Skip to main content

Infix to Postfix Expression Conversion

With a given Infix Expression, we will see how to convert Infix Expression into Postfix Expression using stack.
 

Algorithm to convert Infix expression to Postfix expression:

In this algorithm, we will use operatorStack to store operators during the conversion. The step are as follows:
  • Initialize empty operatorStack
  • While the end of input infix string
    • symbol = next input character
    • If symbol is an operand
      • add symbol to the postfix string
    • Else
      • While( operatorStack is not empty && precedence of top character of operatorStack is higher than symbol)
        • topsymbol = pop the operatorStack
        • add topsymbol to the postfix string
      • End While
      • If (operatorStack is empty || symbol is not equal to '(' )
        • push symbol into operatorStack
      • Else
        • pop the operatorStack
      • End If
    • End If
    • While the operatorStack is not empty
      • topsymbol = pop the operatorStack
      • add topsymbol to the postfix string
    • End While
 


 

Function to convert Infix expression to Postfix expression:


void infix_to_postfix(char *infix_str, char *postfix_str){
 int i = -1, j = -1;
 STACK stk;
 stk.top = -1;
 while(infix_str[++i]){
  if(infix_str[i] == ' '){
   continue;
  }
  if( ischar(infix_str[i]) ){
   postfix_str[++j] = infix_str[i];
  }
  else{
   while( !empty_stack(&stk) && precedence( top_of_stack(&stk), infix_str[i]) ){
   postfix_str[++j] = pop(&stk);
   }
   if(empty_stack(&stk) || infix_str[i] != ')'){
    push(&stk,infix_str[i]);
   }
   else{
    pop(&stk);
   }
  }
 }
 while(!empty_stack(&stk)){
  postfix_str[++j] = pop(&stk);
 }
 postfix_str[++j] = '\0';
}
 

Program to convert Infix expression to Postfix expression:


#include <stdio.h>
#include <stdlib.h>
#define STACK_SIZE 50

typedef struct{
 int top;
 char stack[STACK_SIZE];
} STACK;

void push(STACK *, char );
char pop(STACK *);
void infix_to_postfix(char *, char*);
char top_of_stack(STACK *);
int ischar(char );
int empty_stack(STACK*);
int precedence(char,char);

int main(){
 char *infix_str = "A+(B*C)/D";
 char postfix_str[100];
 infix_to_postfix(infix_str, postfix_str);
 printf("Infix Expression   : %s\n", infix_str);
 printf("Postfix Expression : %s\n", postfix_str);
 return 0;
}

// return true when op1 has higher precedence over op2
int precedence(char op1, char op2){ 
 char *sym = "/*+-";
 int i1 = -1, i2 = -1,i = -1;
 if(op1 == '(')
  return 0;
 if(op2 == '('){
  if(op1 != ')')
   return 0;
  return 1;
 }
 if(op2 == ')'){
  if(op1 != '(')
   return 1;
  return 0;
 }
 if(op1 == ')')
  exit(1);
 while(sym[++i]){
  if(op1 == sym[i])
   i1 = i;
  if(op2 == sym[i])
   i2 = i;
 }
 return i1 < i2;
}

void infix_to_postfix(char *infix_str, char *postfix_str){
 int i = -1, j = -1;
 STACK stk;
 stk.top = -1;
 while(infix_str[++i]){
  if(infix_str[i] == ' '){
   continue;
  }
  if( ischar(infix_str[i]) ){
   postfix_str[++j] = infix_str[i];
  }
  else{
   while( !empty_stack(&stk) && precedence( top_of_stack(&stk), infix_str[i]) ){
   postfix_str[++j] = pop(&stk);
   }
   if(empty_stack(&stk) || infix_str[i] != ')'){
    push(&stk,infix_str[i]);
   }
   else{
    pop(&stk);
   }
  }
 }
 while(!empty_stack(&stk)){
  postfix_str[++j] = pop(&stk);
 }
 postfix_str[++j] = '\0';
}


char top_of_stack(STACK *s){
 return s->stack[s->top];
}

int empty_stack(STACK *stk){
 return stk->top == -1;
}

int ischar(char c){
 return  ( (c >= 'a') && (c <= 'z') ) || 
   ( (c >= 'A') && (c <= 'Z') ) || 
   ( (c >= '0') && (c <= '9') );
}

void push(STACK *s, char c){
 if(s->top == STACK_SIZE-1){
  printf("Stack Overflow\n");
  exit(1);
 }
 else{
  s->stack[++s->top] = c;
 }
}

char pop(STACK *s){
 if(s->top == -1){
  printf("Stack Underflow\n");
  exit(1);
 }
 else{
  return s->stack[s->top--];
 }
}
 
Infix Expression   : A+(B*C)/D
Postfix Expression : ABC*D/+
 

Related topics:

Labels:

Comments

Post a Comment

Popular posts from this blog

Insertion at specific position N in singly link list

Insertion of a new node at position N in singly link list requires traversing the list for N-1 th node so that links are updated to accommodate the new node in the list. The new node's next is set to point to Nth node of the list and then N-1 th node's next pointer is updated so that it reference to new node. The step by step algorithm to insert node at Nth position is as below: Algorithm to insert node at specific position N in singly link list: This algorithm will insert the new node PTR at the position N in the link list. The steps are as follows: Create new node PTR Set the INFO field of PTR If N is less than 1 Node can't be inserted Else If node is to be inserted at first i.e. [N=1] Make new node PTR points to first node i.e. [PTR->NEXT = START] Make START point to new node PTR i.e. [START = PTR] Else Traverse the list to get the (N-1)th node of list into TEMP Make PTR's next pointer point to Nth node in the list i.e. [PTR -> NEXT  =  TEMP-...
Post a Comment
Read more

Implementation of Stack to store different data types

Here we will see how to implement stack using structure and union to store different datatypes in stack. First we define the basic structure for elements/items to be stored in the stack. struct Items{ int ele_type; union { int ivalue; float fvalue; char *strvalue; } stack_element; }; In the above code, we have defined a Items structure to store the info about the type of items in ele_type variable and a union variable named stack_element to store the actual value of stack items. In union the, ivalue is used to store the integer value, fvalue to store floating value and strvalue to store the string value. If you wish to add other datatype, you can add any datatype within the union. Now we will define the structure to implement the stack. The code below: struct Stack{ int top; struct Items element[MAX]; }; In the above code, struct Stack is defined to hold the top of stack and the array of Items structure named element to hold the actual Items defined above. MA...
Post a Comment
Read more

Concatenating two link list

Here we will see how to concat two single link list into other link list. First we copy the content of first list in third list and then the content of second list into third list. Algorithm for concatenation of two link list: This algorithm will use three list. List 1 and List 2 will be concatenated into List 3. The step below: Copy the list 1 into list 3 Copy the list 2 at the last of list 3 Function to concat two link list: void concatLists(NODE **start1, NODE **start2, NODE **mergeinto){ NODE *temp; temp = *start1; while(temp != NULL){ insertAtLast(&*mergeinto, temp->info); temp = temp->next; } temp = *start2; while(temp != NULL){ insertAtLast(&*mergeinto, temp->info); temp = temp->next; } }   Program to concat two link lists: #include <stdio.h> #include <malloc.h> struct node{ int info; struct node *next; }; typedef struct node NODE; void insertAtLast(NODE **, int); void traverse(NODE **); void concatLists(NODE **,...
Post a Comment
Read more