The Postfix notation is used to represent algebraic expressions. The expressions written in postfix form are evaluated faster compared to infix notation as parenthesis are not required in postfix. We have discussed infix to postfix conversion. In this post, evaluation of postfix expressions is discussed.
Following is algorithm for evaluation postfix expressions.
1) Create a stack to store operands (or values).
2) Scan the given expression and do following for every scanned element.
…..a) If the element is a number, push it into the stack
…..b) If the element is a operator, pop operands for the operator from stack. Evaluate the operator and push the result back to the stack
3) When the expression is ended, the number in the stack is the final answer
Example:
Let the given expression be “2 3 1 * + 9 -“. We scan all elements one by one.
1) Scan ‘2’, it’s a number, so push it to stack. Stack contains ‘2’
2) Scan ‘3’, again a number, push it to stack, stack now contains ‘2 3’ (from bottom to top)
3) Scan ‘1’, again a number, push it to stack, stack now contains ‘2 3 1’
4) Scan ‘*’, it’s an operator, pop two operands from stack, apply the * operator on operands, we get 3*1 which results in 3. We push the result ‘3’ to stack. Stack now becomes ‘2 3’.
5) Scan ‘+’, it’s an operator, pop two operands from stack, apply the + operator on operands, we get 3 + 2 which results in 5. We push the result ‘5’ to stack. Stack now becomes ‘5’.
6) Scan ‘9’, it’s a number, we push it to the stack. Stack now becomes ‘5 9’.
7) Scan ‘-‘, it’s an operator, pop two operands from stack, apply the – operator on operands, we get 5 – 9 which results in -4. We push the result ‘-4’ to stack. Stack now becomes ‘-4’.
8) There are no more elements to scan, we return the top element from stack (which is the only element left in stack).
Below is the implementation of above algorithm.
C++
// C++ program to evaluate value of a postfix expression #include <iostream> #include <string.h> using namespace std; // Stack type struct Stack { int top; unsigned capacity; int* array; }; // Stack Operations struct Stack* createStack( unsigned capacity ) { struct Stack* stack = (struct Stack*) malloc(sizeof(struct Stack)); if (!stack) return NULL; stack->top = -1; stack->capacity = capacity; stack->array = (int*) malloc(stack->capacity * sizeof(int)); if (!stack->array) return NULL; return stack; } int isEmpty(struct Stack* stack) { return stack->top == -1 ; } char peek(struct Stack* stack) { return stack->array[stack->top]; } char pop(struct Stack* stack) { if (!isEmpty(stack)) return stack->array[stack->top--] ; return '$'; } void push(struct Stack* stack, char op) { stack->array[++stack->top] = op; } // The main function that returns value of a given postfix expression int evaluatePostfix(char* exp) { // Create a stack of capacity equal to expression size struct Stack* stack = createStack(strlen(exp)); int i; // See if stack was created successfully if (!stack) return -1; // Scan all characters one by one for (i = 0; exp[i]; ++i) { // If the scanned character is an operand (number here), // push it to the stack. if (isdigit(exp[i])) push(stack, exp[i] - '0'); // If the scanned character is an operator, pop two // elements from stack apply the operator else { int val1 = pop(stack); int val2 = pop(stack); switch (exp[i]) { case '+': push(stack, val2 + val1); break; case '-': push(stack, val2 - val1); break; case '*': push(stack, val2 * val1); break; case '/': push(stack, val2/val1); break; } } } return pop(stack); } // Driver program to test above functions int main() { char exp[] = "231*+9-"; cout<<"postfix evaluation: "<< evaluatePostfix(exp); return 0; } |
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C
// C program to evaluate value of a postfix expression #include <stdio.h> #include <string.h> #include <ctype.h> #include <stdlib.h> // Stack type struct Stack { int top; unsigned capacity; int* array; }; // Stack Operations struct Stack* createStack( unsigned capacity ) { struct Stack* stack = (struct Stack*) malloc(sizeof(struct Stack)); if (!stack) return NULL; stack->top = -1; stack->capacity = capacity; stack->array = (int*) malloc(stack->capacity * sizeof(int)); if (!stack->array) return NULL; return stack; } int isEmpty(struct Stack* stack) { return stack->top == -1 ; } char peek(struct Stack* stack) { return stack->array[stack->top]; } char pop(struct Stack* stack) { if (!isEmpty(stack)) return stack->array[stack->top--] ; return '$'; } void push(struct Stack* stack, char op) { stack->array[++stack->top] = op; } // The main function that returns value of a given postfix expression int evaluatePostfix(char* exp) { // Create a stack of capacity equal to expression size struct Stack* stack = createStack(strlen(exp)); int i; // See if stack was created successfully if (!stack) return -1; // Scan all characters one by one for (i = 0; exp[i]; ++i) { // If the scanned character is an operand (number here), // push it to the stack. if (isdigit(exp[i])) push(stack, exp[i] - '0'); // If the scanned character is an operator, pop two // elements from stack apply the operator else { int val1 = pop(stack); int val2 = pop(stack); switch (exp[i]) { case '+': push(stack, val2 + val1); break; case '-': push(stack, val2 - val1); break; case '*': push(stack, val2 * val1); break; case '/': push(stack, val2/val1); break; } } } return pop(stack); } // Driver program to test above functions int main() { char exp[] = "231*+9-"; printf ("postfix evaluation: %d", evaluatePostfix(exp)); return 0; } |
