Two-fork Tree

Tree structure is a kind of important nonlinear data structure, in which two-tree is more commonly used. The characteristics of the binary tree each node at most only two subtrees tree (no more than 2 nodes in the binary tree), and the binary tree has left and right sub-tree points.

Binary Tree Properties:

1, the binary tree has 5 basic forms, (a) empty binary tree (b) only the root node of the two fork Tree (c) The right subtree is empty two fork tree (d) The subtree is non-empty of the two fork Tree (e) left dial hand tree is empty two

The nature of the binary tree;

Property 1 There are at most 2^ (i-1) nodes on the first layer of the binary tree (i≧1)

Nature 2 Two-tree with a depth of k at most 2^k-1 nodes, (k≧1)

Property 3 for any of the binary tree T, if its terminal node number is n0, the degree of 2 node is n2, then N0 = n2 + 1. (degrees: Refers to the parent node below a few child nodes);

Property 4 The depth of a complete binary tree with n nodes is [㏒?n] + 1

Property 5 If there is a complete binary tree with n nodes (its depth is [㏒?n] + 1) by the sequence number (from the 1th level to the [㏒?n] + 1 layers, each layer from left to right), then to any node I (1≤i≤n), there is

① If i = 1, then node i is the root of the two fork tree, with no parents; if i > 1, then the parent node is [I/2];

② if 2i > N, then node I has no left child (node I is the node of the leaf); otherwise the left child is 2i.

③ if 2i + 1 > N, then it has no children, otherwise its right child's node is 2i + 1

How to traverse a binary tree:

1, hierarchical traversal (from top to bottom, from left to right in order to traverse)

2. Ordinal traversal (preorder (t) = root node of T + preorder (Zuozi of T) + preorder (right subtree of T))

3, Middle sequence traversal (inorder (t) = inorder (t Zuozi) + t root node + inorder (right subtree of T))

4. Post-sequential traversal (postorder (t) = Postorder (Zuozi of T) + postorder (right subtree of T) + t root node)



Two-fork Tree