Binary search Tree

Binary search Tree

Defined:

Binary search tree is organized by a binary tree. The keywords in binary search are always stored in a way that satisfies the nature of binary tree search.

Set X is a node in a two-fork tree. If Y is a node in the X left dial hand tree, then Y.key <= X.key.

If Y is a node in the X right subtree, then Y.key >= X.key.

Analysis of the algorithm:

If we choose the middle order to traverse the entire binary tree. For example

6

5 7

2 5 8

Such a binary tree, (the middle line itself imagines).

Inorder-tree-walk

1 if x! = NULL

2 Inorder-tree-walk (x, left)

3 Print X.key;

4 Inorder-tree-walk (x, right)

Very simple we can get the results of the sequence traversal of the tree: 2 5 5 6 7 8

The time to traverse a two-fork search tree with n nodes is: Θ (n)

Prove:

Use T (n) to indicate the time required, since the middle order requires access to all n nodes of the tree, so there is t (n) =ω (n), as long as the t (n) = O (n) is shown below.

For an empty tree, you need to consume a very small constant time C, for a constant,c>0; has t (0) = C;

n > 0, if there are k nodes on the left subtree of x, then there are n-k-1 on the right subtree;

For t (n) there is t (n) <= t (k) + t (n-k-1) +d; D >0;

Use substitution method: T (N) <= (c+d) n +c; It can be concluded that T (n) = O (n);

Binary search Tree