1. 1 CS 17700 Review, iClicker -Questions Week 15

2. ANY QUESTIONS? 2

3. Decision Tree 3

4. Trees can be more complex Tree = [‘Root’, ‘Leaf1’, ‘Leaf2’, [‘Node1’, ‘Leaf3’, ‘Leaf4’, ‘Leaf5’]] Root Leaf1Leaf2 Leaf3 Leaf4Leaf5 Node1

5. Trees can be more complex Tree = [‘Root’, ‘Leaf1’, ‘Leaf2’, [‘Node1’, ‘Leaf3’, ‘Leaf4’, ‘Leaf5’]] Root Leaf1Leaf2 Leaf3 Leaf4Leaf5 Node1

6. Trees can be more complex Tree = [‘Root’, ‘Leaf1’, ‘Leaf2’, [‘Node1’, ‘Leaf3’, ‘Leaf4’, ‘Leaf5’]] Root Leaf1Leaf2 Leaf3 Leaf4Leaf5 Node1

7. Indices allow us to “traverse” the tree Root Leaf1 Leaf2 Leaf3Leaf4 Leaf6 Tree = [‘Root’, [‘Node1’, ‘Leaf0’, ‘Leaf1’], ‘Leaf2’, [‘Node2’, ‘Leaf3’, ‘Leaf4’, [‘Node3’, ‘Leaf5’, ‘Leaf6’]]] Leaf0 Leaf5 [0] [3][1] [3][3][1] [1][1][1][2] [1] [3][2] [3][3][2] [2] [3][3] [3] [1][0] [3][0] [3][3][0] Node1 Node2 Node3

8. Recursion 8

11. 11 Recursion : String Reversal def reverse(s): if s == "": return s else: return reverse(s[1:]) + s[0] >>> reverse("Hello") 'olleH'

12. Big-O Notation 12

13. Big-O Notation

14. Why Size Matters?

15. CQ: Arithmetic Series

16. CQ: Series If it is an arithmetic series : ½ n (n+1)….. T(n) is O(n 2 )

17. Clicker Question def getFirst(list): if len(list) == 0: return -1 return (list[0]) A: O(n) B: O(n 2 ) C: O(1) >>> getFirst([]) >>> getFirst([0,1,2,3]) 0 >>> getFirst(["a", "b", "c"]) 'a’

18. Clicker Question def getFirst(list): if len(list) == 0: return -1 return (list[0]) A: O(n) B: O(n 2 ) C: O(1) >>> getFirst([]) >>> getFirst([0,1,2,3]) 0 >>> getFirst(["a", "b", "c"]) 'a’

19. Sorting Arrays 19

20. How to find an alien Logic Puzzle: You have 9 marbles. 8 marbles weigh 1 ounce each, & one marble weighs 1.5 ounces. You are unable to determine which is the heavier marble by looking at them. How do you find the marble which weighs more?

21. Solution 1: Weigh one marble vs another What is the complexity of this solution?

22. Clicker Question: What is the complexity of this algorithm? A: O(n) B: O(n 2 ) C: O(1) D: O(log n)

23. Finding the complexity of the optimal solution Step 1: What is our input? The marbles Step 2: How much work do we do per marble? LOGARITHMIC Step 3: What is the total work we did? 2 measurements What if we had 100 marbles or 1000?

24. Clicker Question: What is the complexity of this algorithm? A: O(n) B: O(n 2 ) C: O(1) D: O(log n)

25. Big-O – Sorting Arrays Type of SortBestWorstAverageMemory Space Bubble SortO(N)O(N 2 ) 1 Selection Sort O(N 2 ) 1 Heap Sort O(N log N) 1 Merge SortO(N log N) Worst =N

26. Two Phases using a Priority Queue 1. Put all items in the input list into a priority queue 2. Extract items by decreasing magnitude and put them into the output list We get a sorted list that way [3,7,2,9,… [9,8,7,6,…

27. Example Tree, Encoding & Access Tree encoding: a = [9, 6, 4, 5, 1, 2] 9 64 52 1 2:1: 0: 3:4:5: 6: Find Parent of: 4 a[2]=4 i=(2-1)//2 = 0 Parent is at a[0] =9

28. Heap Representation

29. Step- 1 Step-3 Step- 2 Heap- Insert

30. Tree-Complexity

31. CQ: Is this a Priority Queue? A. Yes B. No 9 64 52 4 2:1: 0: 3:4:5: 6: x yz ≥≥

32. CQ: Is this a Priority Queue? A. Yes B. No 9 64 52 4 2:1: 0: 3:4:5: 6: x yz ≥≥

33. CQ: Is this a priority queue? [9,8,4,7,3,2,5,6,1] A. Yes B. No

34. CQ: Is this a priority queue? [9,8,4,7,3,2,5,6,1] A. Yes B. No Tree encoding: a = [9,8,4,7,3,2,5,6,1] Find Parent of: 5 a[6]=5 i=(6-1)//2 =2 Parent is at a[2] =4

35. CQ: how many children for L[5]? [9,7,4,6,5,4,2,2,1,1,1,1] A. 0 B. 1 C. 2

36. CQ: how many children for L[5]? [9,7,4,6,5,4,2,2,1,1,1,1] A. 0 B. 1 C. 2 9 74 5 6 42 2 1 1 1 1

37. Merge Sort log(n) n elements merged

38. Putting it all together We know that there are log(n) splits At each “level” we split each list in two We know that we need to merge a total of n elements at each “level” n * log(n) thus O(n log n)