1. Data Structures and Algorithms
Prof. Ajit A. Diwan
Prof. Ganesh Ramakrishnan
Prof. Deepak B. Phatak
Department of Computer Science and Engineering
IIT Bombay
Session: Postfix Evaluation (Program)
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. Algorithm Input: Postfix Expression
Output: Numerical value of the evaluated postfix expression
Get values of all operands present in the postfix expression
Traverse the postfix expression
If it is an operand, push the value of that operand on the stack
Else, it is an operator, so do the following:
Assign the value from the top of stack to a variable ‘operand2’
Pop the element from the stack
Assign the value from the top of stack to a variable ‘operand1’
Evaluate the result of operand1 and operand2 and push the result back on the stack
Return the top value of the stack (answer)
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

3. Program: Functions Name Parameter Returns Purpose getValues()
Postfix expression, values (array)
Called from evaluatePostfix(). Does not return any value
To store the values of operands in the array ‘value’ which is passed from evaluatePostfix()
isOperator()
Current character
Called from evaluatePostfix(). Returns ‘true’ or ‘false’
To check whether character is an operator or not
calculateValues()
operand1, operand2, operator
Called from evaluatePostfix(). Returns numerical value
Evaluate operand1 and operand2
evaluatePostfix()
Postfix expression
Called from ‘main()’. Returns numerical value
To evaluate postfix expression
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

4. Program Examine the ‘currentChar’ If it is an operator, return true
Else return false
bool isOperator(char currentChar) {
if (currentChar=='+' || currentChar=='-' ||
currentChar=='*' || currentChar=='/' ||
currentChar=='^')
return true;
else
return false;
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

5. Program Traverse the postfix expression
If the character is an operand:
Accept the value of operand from the user and store it in the array ‘value’ at the index ‘operand’
Using Associative arrays for storing values
For a few operands, we need a small array to store their values. In our examples, we are using operands represented by single character (a-z and A –Z). Their ASCII codes are within 0 to 255
We will use array ‘value’ of size 256 to store operand values, in locations corresponding to their ASCII codes, which can be used directly as an index to the array ‘value’
E.g. Postfix expression: ac+
Here, ‘a’ and ‘c’ are operands
Assume that user has entered:
number 5 for operand ‘a’ and
number 7 for operand ‘c’.
value[97] = 5 //ASCII value of ‘a’ is 97
value[99] = 7 //ASCII value of ‘c’ is 99
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

6. Program Traverse the postfix expression
If the character is an operand:
Accept the value of operand from the user and store it in the array ‘value’ at the index ‘operand’
void getValues(char postfix[], float value[]) {
int i=0;
char currentChar;
while(postfix[i]!='\0') {
currentChar=postfix[i];
if (!isOperator(currentChar)) { //Operand
cout << "Enter value of "
<< currentChar << ": ";
cin >> value[currentChar]; }
i++;
} //End of function
E.g. Postfix expression: ac+
Here, ‘a’ and ‘c’ are operands
Assume that user has entered:
number 5 for operand ‘a’ and
number 7 for operand ‘c’.
value[97] = 5 //ASCII value of ‘a’ is 97
value[99] = 7 //ASCII value of ‘c’ is 99
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

7. Program Perform the operation on ‘operand1’ and ‘operand2’
Return the result to the function ‘evaluatePostfix’.
float calculateValues(float operand1, float operand2, char Operator) {
if (Operator == '+') return operand1 + operand2;
if (Operator == '-') return operand1 - operand2;
if (Operator == '*') return operand1 * operand2;
if (Operator == '/') return operand1 / operand2;
if (Operator == '^') return pow(operand1,operand2);
} //End of function
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

8. Program float evaluatePostfix(char postfix[]) {
stack<float> Stack; //stack
char currentChar;
int i=0;
float result, operand1, operand2, value[256];
getValues(postfix, value);
while(postfix[i]!='\0') {
currentChar = postfix[i];
i++;
} //End of while (expression traversed)
return Stack.top(); //Final answer
} //End of function
Code for evaluation
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

9. Program if (isOperator(currentChar)) { operand2 = Stack.top();
Stack.pop();
operand1 = Stack.top();
result = calculateValues (operand1,
operand2, currentChar);
Stack.push(result); }
else { //It is an operand
Stack.push(value[currentChar]);
float evaluatePostfix(char postfix[]) {
stack<float> Stack; //stack
char currentChar;
int i=0;
float result, operand1, operand2, value[200];
getValues(postfix, value);
while(postfix[i]!='\0') {
currentChar = postfix[i];
i++;
} //End of while (expression traversed)
return Stack.top(); //Final answer
} //End of function
Code for evaluation
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

10. Thank you
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay