A loose end: binary search

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1 COSC311 CRN Session 20 (Dec. 3, 2018) A loose end: binary search binary search algorithm vs binary search tree A binary search tree, such as AVL, is a data structure. Binary search is an algorithm for. binarysearch(element, tree_node): if the subtree rooted at tree_node is empty: return NOT_FOUND else if element == tree_node.element: return tree_node else if element < tree_node.element: return binarysearch(element, tree_node.left) else: return binarysearch(element, tree_node.right) The binary search can also work for a sorted array. (in quiz 4) 1

2 Today s topic: DFS: depth first search DFS for a tree: DFS for a graph starting at a vertex: Input: A graph G and a vertex u of G Output: A collection of vertices reachable from u, with their discovery edges line 1: line 2: for each of u s outgoing edges, e = (u, v) do line 3: line 4: record edge e as the discovery edge for vertex v line 5: recursively call DFS(G, v) DFS for an entire graph: 2

3 COSC311 CRN Session 20 (Dec. 3, 2018) Review for Quiz 4 Sorting: Selection sort: Insertion sort: Bubble sort: 3

4 Merge sort: will be in the quiz Quick sort: will be in the quiz Which of the following sorting algorithms is most efficient for sorting arrays that are already almost sorted? a. selection b. insertion c. merge Which of the following is NOT a divide and conquer approach? a. insertion b. merge c. heap d. quick Which of the following algorithm is not stable? A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input array to be sorted. a. bubble b. quick c. merge d. insertion 4

5 COSC311 CRN Session 20 (Dec. 3, 2018) Suppose m is length(a1) and n is length(a2), the time for the following pseudocode is: a. O(max(m, n)) b. O(m+n) c. O(mlogn) d. O(nlogm) Pseudocode: i = 0 j = 0 while i + j < length(a) // A1 is the first half of A; A2 is the second half of A if j == length(a2) A[i+j] = A1[i] i++ else if i < length(a1) and A1[i] < A2[j] A[i+j] = A1[i] i++ else A[i+j] = A2[j] j++ end if end while For a 5-element list, how many comparisons will be made in insertion sort if the list is already sorted? How many swaps will be made if the list is already sorted? What s the worst-case runtime for bubble sort? (in quiz, the questions may be for merge sort, selection sort, insertion sort, heap sort, quick sort using queues, quick sort in place, quick select.) 5

6 The following pseudocode is an incomplete selection sort. sort(a): i = 0 while i < length(a) - 1 min_index = i // the part to be finished i ++ end while Please finish the part in the while loop so that the pseudocode works as a selection sort algorithm. (in quiz, I may also ask similar questions about bubble sort, merge sort, insertion sort, heap sort, quick sort using queues, quick sort in place, and quick select) About removing an entry from (2, 4) tree remove 13 OR remove 17 OR remove 13, 14 OR remove 10 6

7 COSC311 CRN Session 20 (Dec. 3, 2018) About graphs For the above graph, which of the following statements is true (you can choose multiple statements)? a. Vertex A and vertex B are adjacent b. Vertex C and vertex B are adjacent c. Edge (C, E) is incident to vertex A d. Vertex A is an endpoint of edge (B, E) e. This graph is a simple graph f. Path: (A, C), (C, E), (E, B), (B, A) is a simple path g. Vertex C is reachable from vertex B h. This graph is a connected graph i. The following graph is a spanning graph of the above graph. (Other terminology in slides 19, 11/28, may be tested in the quiz 4.) Is the following graph a strongly connected graph? Write the pseudocode for graph DFS (page 2). 7

8 For the above graph, what is the DFS traversal starting from vertex A? 8

Priority queues. Priority queues. Priority queue operations

Priority queues. Priority queues. Priority queue operations Priority queues March 30, 018 1 Priority queues The ADT priority queue stores arbitrary objects with priorities. An object with the highest priority gets served first. Objects with priorities are defined