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Evaluate Postfix Expression
For solving a mathematical expression, we need prefix or postfix form. After converting infix to postfix, we need postfix evaluation algorithm to find the correct answer.
Here also we have to use the stack data structure to solve the postfix expressions.
From the postfix expression, when some operands are found, pushed them in the stack. When some operator is found, two items are popped from the stack and the operation is performed in correct sequence. After that, the result is also pushed in the stack for future use. After completing the whole expression, the final result is also stored in the stack top.
Input and Output
Input: Postfix expression: 53+62/*35*+ Output: The result is: 39
Algorithm
postfixEvaluation(postfix)
Input: Postfix expression to evaluate.
Output: Answer after evaluating postfix form.
Begin for each character ch in the postfix expression, do if ch is an operator ⨀ , then a := pop first element from stack b := pop second element from the stack res := b ⨀ a push res into the stack else if ch is an operand, then add ch into the stack done return element of stack top End
Example
#include<iostream> #include<cmath> #include<stack> using namespace std; float scanNum(char ch) { int value; value = ch; return float(value-'0'); //return float from character } int isOperator(char ch) { if(ch == '+'|| ch == '-'|| ch == '*'|| ch == '/' || ch == '^') return 1; //character is an operator return -1; //not an operator } int isOperand(char ch) { if(ch >= '0' && ch <= '9') return 1; //character is an operand return -1; //not an operand } float operation(int a, int b, char op) { //Perform operation if(op == '+') return b+a; else if(op == '-') return b-a; else if(op == '*') return b*a; else if(op == '/') return b/a; else if(op == '^') return pow(b,a); //find b^a else return INT_MIN; //return negative infinity } float postfixEval(string postfix) { int a, b; stack<float> stk; string::iterator it; for(it=postfix.begin(); it!=postfix.end(); it++) { //read elements and perform postfix evaluation if(isOperator(*it) != -1) { a = stk.top(); stk.pop(); b = stk.top(); stk.pop(); stk.push(operation(a, b, *it)); }else if(isOperand(*it) > 0) { stk.push(scanNum(*it)); } } return stk.top(); } main() { string post = "53+62/*35*+"; cout << "The result is: "<<postfixEval(post); }
Output
The result is: 39
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