserting into Sorted Arrays How is this done? –loop – larger values get moved into the next slot –when done, copy new value into next slot What is the complexity for inserting into a sorted array? –Is there a best, worst, and average case? do you always insert into the same location? –How many times, what does it cost? Best  0 moves  O(1) Worst  n moves, 1 swap per  O(n) Avg  n/2 moves, 1 swap per  O(n)

5. 5 Inserting into Full Arrays What happens if we want to insert another element into this array? –Copy entire array into a larger array (time consuming) How do we avoid this? –Store data in an array with extra space Time-Space trade-off –What saves time can often waste space –What saves space can often waste time

6. 6 Dynamic Data Structures Would like to create extra memory slots one at a time… Creating Links Inserting Links

7. 7 Arrays vs. Linked-Lists Arrays –fixed length –contiguous memory locations –direct access Linked-Lists –dynamic length –arbitrary memory locations –access by following links

8. 8 Comparing Arrays and Linked- Lists Find and delete a value in a sorted array and a linked-list –Arrays find value with binary search (assume value is in array) shuffle all higher values down what is the complexity for find? –Best  O(1) –Worst  O( log n) –Avg  O( log n)

9. 9 Comparing Arrays and Linked- Lists (Cont’d) Array –What is the complexity for delete? Best  last element  O(1) Worst  first element  O(n) Avg  middle element  O(n) –What is the overall complexity? Best  last element  O( log n)+O(1) = O( log n) Worst  first element  O( log n)+O(n) = O(n) Avg  mid-area element  O(logn)+O(n) = O(n)

10. 10 Comparing Arrays and Linked- Lists (Cont’d) Linked-Lists –find value by following links –link past target link (garbage collecting will remove it) –what is the complexity for find? Best  first element  O(1) Worst  last element  O(n) Avg  middle element  O(n)

11. 11 Comparing Arrays and Linked- Lists (Cont’d) What is the complexity for delete? –Always  O(1) What is the overall complexity? –Best  first element  O(1)+O(1) = O(1) –Worst  last element  O(n)+O(1) = O(n) –Avg  middle element  O(n)+O(1) = O(n)