Infix To Postfix Conversion using Stack in C++

//Using inbuilt stack library to create stack
#include <iostream>
#include <stack>
using namespace std;

int priority (char alpha){
    if(alpha == '+' || alpha =='-')
        return 1;
 
    if(alpha == '*' || alpha =='/')
        return 2;
 
    if(alpha == '^')
        return 3;

 
    return 0;
}
string convert(string infix)
{
    int i = 0;
    string postfix = "";
    // using inbuilt stack< > from C++ stack library
    stack <int>s;

    while(infix[i]!='\0')
    {
        // if operand add to the postfix expression
        if(infix[i]>='a' && infix[i]<='z'|| infix[i]>='A'&& infix[i]<='Z')          
        {
            postfix += infix[i];
            i++;
        }
        // if opening bracket then push the stack
        else if(infix[i]=='(')
        {
            s.push(infix[i]);
            i++;
        }
        // if closing bracket encounted then keep popping from stack until 
        // closing a pair opening bracket is not encountered
        else if(infix[i]==')')
        {
            while(s.top()!='('){
                postfix += s.top();
                s.pop();
            }
            s.pop();
            i++;
        }
        else            
        {
            while (!s.empty() && priority(infix[i]) <= priority(s.top())){
                postfix += s.top();
                s.pop();
            }
            s.push(infix[i]);
            i++;
        }
    }
    while(!s.empty()){
        postfix += s.top();
        s.pop();
    }


    cout << "Postfix is : " << postfix; //it will print postfix conversion  
    return postfix;
}

int main()
{
    string infix = "((a+(b*c))-d)"; 
    string postfix;
    postfix = convert(infix);
    
    return 0;
}

// custom class based stack implimentation
#include<bits/stdc++.h>
using namespace std;

class Stack {
    int top;
    int MAX;
    int* a;
 
public:

    Stack(int size){
        top = -1;
        MAX = size;
        a = new int [MAX];
    }
    bool push(int x);
    int pop();
    int peek();
    bool isEmpty();
    bool isFull();
};

bool Stack::isEmpty(){
    return (top < 0); } bool Stack::isFull(){ return (top == MAX - 1); } int Stack::peek(){ return a[top]; } bool Stack::push(int x) { if (top >= (MAX - 1)) {
        cout << "Stack Overflow";
        return false;
    }
    else {
        top++;
        a[top] = x;
        return true;
    }
}
int Stack::pop()
{
    if (top < 0) {
        cout << "Stack Underflow"; 
        return INT_MIN;
        } 
        else { 
            int x = a[top];
            top--;
            return x;
            }
            } 
        int priority (char alpha) {
            if(alpha == '+' || alpha =='-')
            return 1; 
            if(alpha == '*' || alpha =='/')
            return 2;
            if(alpha == '^')
            return 3; return 0; 
            
        } 
        string convert(string infix) {
            int i = 0;
            string postfix = ""; 
            Stack s(20);
            while(infix[i]!='\0') { // if operand add to the postfix expression 
            if(infix[i]>='a' && infix[i]<='z'|| infix[i]>='A'&& infix[i]<='Z')
       {
           postfix += infix[i]; 
            i++; 
       } 
    // if opening bracket then push the stack 
       else if(infix[i]=='(') {
           s.push(infix[i]);
           i++; 
           
       } 
    
    // if closing bracket encounted then keep popping from stack until 
    // closing a pair opening bracket is not encountered 
    else if(infix[i]==')') { 
        while(s.peek()!='(')
            postfix += s.pop(); 
        s.pop(); 
        i++;
        } 
    else { 
        while (!s.isEmpty() && priority(infix[i]) <= priority(s.peek())){
            postfix += s.pop();
        } 
        s.push(infix[i]);
        i++;
    }
    } 
    while(!s.isEmpty()){
        postfix += s.pop();
        }
    cout << "Postfix is : " << postfix; 
    //it will print postfix conversion
    return postfix;
    
} 

int main() {
    string infix = "((a+(b*c))-d)";
    string postfix; 
    postfix = convert(infix);
    return 0;
}