Exercise: Questions on Balanced Binary Search Trees


Questions on Balanced Binary Search Trees : Question 1 :
The worst case running time to search for an element in a balanced in a binary search tree with n2^n elements is
(A) \Theta(n log n)
(B) \Theta (n2^n)
(C) \Theta (n)
(D) \Theta (log n)

A
B
C
D
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Questions on Balanced Binary Search Trees : Question 2 :
What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0.

2
3
4
5
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Questions on Balanced Binary Search Trees : Question 3 :
What is the worst case possible height of AVL tree?

2Logn
Assume base of log is 2
1.44log n
Assume base of log is 2
Depends upon implementation
Theta(n)
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Questions on Balanced Binary Search Trees : Question 4 :
Which of the following is AVL Tree?
A
        100
     /      \
    50       200
   /           \
 10            300


B
           100
       /       \
     50        200
    /        /     \
  10       150     300
 /
5


C
            100
       /          \
     50            200
    /  \          /     \
  10    60       150     300
 /                 \        \
5                   180       400

Only A
A and C
A, B and C
Only B
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Questions on Balanced Binary Search Trees : Question 5 :
Consider the following AVL tree.
         60
      /     \  
    20      100
           /   \
         80    120     
Which of the following is updated AVL tree after insertion of 70
A
        70
      /    \  
    60      100
   /       /    \
 20       80    120 

B
        100
      /    \  
    60      120
   /  \     /  
 20   70   80   


C
        80
      /    \  
    60      100
   /  \       \
 20   70      120

D
        80
      /    \  
    60      100
   /       /   \
 20      70    120  

A
B
C
D
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Questions on Balanced Binary Search Trees : Question 6 :
Which of the following is a self-adjusting or self-balancing Binary Search Tree

Splay Tree
AVL Tree
Red Black Tree
All of the above
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Questions on Balanced Binary Search Trees : Question 7 :
Consider the following left-rotate and right-rotate functions commonly used in self-adjusting BSTs
T1, T2 and T3 are subtrees of the tree rooted with y (on left side) 
or x (on right side)           
                y                               x
               / \     Right Rotation          /  \
              x   T3   – - – - – - – >        T1   y 
             / \       < - - - - - - -            / \
            T1  T2     Left Rotation            T2  T3
Which of the following is tightest upper bound for left-rotate and right-rotate operations.

O(1)
O(Logn)
O(LogLogn)
O(n)
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Questions on Balanced Binary Search Trees : Question 8 :
Which of the following is true

The AVL trees are more balanced compared to Red Black Trees, but they may cause more rotations during insertion and deletion.
Heights of AVL and Red-Black trees are generally same, but AVL Trees may cause more rotations during insertion and deletion.
Red Black trees are more balanced compared to AVL Trees, but may cause more rotations during insertion and deletion.
Heights of AVL and Red-Black trees are generally same, but Red Black rees may cause more rotations during insertion and deletion.
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Questions on Balanced Binary Search Trees : Question 9 :
Which of the following is true about Red Black Trees?

The path from the root to the furthest leaf is no more than twice as long as the path from the root to the nearest leaf
At least one children of every black node is red
Root may be red
A leaf node may be red
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Questions on Balanced Binary Search Trees : Question 10 :
Which of the following is true about AVL and Red Black Trees?

In AVL tree insert() operation, we first traverse from root to newly inserted node and then from newly inserted node to root. While in Red Black tree insert(), we only traverse once from root to newly inserted node.
In both AVL and Red Black insert operations, we traverse only once from root to newly inserted node,
In both AVL and Red Black insert operations, we traverse twiceL first traverse root to newly inserted node and then from newly inserted node to root.
None of the above
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