Infix to prefix (expression)

Problem description:

Example of prefix fix:

(4 + 2) * (3 + 6) => * + 4 2 + 3 6

(3/4 + 2)-5 =>-+/3 4 2 5

(3 + 4/2)-5 =>-+ 3/4 2 5

If the expression is drawn into a tree structure, the prefix, infix, and suffix are the first, middle, and last traversal of the tree.

-----------------*------------------

------------/-----------\-----------

-------- + ---------------- + ---------

------/----\------------/-----\------

---- 4-------2---------3-------6 ----

 

Thought 1 (stack ):

1. Read from right to left

2. When a number is added to the output stream header, the stack is determined based on the priority when a symbol is encountered:

1) low entry is higher

2) Right parenthesis. the stack is output until the left parenthesis is encountered.

 

Idea 2 (brackets ):

1. infix: A + B * C-(D + E)

2. brackets are filled by priority: (a + (B * C)-(D + E ))

3. Move the operator to the beginning of brackets:-(+ (A * (BC) + (de ))

4. parentheses:-+ a * B C + D E

PS:

The suffix is similar to this, but only after the operators are transplanted to the corresponding brackets.

 

Idea 3 (tree ):

1. Change the infix to a tree structure (by operator priority)

2. traverse the tree structure in sequence

 

Reprinted, please indicate the reference from:

Http://www.cnblogs.com/breakthings/p/4051909.html

 

Infix to prefix (expression)