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Java
// Java proram to evaluate value of a postfix expression import java.util.Stack; public class Test { // Method to evaluate value of a postfix expression static int evaluatePostfix(String exp) { //create a stack Stack<Integer> stack=new Stack<>(); // Scan all characters one by one for(int i=0;i<exp.length();i++) { char c=exp.charAt(i); // If the scanned character is an operand (number here), // push it to the stack. if(Character.isDigit(c)) stack.push(c - '0'); // If the scanned character is an operator, pop two // elements from stack apply the operator else { int val1 = stack.pop(); int val2 = stack.pop(); switch(c) { case '+': stack.push(val2+val1); break; case '-': stack.push(val2- val1); break; case '/': stack.push(val2/val1); break; case '*': stack.push(val2*val1); break; } } } return stack.pop(); } // Driver program to test above functions public static void main(String[] args) { String exp="231*+9-"; System.out.println("postfix evaluation: "+evaluatePostfix(exp)); } } // Contributed by Sumit Ghosh |
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Python
# Python program to evaluate value of a postfix expression # Class to convert the expression class Evaluate: # Constructor to initialize the class variables def __init__(self, capacity): self.top = -1 self.capacity = capacity # This array is used a stack self.array = [] # check if the stack is empty def isEmpty(self): return True if self.top == -1 else False # Return the value of the top of the stack def peek(self): return self.array[-1] # Pop the element from the stack def pop(self): if not self.isEmpty(): self.top -= 1 return self.array.pop() else: return "$" # Push the element to the stack def push(self, op): self.top += 1 self.array.append(op) # The main function that converts given infix expression # to postfix expression def evaluatePostfix(self, exp): # Iterate over the expression for conversion for i in exp: # If the scanned character is an operand # (number here) push it to the stack if i.isdigit(): self.push(i) # If the scanned character is an operator, # pop two elements from stack and apply it. else: val1 = self.pop() val2 = self.pop() self.push(str(eval(val2 + i + val1))) return int(self.pop()) # Driver program to test above function exp = "231*+9-"obj = Evaluate(len(exp)) print "postfix evaluation: %d"%(obj.evaluatePostfix(exp)) # This code is contributed by Nikhil Kumar Singh(nickzuck_007) |
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C#
// C# proram to evaluate value of a postfix expression using System; using System.Collections; namespace GFG { class Geek { //Main() method static void Main() { Geek e = new Geek(); e.v = ("231*+9-"); e.expression(); Console.WriteLine("postfix evaluation: " + e.answer); Console.Read(); } public string v; //'v' is variable to store the string value public string answer; Stack i = new Stack(); //'Stack()' is inbuilt function for namespace 'System.Collections' public void expression() //evaluation method { int a, b, ans; for (int j = 0; j < v.Length; j++) //'v.Length' means length of the string { String c = v.Substring(j, 1); if (c.Equals("*")) { String sa = (String)i.Pop(); String sb = (String)i.Pop(); a = Convert.ToInt32(sb); b = Convert.ToInt32(sa); ans = a * b; i.Push(ans.ToString()); } else if (c.Equals("/")) { String sa = (String)i.Pop(); String sb = (String)i.Pop(); a = Convert.ToInt32(sb); b = Convert.ToInt32(sa); ans = a / b; i.Push(ans.ToString()); } else if (c.Equals("+")) { String sa = (String)i.Pop(); String sb = (String)i.Pop(); a = Convert.ToInt32(sb); b = Convert.ToInt32(sa); ans = a + b; i.Push(ans.ToString()); } else if (c.Equals("-")) { String sa = (String)i.Pop(); String sb = (String)i.Pop(); a = Convert.ToInt32(sb); b = Convert.ToInt32(sa); ans = a - b; i.Push(ans.ToString()); } else { i.Push(v.Substring(j, 1)); } } answer = (String)i.Pop(); } } } |
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Output:
postfix evaluation: -4
Time complexity of evaluation algorithm is O(n) where n is number of characters in input expression.
