Infix to Postfix Conversion - c++-cli

Question

I'm trying to code that converts infix expressions to postfix expressions. Currently, the program works correctly if I enter for e.g "5+6" it will output the correct answer which is "5 6 +". The problem occurs when I enter more than one operator for e.g "5+6-3", it outputs and incorrect answer "+3-". Can someone please point out where I'm making the error ? Thanks, in advance !
void main(){
Stack *s = new Stack;
string input;
cout <<"Enter Expression"<<endl;
cin>>input;
InfixToPostfix(input);
system("PAUSE");
}
string InfixToPostfix(string input){
Stack *S = new Stack();
string postfix = "";
for (int i=0; i < input.length();i++){
if (input[i]== ' '||input[i]==',') continue;
else if (IsOperator(input[i]))
{
while(!S->IsStackEmpty() && S->StackTop() != '(' && HasHigherPrecedence(S->StackTop(),input[i]))
{
postfix=S->StackTop();
S->Pop();
}
S->Push(input[i]);
}
else if(IsOperand(input[i]))
{
postfix +=input[i];
}
else if (input[i] == '(')
{
S->Push(input[i]);
}
else if (input[i]==')')
{
while(!S->IsStackEmpty() && S->StackTop() != '('){
postfix += S->StackTop();
S->Pop();
}
S->Pop();
}
}
while(!S->IsStackEmpty()){
postfix +=S->StackTop();
S->Pop();
}
cout <<""<<postfix;
return postfix;
}
bool IsOperand(char C)
{
if(C>= '0' && C<= '9') return true;
if(C>= 'a' && C<= 'z') return true;
if(C>= 'A' && C<= 'Z') return true;
return false;
}
bool IsOperator(char C)
{
if(C=='+' || C== '-' || C =='*' || C == '/' ||C == '$')
{
return true;
}else{
return false;
}
}
int IsRightAssociative(char op)
{
if(op=='$'){
return true;
}else{
return false;
}
}
int GetOperatorWeight(char op){
int weight = -1;
switch(op)
{
case'+':
case '-':
weight=1;
break;
case '*':
case '/':
weight=2;
break;
case '$':
weight=3;
break;
}
return weight;
}
int HasHigherPrecedence ( char op1, char op2)
{
int op1Weight= GetOperatorWeight(op1);
int op2Weight = GetOperatorWeight(op2);
if(op1Weight == op2Weight)
{
if(IsRightAssociative(op1))
{
return false;
}else{
return true;
}
return op1Weight > op2Weight ? true:false;
}
}

Answer 1

One suggestion: use a tree, rather than a stack, as an intermediate data structure. Let the operator with lowest precedence be the root of the tree and build it recursively from there. Then walk through the tree from left to right, again recursively, to generate the postfix version. That way, you can also keep track of the maximum stack depth for the postfix version, which can be important as many hand-held RPN calculators, for example, have very limited stack depths.