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Adding Time Analysis for B-Trees (#31013)

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* Adding Time Analysis for B-Trees

Time Analysis for B-Tree:

Suppose a B-tree has n elements and M is the maximum number of children a node can have. What is the maximum depth the tree could have? What is the minimum depth the tree could have?

    The worst-case depth (maximum depth) of a B-tree is: logM/2 n.
    The best-case depth (minimum depth) of a B-tree is: logM n.

Worst-Case Times for B-Trees:

    Adding or removing an element in a B-tree with n elements is O(log n).

* fix: removed duplicate info
This commit is contained in:
Harshit Omer
2019-05-13 03:49:23 +05:30
committed by Randell Dawson
parent 3e404cd075
commit c4f17674cf
1 changed files with 7 additions and 0 deletions
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guide/english/algorithms/b-trees/index.md
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@@ -25,3 +25,10 @@ Traversal is also similar to Inorder traversal of Binary Tree. We start from the
Insertion: Insertion:
We insert into the bottom of a B-tree, similar to binary search trees. First, find an appropriate place at the bottom of the tree to insert a given key, and perform the insertion (also adding an additional empty child). If the node is too big (it has m keys and m + 1 (empty) children), split the node. We insert into the bottom of a B-tree, similar to binary search trees. First, find an appropriate place at the bottom of the tree to insert a given key, and perform the insertion (also adding an additional empty child). If the node is too big (it has m keys and m + 1 (empty) children), split the node.
Time Analysis for B-Tree:
Suppose a B-tree has n elements and M is the maximum number of children a node can have. What is the maximum depth the tree could have? What is the minimum depth the tree could have?
- The worst-case depth (maximum depth) of a B-tree is: logM/2 n.
- The best-case depth (minimum depth) of a B-tree is: logM n.