It avoids the problem of operator precedence and association while making calculations in programming languages.

Never pop out ( ( ) or ( ) ) whatever may be the precedence level of scanned character.

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It uses a stack; but in this case, the stack is used to hold operators rather than numbers.

The purpose of the stack is to reverse the order of the operators in the expression.

It also serves as a storage structure, since no operator can be printed until both of its operands have appeared.

There are more complicated rules to handle operators and parentheses.

When the is read, it has lower precedence than the, so the must be printed first.

The second will show what is on the stack and the third will show the current contents of the postfix string.

The stack will be written from left to right with the bottom of the stack to the left.

The rule for line 2 is to push an operator onto the stack if it is empty.

The rule for line 4 is if the operator on the top of the stack has higher precedence than the one being read, pop and print the one on top and then push the new operator on.

The rule for line 6 is that when the end of the expression has been reached, pop the operators on the stack one at a time and print them.

The stack is suitable for this, since operators will be popped off in the reverse order from that in which they were pushed.

Then when the are both popped off in lines 6 and 7, their order will be reversed.

When the next operator is read, the stack is treated as though it were empty and the new operator (here the sign) is pushed on.

Then when the right parenthesis is read, the stack is popped until the corresponding left parenthesis is found.

Left to right association means that the operator on the stack must be done first, while right to left association means the reverse.

Both operators have the same precedence level, so left to right association tells us to do the first one found before the second.

But instead of pushing the sign onto the stack now, we must compare it with the new top of the stack, the.

Since the operator also has higher precedence than the, it also must be popped and printed.

Now the stack is empty, so the can be pushed onto the stack.

If the association is left to right, pop and print the top of the stack and then push the incoming operator.

If the association is right to left, push the incoming operator.

Then test the incoming operator against the new top of stack.

Infix To Postfix Converter Online