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# Data Structure Sample Questions

1. In an AVL tree, at what condition the balancing is to be done?

Answer: If the 'pivotal value' (or the 'Height factor') is greater than 1 or less than -1.

2. What is the bucket size, when the overlapping and collision occur at same time?

Answer: One. If there is only one entry possible in the bucket, when the collision occurs, there is no way to accommodate the colliding value. This results in the overlapping of values.

3. Traverse the given tree using Inorder, Preorder and Postorder traversals.

• Inorder : D H B E A F C I G J
• Preorder: A B D H E C F G I J
• Postorder: H D E B F I J G C A

4. There are 8, 15, 13, 14 nodes were there in 4 different trees. Which of them could have formed a full binary tree?

In general:
There are 2n-1 nodes in a full binary tree.

By the method of elimination:
Full binary trees contain odd number of nodes. So there cannot be full binary trees with 8 or 14 nodes, so rejected. With 13 nodes you can form a complete binary tree but not a full binary tree. So the correct answer is 15.

5. In the given binary tree, using array you can store the node 4 at which location?

 1 2 3 - - 4 - - 5

 Root LC1 RC1 LC2 RC2 LC3 RC3 LC4 RC4

where LCn means Left Child of node n and RCn means Right Child of node n

6. Sort the given values using Quick Sort?

 65 70 75 80 85 60 55 50 45

Sorting takes place from the pivot value, which is the first value of the given elements, this is marked bold. The values at the left pointer and right pointer are indicated using L and R respectively.

 65 70L 75 80 85 60 55 50 45R

Since pivot is not yet changed the same process is continued after interchanging the values at L and R positions

 65 45 75L 80 85 60 55 50R 70

 65 45 50 80L 85 60 55R 75 70

 65 45 50 55 85L 60R 80 75 70

 65 45 50 55 60R 85L 80 75 70

When the L and R pointers cross each other the pivot value is interchanged with the value at right pointer. If the pivot is changed it means that the pivot has occupied its original position in the sorted order (shown in bold italics) and hence two different arrays are formed, one from start of the original array to the pivot position-1 and the other from pivot position+1 to end.

 60L 45 50 55R 65 85L 80 75 70R

 55L5 45 50R 60 65 70R 80L 75 85

 50L 45R 55 60 65 70 80L 75R 85

In the next pass we get the sorted form of the array.

 45 50 55 60 65 70 75 80 85

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