S: Stack
while(more tokens)
{
x<-next token;
if(x is an operand)
print x
else
{
while(precedence(x) <= precedence(top(s))
print(pop(s))
push(s,x)
}
}
while(!empty(s))
print(pop(s));
Written by: Fabianski Benjamin
STACK
the STACK data structure can be implemented in java through ARRAYs and LINKED LISTS.
it is needed in compiler designing
A stack.
people almost exclusively use infix notation to write mathematical expressions, computer languages almost exclusively allow programmers to use infix notation. However, if a compiler allowed infix expressions into the binary code used in the compiled version of a program, the resulting code would be larger than needed and very inefficient. Because of this, compilers convert infix expressions into postfix notation expressions, which have a much simpler set of rules for expression evaluation. Postfix notation gets its name from the fact that operators in a postfix expression follow the operands that they specify an operation on. Here are some examples of equivalent infix and postfix expressions Infix Notation Postfix Notation 2 + 3 2 3 + 2 + 3 * 6 3 6 * 2 + (2 + 3) * 6 2 3 + 6 * A / (B * C) + D * E - A - C A B C * / D E * + A C * - Where as infix notation expressions need a long list or rules for evaluation, postfix expressions need very few.
infix: old Egyptians/Assirs some thousands year before prefix: Jan Łukasiewicz (Polish Notation) postfix: Burks, Warren, and Wright (Reverse Polish Notation)
struct stack { char ele; struct stack *next; }; void push(int); int pop(); int precedence(char); struct stack *top = NULL; int main() { char infix[20], postfix[20]; int i=0,j=0; printf("ENTER INFIX EXPRESSION: "); gets(infix); while(infix[i]!='\0') { if(isalnum(infix[i])) postfix[j++]=infix[i]; else { if(top==NULL) push(infix[i]); else { while(top!=NULL && (precedence(top->ele)>=precedence(infix[i]))) postfix[j++]=pop(); push(infix[i]); } } ++i; } while(top!=NULL) postfix[j++]=pop(); postfix[j]='\0'; puts(postfix); getchar(); return 0; } int precedence(char x) { switch(x) { case '^': return 4; case '*': case '/': return 3; case '+': case '-': return 2; default: return 0; } } void push(int x) { int item; struct stack *tmp; if(top==NULL) { top=(struct stack *)malloc(sizeof(struct stack)); top->ele=x; top->next=NULL; } else { tmp=top; top->ele=x; top->next=tmp; } } int pop() { struct stack *tmp; int item; if(top==NULL) puts("EMPTY STACK"); else if(top->next==NULL) { tmp=top; item=top->ele; top=NULL; free(tmp); } else { tmp=top; item=top->ele; top=top->next; free(tmp); } return item; }
O(nlogn)
#include <iostream> #include <stack> using namespace std; int prec (char ch){ // Gives precedence to different operators switch (ch) { case '^': return 5; case '/': return 4; case '*': return 4; case '+': return 2; case '-': return 1; default : return 0; } } bool isOperand(char ch){ // Finds out is a character is an operand or not if ((ch>='0' && ch<='9') (ch>='a' && ch<='z')) return true; else return false; } string postFix (string infix){ string pfix = ""; stack<char> opstack; for (int i=0; i<infix.length(); i++){ // Scan character by character if (isOperand(infix[i])) { pfix += infix[i]; } else if (infix[i] ')') { // Retrace to last ( closure while (opstack.top() != '(') { pfix += opstack.top(); opstack.pop(); } // Remove the '(' found by while loop opstack.pop(); }
stack is the basic data structure needed to convert infix notation to postfix
Linear data structure is used to convert the logical address to physical address .Stack is used in this and the various conversion such as postfix,prefix and infix notation are come in this
(a + b) * c / ((x - y) * z)
I dont have the idea about the program but I know that prefix means the first starting letters of a particular things. I really think so there is a progam to convert infix to prefix but i might have misunderstood your question can you make it little simpler please.
You convert an (infix) expression into a postfix expression as part of the process of generating code to evaluate that expression.
An algorithm can not be written with the following infix expression without knowing what the expression is. Once this information is included a person will be able to know how to write the algorithm.
people almost exclusively use infix notation to write mathematical expressions, computer languages almost exclusively allow programmers to use infix notation. However, if a compiler allowed infix expressions into the binary code used in the compiled version of a program, the resulting code would be larger than needed and very inefficient. Because of this, compilers convert infix expressions into postfix notation expressions, which have a much simpler set of rules for expression evaluation. Postfix notation gets its name from the fact that operators in a postfix expression follow the operands that they specify an operation on. Here are some examples of equivalent infix and postfix expressions Infix Notation Postfix Notation 2 + 3 2 3 + 2 + 3 * 6 3 6 * 2 + (2 + 3) * 6 2 3 + 6 * A / (B * C) + D * E - A - C A B C * / D E * + A C * - Where as infix notation expressions need a long list or rules for evaluation, postfix expressions need very few.
Without data-structures you cannot even store expressions, let alone convert or evaluate them.
The cast of Index of Infix - 2004 includes: Infix as Themselves
give 5 examples of infix
Infix
To set; to fasten or fix by piercing or thrusting in; as, to infix a sting, spear, or dart., To implant or fix; to instill; to inculcate, as principles, thoughts, or instructions; as, to infix good principles in the mind, or ideas in the memory., Something infixed.