Answer:
Explanation:
Program:
#include<iostream>
#include <bits/stdc++.h>
using namespace std;
//check for operator
bool isOperator(char c)
{
switch(c)
{
case '+': case '-': case '/': case '*': case '^':
return true;
}
return false;
}
//Converter class
class Converter
{
private:
string str;
public:
//constructor
Converter(string s):str(s){}
//convert from infix to postfix expression
string toPostFix(string str)
{
stack <char> as;
int i, pre1, pre2;
string result="";
as.push('(');
str = str + ")";
for (i = 0; i < str.size(); i++)
{
char ch = str[i];
if(ch==' ') continue;
if (ch == '(')
as.push(ch);
else if (ch == ')')
{
while (as.size() != 0 && as.top() != '('){
result = result + as.top() + " ";
as.pop();
}
as.pop();
}
else if(isOperator(ch))
{
while (as.size() != 0 && as.top() != '(')
{
pre1 = precedence(ch);
pre2 = precedence(as.top());
if (pre2 >= pre1){
result = result + as.top() + " ";
as.pop();
}
else break;
}
as.push(ch);
}
else
{
result = result + ch;
}
}
while(as.size() != 0 && as.top() != '(') {
result += as.top() + " ";
as.pop();
}
return result;
}
//return the precedence of an operator
int precedence(char ch)
{
int choice = 0;
switch (ch) {
case '+':
choice = 0;
break;
case '-':
choice = 0;
break;
case '*':
choice = 1;
break;
case '/':
choice = 1;
break;
case '^':
choice = 2;
default:
choice = -999;
}
return choice;
}
};
//Node class
class Node
{
public:
string element;
Node *leftChild;
Node *rightChild;
//constructors
Node (string s):element(s),leftChild(nullptr),rightChild(nullptr) {}
Node (string s, Node* l, Node* r):element(s),leftChild(l),rightChild(r) {}
};
//ExpressionTree class
class ExpressionTree
{
public:
//expression tree construction
Node* covert(string postfix)
{
stack <Node*> stk;
Node *t = nullptr;
for(int i=0; i<postfix.size(); i++)
{
if(postfix[i]==' ') continue;
string s(1, postfix[i]);
t = new Node(s);
if(!isOperator(postfix[i]))
{
stk.push(t);
}
else
{
Node *r = nullptr, *l = nullptr;
if(!stk.empty()){
r = stk.top();
stk.pop();
}
if(!stk.empty()){
l = stk.top();
stk.pop();
}
t->leftChild = l;
t->rightChild = r;
stk.push(t);
}
}
return stk.top();
}
//inorder traversal
void infix(Node *root)
{
if(root!=nullptr)
{
cout<< "(";
infix(root->leftChild);
cout<<root->element;
infix(root->rightChild);
cout<<")";
}
}
//postorder traversal
void postfix(Node *root)
{
if(root!=nullptr)
{
postfix(root->leftChild);
postfix(root->rightChild);
cout << root->element << " ";
}
}
//preorder traversal
void prefix(Node *root)
{
if(root!=nullptr)
{
cout<< root->element << " ";
prefix(root->leftChild);
prefix(root->rightChild);
}
}
};
//main method
int main()
{
string infix;
cout<<"Enter the expression: ";
cin >> infix;
Converter conv(infix);
string postfix = conv.toPostFix(infix);
cout<<"Postfix Expression: " << postfix<<endl;
if(postfix == "")
{
cout<<"Invalid expression";
return 1;
}
ExpressionTree etree;
Node *root = etree.covert(postfix);
cout<<"Infix: ";
etree.infix(root);
cout<<endl;
cout<<"Prefix: ";
etree.prefix(root);
cout<<endl;
cout<< "Postfix: ";
etree.postfix(root);
cout<<endl;
return 0;
}
