Infix expression to suffix expression

Infix expression to suffix expression
Infix expression to suffix expression

1. Basic Concepts

There are three expressions in a computer: prefix expression (Polish expression), infix expression, and suffix expression (inverse polish expression ).

For example, expression: a + B * (c-d)-e/f

Prefix expression:-+ a * B-cd/ef

Infix expression: a + B * (c-d)-e/f

Suffix expression: abcd-* + ef /-

1.1 features and advantages and disadvantages

Brackets of an infix expression are indispensable. Its advantage is that it complies with our human writing and reading habits, but its disadvantage is that it is not convenient for computer processing.

The disadvantages of prefix and suffix expressions are not our reading habits, but they are easy for computer processing. For example, for a suffix expression, it pushes the operands into the stack all the time. When an operator is encountered, it extracts two numbers from the stack for calculation, then, press the result into the stack. Therefore, prefixes and suffixes are very convenient for computers to process.

Now we want to convert an infix expression to a suffix expression or an input infix expression to a suffix expression.

2 conversion Principle

The principle is not difficult. When we encounter operands, we can directly output them. When we encounter operators (including '(', '+, we need to press the symbol into the stack,

2.1 When:

We need to pop up the symbol from the top of the stack in sequence until '(' is encountered and '(' is popped up. For example: (a * (B + c) in the stack is (* (+, when ')', we will pop up '+ ','('.

2.2 When '(')

There is nothing to say at this time. Press the stack directly.

2.3 when you encounter '+:

We need to compare the priority of the symbol of the top element of the stack with the priority of the input symbol. If the top element of the stack has a high priority, we need to pop up the top element of the stack in sequence, until the top priority of the stack is lower than the input priority or the stack is empty.

For example, a + B + c + d is different from a + B * c + d because of this priority.

2.4 When an operand is encountered:

No doubt, direct output

3 Programs

#include 
 
  #include 
  
   using namespace std; void changePosfix();int priorty(charch); void main(){         changePosfix();} void changePosfix(){         stack
   
    chStack;         charch;         bool bg= false;         while(ch = getchar() )         {                   switch(ch)                   {                   case'(':                            chStack.push(ch);                            break;                    case')':                            while( chStack.top() != '(')                            {                                     cout<
    
     =priorty(ch) )                            {                                     cout<