### with two model answers - one correct (yes) and one incorrect (no)

1 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.

2 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)

3 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)

4 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

5 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

6 Let us have a binary tree in parenthetic string representation. Is the given sequence a part of the sequence of nodes, obtained in inorder traversal of this binary tree?
(yes) c(b(a,d),e); bdc
(no) d(e,c(g,a(f,b))); cfb

7
Create a binary tree representation of the given arithmetic expression and check that the sequence x2y is a part of the postorder traversal.
(yes) (x+2*(y-2))/2
(no) (x-2)*y

8 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

9 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.

10 Let us have a priority queue ADT with n elements implementation with unsorted sequence, denoted by "U:"
or
with sorted sequence, denoted by "S:".
Mark the correct/incorrect correspondence between a function of this ADT and its performance.
(yes)
U: minElement() - O(n)
(no) U:
minKey() - O(1)

11 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

12 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

13 Specify true and false claims to the following definition of the member function
Element& element(const Position& p)
{
return p.element().element();
}

in the class
HeapPriorityQueue (see html-7.8 (HPQ1)).
(yes)
p is an object of the class Position.
(no) The function is recursive.

14 Let n be number of nodes, e - number of external nodes, i - number of internal nodes of a proper binary tree, and h be its height. Mark correct and incorrect equalities and inequalities.
(yes) i = e - 1
(no) 2e = n

15 Look at Code Fragment: SSPQ2. Mark the correct/incorrect assertions.
(yes) The object
S is an implementation of Sequence ADT.
(no) comp is a comparator class name.