Predictive Parser

#include <bits/stdc++.h>
using namespace std;
char rel(string& s, string& r) {
    if (s == "id" && r == "id") return '-'; if (s == "$" && r == "$" ) return 'A';
    if (s == "id" or r == "$") return '>'; if (s == "$" or r == "id") return '<';
    if (s == "+") { if (r == "*" or r == "^") return '<'; return '>'; }
    if (s == "*") { if (r == "+" or r == "^") return '>'; return '<'; }
    if (s == "^") { if (r == "+" or r == "*") return '>'; return '<'; }
}
int main() {
    map<string, string> grammar;
    grammar["E + E"] = grammar["E * E"] = grammar["E ^ E"] = grammar["id"] = "E";
    cout << "Enter the production: "; string s; getline(cin, s);
    vector<string> w; string r;
    for (char c : s) { if (c == ' ') w.push_back(r), r.clear(); else r += c; }
    if (!r.empty()) w.push_back(r); w.push_back("$");
    int i = 0; string ip = w[i]; stack<string> sk, terminal; sk.push("$");
    while (true) {
        if (sk.top() == "$" && ip == "$" && terminal.size() == 1 && terminal.top() == grammar.begin()->second) { cout << "Accepted!\n"; break; }
        string a = sk.top(), b = ip; char relation = rel(a, b);
        if (relation == '<') {
            sk.push(b); ip = w[++i]; cout << "Shift Operation Performed!\n";
        }
        else if (relation == '>') {
            do {
                string recent = sk.top(); sk.pop();
                if (recent != w[0]) {
                    string st = terminal.top(); terminal.pop();
                    st += " " + recent + " " + terminal.top();
                    terminal.pop(); terminal.push(grammar[st]);
                }
                else terminal.push(grammar[w[0]]);
                cout << "Reduce Operation Performed!\n";
            } while (rel(sk.top(), ip) == '>');
        }
    }
    return 0;
}

/*
Input:
id * id + id
*/