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The height of a complete m-ary tree with n nodes is ceiling(logmn).
An m-way search tree
a. is empty or
b.consists of a root containing j (1<=j< m) keys, kj, and
a set of sub-trees, Ti, (i = 0..j), such that
i. if k is a key in T0, then k <= k1
ii. if k is a key in Ti (0 < i < j), then ki <= k <= ki+1
iii. if k is a key in Tj, then k > kj and
iv. all Ti are nonempty m-way search trees or all Ti are empty
A B-tree of order m is an m-way tree in which
a. all leaves are on the same level and
b. all nodes except for the root and the leaves have at least m/2 children and at most m children. The root has at least 2 children and at most m children.
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