write a postfix notation of the sequence 499 106 599 699

write a postfix notation of the sequence: 4.99 * 1.06 + 5.99 + 6.99 * 1.06

C++

Solution

Below is the C++ program to convert the sequene into postfix notation form:

#include<iostream>
#include<cstring>
#include<stack>
using namespace std;

// get weight of operators as per precedence
// higher weight given to operators with higher precedence
// for non operators, return 0
int getWeight(char ch) {
switch (ch) {
case \'/\':
case \'*\': return 2;
case \'+\':
case \'-\': return 1;
default : return 0;
}
}

// convert infix expression to postfix using a stack
void infix2postfix(char infix[], char postfix[], int size) {
stack<char> s;
int weight;
int i = 0;
int k = 0;
char ch;
// iterate over the infix expression   
while (i < size) {
ch = infix[i];
if (ch == \'(\') {
// simply push the opening parenthesis
s.push(ch);
i++;
continue;
}
  

if (ch == \')\') {
// if we see a closing parenthesis,
// pop of all the elements and append it to
// the postfix expression till we encounter
// a opening parenthesis
while (!s.empty() && s.top() != \'(\') {
postfix[k++] = s.top();
s.pop();

}
// pop off the opening parenthesis also
if (!s.empty()) {
s.pop();
}
i++;
continue;
}
weight = getWeight(ch);
if (weight == 0) {
// we saw an operand
// simply append it to postfix expression
postfix[k++] = ch;

}
else {
// we saw an operator
if (s.empty()) {
// simply push the operator onto stack if
// stack is empty
s.push(ch);
}
     

else {
// pop of all the operators from the stack and
// append it to the postfix expression till we
// see an operator with a lower precedence that
// the current operator
while (!s.empty() && s.top() != \'(\' &&
weight <= getWeight(s.top())) {
postfix[k++] = s.top();
s.pop();

}
// push the current operator onto stack
s.push(ch);
}
}
i++;
}
// pop of the remaining operators present in the stack
// and append it to postfix expression
while (!s.empty()) {
postfix[k++] = s.top();
s.pop();
}
postfix[k] = 0; // null terminate the postfix expression
}

// main
int main() {
char infix[] = \"4.99 * 1.06 + 5.99 + 6.99 * 1.06\";
int size = strlen(infix);
char postfix[size];
infix2postfix(infix,postfix,size);
cout<<\"\ Infix Expression :: \"<<infix;
cout<<\"\ Postfix Expression :: \"<<postfix;
cout<<endl;
return 0;
}

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Sample O/P:

Infix Expression :: 4.99 * 1.06 + 5.99 + 6.99 * 1.06
Postfix Expression :: 4.99 1.06 * 5.99 + 6.99 1.06*+

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