Computer Science GATE-Data Structures and Algorithms Set 2

2Logn
Assume base of log is 2 ✘ 1.44log n
Assume base of log is 2 ✘ Depends upon implementation ✘ Theta(n) ✔

Splay Tree ✘ AVL Tree ✘ Red Black Tree ✘ All of the above ✔

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. ✔

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 ✔

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 ✔

1 ✘ 2 ✘ 3 ✘ 4 ✔

Database relations have a large number of records ✘ Database relations are sorted on the primary key ✘ B-trees require less memory than binary search trees ✘ Data transfer form disks is in blocks. ✔

Disk capacities are greater than memory capacities ✘ Disk access is much slower than memory access ✘ Disk data transfer rates are much less than memory data transfer rates ✘ Disks are more reliable than memory ✔

B/B+ trees grow upward while Binary Search Trees grow downward. ✘ Time complexity of search operation in B/B+ tree is better than Red Black Trees in general. ✘ Number of child pointers in a B/B+ tree node is always equals to number of keys in it plus one. ✘ A B/B+ tree is defined by a term minimum degree. And minimum degree depends on hard disk block size, key and address sizes. ✔

Root is visited before right subtree ✘ Left subtree is always visited before right subtree ✘ Root is visited after left subtree ✘ All of the above ✔ None of the above ✔