Readme_Precedence.md

Sections

i) Description

1. Introdution of operator precedence
2. Working of operator precedence

ii) Reference

Introducction

What is operator precedence?

Operator precedence is an order of operations which reflects the convention of which operation should be done first for any given mathematical expression.

Why used operator precedence in Shunting Yard

Since computer will read the expression from left to right, it will operate the expression based on what operator read first not based on precedence. This may cause error in some mathemtical expression. For exaxmple,

Expression = 5 - 2 * 10

By right, the multiplication of 2 and 10 should be done first but without any precedence, the computer will calculate ("5 - 2") first then multiply by 10 which results 30 but the correct answer is -15.

Working of operator precedence

Binding energy

Binding energy is the strength of bond between the operator and operand. If the binding energy is high mean the operation of that operator will be performed first or vice versa.

How to know the precedence of an operator

Low precedence in term of binding energy

If there are operand on the left hand side of the operator exclude brackets and there are operands after the operand. Then, the operator is considered binary (weakest precedence).

Expression = 1 + 10
  Binary-------^

High precedence in term of binding energy

If there are already an binary operator or the previous operator is an unary then current operator is consider unary (higher precedence than binary)

Expression = 1 + - 10
  Unary----------^
  
  OR
  
 Expression = 1 + + - 10
  Unary-------------^ 

Reference

1. Operator precedence wiki