There are following limitations of above implementation.
1) It supports only 4 binary operators ‘+’, ‘*’, ‘-‘ and ‘/’. It can be extended for more operators by adding more switch cases.
2) The allowed operands are only single digit operands. The program can be extended for multiple digits by adding a separator like space between all elements (operators and operands) of given expression.
Below given is the extended program which allows operands having multiple digits.
C++
// CPP program to evaluate value of a postfix // expression having multiple digit operands #include <bits/stdc++.h> using namespace std; // Stack type class Stack { public: int top; unsigned capacity; int* array; }; // Stack Operations Stack* createStack( unsigned capacity ) { Stack* stack = new Stack(); if (!stack) return NULL; stack->top = -1; stack->capacity = capacity; stack->array = new int[(stack->capacity * sizeof(int))]; if (!stack->array) return NULL; return stack; } int isEmpty(Stack* stack) { return stack->top == -1 ; } int peek(Stack* stack) { return stack->array[stack->top]; } int pop(Stack* stack) { if (!isEmpty(stack)) return stack->array[stack->top--] ; return '$'; } void push(Stack* stack,int op) { stack->array[++stack->top] = op; } // The main function that returns value // of a given postfix expression int evaluatePostfix(char* exp) { // Create a stack of capacity equal to expression size Stack* stack = createStack(strlen(exp)); int i; // See if stack was created successfully if (!stack) return -1; // Scan all characters one by one for (i = 0; exp[i]; ++i) { //if the character is blank space then continue if(exp[i] == ' ')continue; // If the scanned character is an // operand (number here),extract the full number // Push it to the stack. else if (isdigit(exp[i])) { int num=0; //extract full number while(isdigit(exp[i])) { num = num * 10 + (int)(exp[i] - '0'); i++; } i--; //push the element in the stack push(stack,num); } // If the scanned character is an operator, pop two // elements from stack apply the operator else { int val1 = pop(stack); int val2 = pop(stack); switch (exp[i]) { case '+': push(stack, val2 + val1); break; case '-': push(stack, val2 - val1); break; case '*': push(stack, val2 * val1); break; case '/': push(stack, val2/val1); break; } } } return pop(stack); } // Driver code int main() { char exp[] = "100 200 + 2 / 5 * 7 +"; cout << evaluatePostfix(exp); return 0; } // This code is contributed by rathbhupendra |
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C
// C program to evaluate value of a postfix // expression having multiple digit operands #include <stdio.h> #include <string.h> #include <ctype.h> #include <stdlib.h> // Stack type struct Stack { int top; unsigned capacity; int* array; }; // Stack Operations struct Stack* createStack( unsigned capacity ) { struct Stack* stack = (struct Stack*) malloc(sizeof(struct Stack)); if (!stack) return NULL; stack->top = -1; stack->capacity = capacity; stack->array = (int*) malloc(stack->capacity * sizeof(int)); if (!stack->array) return NULL; return stack; } int isEmpty(struct Stack* stack) { return stack->top == -1 ; } int peek(struct Stack* stack) { return stack->array[stack->top]; } int pop(struct Stack* stack) { if (!isEmpty(stack)) return stack->array[stack->top--] ; return '$'; } void push(struct Stack* stack,int op) { stack->array[++stack->top] = op; } // The main function that returns value // of a given postfix expression int evaluatePostfix(char* exp) { // Create a stack of capacity equal to expression size struct Stack* stack = createStack(strlen(exp)); int i; // See if stack was created successfully if (!stack) return -1; // Scan all characters one by one for (i = 0; exp[i]; ++i) { //if the character is blank space then continue if(exp[i]==' ')continue; // If the scanned character is an // operand (number here),extract the full number // Push it to the stack. else if (isdigit(exp[i])) { int num=0; //extract full number while(isdigit(exp[i])) { num=num*10 + (int)(exp[i]-'0'); i++; } i--; //push the element in the stack push(stack,num); } // If the scanned character is an operator, pop two // elements from stack apply the operator else { int val1 = pop(stack); int val2 = pop(stack); switch (exp[i]) { case '+': push(stack, val2 + val1); break; case '-': push(stack, val2 - val1); break; case '*': push(stack, val2 * val1); break; case '/': push(stack, val2/val1); break; } } } return pop(stack); } // Driver program to test above functions int main() { char exp[] = "100 200 + 2 / 5 * 7 +"; printf ("%d", evaluatePostfix(exp)); return 0; } // This code is contributed by Arnab Kundu |
