Prefix, infix, suffix expression, and binary tree prefix, infix, and suffix Traversal

1. Relationship Between Expressions and Binary Trees

Prefix expressions correspond to the forward traversal of Binary trees;

The infix expression corresponds to the ordinal traversal of a binary tree;

Suffix expressions correspond to post-sequential traversal of Binary trees;

 

Ii. Generate a binary tree based on the infix expression

Infix expression: A + B * (c-d)-E/F

The traversal in the middle order is: Left son, right son, and root node

Based on the operator priority, the binary tree generation process is as follows:

1. c-d has a high priority. The root is the-operator. C and D are the right and right sons respectively.

-

|

C d

2. The next step is multiplication. The root is the * operator. The content in B and 1 is the left and right sons respectively.

*

|

B-

|

C d

3. Next is the trigger. The root is the/operator. E and F are the right and right sons.

/

|

E F

4. The next step is addition. The root is the + operator. The content in A and 2 is the left and right sons respectively.

+

|

A *

|

B-

|

C d

It also includes the tree in step 3.

5. The next step is subtraction. The root is the-operator. The two operators in 4 are the right and right sons.

-

|

+/

|

A * E F

|

B-

|

C d

 

3. Obtain the prefix expression by traversing the binary tree in the forward order.

The first traversal is: root node, left son, right son

The prefix expression is-+ a * B-CD/EF.

 

4. Obtain the suffix expression based on the Post-order traversal of the Binary Tree

Backward traversal: Left son, right son, and root node

The suffix expression is ABCD-* + EF /-

 

V. Summary

If you can determine a binary tree based on the prefix, infix, or suffix expression, you can generate the corresponding prefix, infix, and suffix expression.

The methods of pre-order traversal, middle-order traversal, and subsequent traversal are as follows:

1. The first order is that the root node is in the front edge, the middle order is that the root node is in the middle, and the root node is in the back

2. always start with the left son and then the right son.

Preface:Root Node, Left son, right son

Central order: Left son,Root NodeRight son

Follow-up: Left son, right son,Root Node