Mark the correct and incorrect definitions and assertions about trees.

(yes) If node u is the parent of node v, we say that v is a child of u.

(no) Nodes that are children of the same parent are called leaves.

Let us have a tree ADT with n elements. Let v and w be positions in the tree. Mark the correct/incorrect correspondence between a function of this ADT and its run-time assumptions.

(yes) root(v) - O(1)

(no) parent(v) - O(n)

Let us have an ordered tree ADT in parenthetic string representation T=A(B(H,E(I,J),F),C(G),D). Determine the correct/incorrect pairs: function, its output value. p(X) means the position of the element X. [Hint: See p.268 for "parenthetic string representation".]

(yes) root(), p(A)

(no) root(), p(D)

Let us have an ordered tree ADT in parenthetic string representation T=A(B(H,E(I,J),F),C(G),D). Is the given sequence a part of the sequence of nodes, obtained in preorder traversal of the tree?

(yes) ABH

(no) EB

Let us have an ordered tree ADT in parenthetic string representation T=A(B(H,E(I,J),F),C(G),D). Is the given sequence a part of the sequence of nodes, obtained in postorder traversal of the tree?

(yes) HIJ

(no) EB

Let us have a binary tree ADT in parenthetic string representation T=a(b(d(h,i),e),c(f,g(j(l,m),k)). Is the given sequence a part of the sequence of nodes, obtained in inorder traversal of this binary tree?

(yes) hdib

(no) hdie

Let us have a binary tree ADT in parenthetic string representation T=a(b(d(h,i),e),c(f,g(j(l,m),k)). Is the given sequence a part of the sequence of nodes, obtained in Euler tour traversal of this binary tree.

(yes) abdhd

(no) bdhid

Create a binary tree representation of the following arithmetic expression: (9 * (5 + a) + b) / 2. Is the given sequence a part of the sequence of nodes, obtained in preorder traversal of this binary tree. [Hint: See p.258, Example 6.5.]

(yes) /+*

(no) 9/2

Create a binary tree representation of the following arithmetic expression: (9 * (5 + a) + b) / 2. Is the given sequence a part of the postorder traversal sequence of this binary tree.

(yes) 95a

(no) 9/2

Mark the correct/incorrect definitions and assertions about priority queues and heaps.

(yes) A key is an object that is assigned to an element as a specific attribute for that element and that can be used to identify, rank, or weight that element.

(no) In a heap storing n keys, upheap (bubbling) algorithm runs O(n) time.

Let us have a priority queue ADT with n elements implementation with an unsorted sequence. Mark the correct/incorrect correspondence between a function of this ADT and its performance.

(yes) minElement() - O(n)

(no) minKey() - O(1)

Let us have a priority queue ADT P={(5,A),(7,D),(9,C)}. For a function of this ADT determine the return value and its effect on P.

(yes) insertItem(3,B)-NONE-{(3,B),(5,A),(7,D),(9,C)}

(no) minElement()-5-{(5,A),(7,D),(9,C)}

Let us have a priority queue ADT with n elements implementation with a sorted sequence. Mark the correct/incorrect correspondence between a function of this ADT and its performance.

(yes) minElement() - O(1)

(no) minElement() - O(n)

Let us have a priority queue ADT with n elements for the heap implementation. Mark the correct/incorrect correspondence between a function of this ADT and its performance.

(yes) minElement() - O(1)

(no) minElement() - O(n)

Let us have the vector representation of a heap. Guess the correct representation after applying the method InsertItem(1,1).

(yes) 2,4,5 -> 1,2,5,4

(no) 2,4,5 -> 1,2,4,5

Let us have the vector representation of a heap.Guess the correct representation after applying the method RemoveMin().

(yes) 1,2,5,4 -> 2,4,5

(no) 1,2,5,4 -> 4,2,5