GATE | GATE CS 1997 | Question 63

A B+ tree of order d is a tree in which each internal node has between d and 2d key values. An internal node with M key values has M+1 children. The root (if it is an internal node) has between 1 and 2d key values. The distance of a node from the root is the length of the path from the root to the node. All leaves are at the same distance from the root. The height of the tree is the distance of a leaf from the root.

a). What is the total number of key values in the internal nodes of a B+ tree with l leaves (l≥2)?
b). What is the maximum number of internal nodes in a B+ tree of order 4 with 52 leaves?
c). What is the minimum number of leaves in a B+ tree of order d and height h(h≥1)?

(A)

a)L+1 b)8 c)2(d+1)^h−1

(B)

a)L-1 b)13 c)2(d+1)^h−1

(C)

a)L-1 b)17 c)2(d-1)^h−1

(D)

a)L-1 b)9 c)2(d-1)^h+1

Answer

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