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Java
// Java proram to evaluate value of a postfix // expression having multiple digit operands import java.util.Stack; class Test1 { // Method to evaluate value of a postfix expression static int evaluatePostfix(String exp) { //create a stack Stack<Integer> stack = new Stack<>(); // Scan all characters one by one for(int i = 0; i < exp.length(); i++) { char c = exp.charAt(i); if(c == ' ') continue; // If the scanned character is an operand // (number here),extract the number // Push it to the stack. else if(Character.isDigit(c)) { int n = 0; //extract the characters and store it in num while(Character.isDigit(c)) { n = n*10 + (int)(c-'0'); i++; c = exp.charAt(i); } i--; //push the number in stack stack.push(n); } // If the scanned character is an operator, pop two // elements from stack apply the operator else { int val1 = stack.pop(); int val2 = stack.pop(); switch(c) { case '+': stack.push(val2+val1); break; case '-': stack.push(val2- val1); break; case '/': stack.push(val2/val1); break; case '*': stack.push(val2*val1); break; } } } return stack.pop(); } // Driver program to test above functions public static void main(String[] args) { String exp = "100 200 + 2 / 5 * 7 +"; System.out.println(evaluatePostfix(exp)); } } // This code is contributed by Arnab Kundu |
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C#
// C# proram to evaluate value of a postfix // expression having multiple digit operands using System; using System.Collections.Generic; class GFG { // Method to evaluate value of // a postfix expression public static int evaluatePostfix(string exp) { // create a stack Stack<int> stack = new Stack<int>(); // Scan all characters one by one for (int i = 0; i < exp.Length; i++) { char c = exp[i]; if (c == ' ') { continue; } // If the scanned character is an // operand (number here),extract // the number. Push it to the stack. else if (char.IsDigit(c)) { int n = 0; // extract the characters and // store it in num while (char.IsDigit(c)) { n = n * 10 + (int)(c - '0'); i++; c = exp[i]; } i--; // push the number in stack stack.Push(n); } // If the scanned character is // an operator, pop two elements // from stack apply the operator else { int val1 = stack.Pop(); int val2 = stack.Pop(); switch (c) { case '+': stack.Push(val2 + val1); break; case '-': stack.Push(val2 - val1); break; case '/': stack.Push(val2 / val1); break; case '*': stack.Push(val2 * val1); break; } } } return stack.Pop(); } // Driver Code public static void Main(string[] args) { string exp = "100 200 + 2 / 5 * 7 +"; Console.WriteLine(evaluatePostfix(exp)); } } // This code is contributed by Shrikant13 |
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Python
# Python program to evaluate value of a postfix # expression with integers containing multiple digits class evalpostfix: def __init__(self): self.stack =[] self.top =-1 def pop(self): if self.top ==-1: return else: self.top-= 1 return self.stack.pop() def push(self, i): self.top+= 1 self.stack.append(i) def centralfunc(self, ab): for i in ab: # if the component of the list is an integer try: self.push(int(i)) # if the component of the list is not an integer, # it must be an operator. Using ValueError, we can # evaluate components of the list other than type int except ValueError: val1 = self.pop() val2 = self.pop() # switch statement to perform operation switcher ={'+':val2 + val1, '-':val2-val1, '*':val2 * val1, '/':val2 / val1, '^':val2**val1} self.push(switcher.get(i)) return int(self.pop()) str ='100 200 + 2 / 5 * 7 +' # splitting the given string to obtain # integers and operators into a list strconv = str.split(' ') obj = evalpostfix() print(obj.centralfunc(strconv)) # This code is contributed by Amarnath Reddy |
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Output :
757
References:
http://www.cs.nthu.edu.tw/~wkhon/ds/ds10/tutorial/tutorial2.pdf
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