Check Balanced Parenthesis in an Expression.

Given an expression containing various types of parentheses ((), {}, []), you need to determine if the parentheses are balanced. An expression is considered balanced if every opening parenthesis has a corresponding closing parenthesis and they occur in the correct order.

Example:

Input: ({[]})

Output: true

Explanation: All pairs of parenthesis are balanced.

Input: ())(

Output: false

Explanation: All pairs of parenthesis are not balanced.

Input: [(){}]

Output: true

There are different ways to solve this problem and here we are going to discuss two of them:

Check Valid Balanced Parenthesis Using Stack.

In this approach, we use a stack data structure to solve this problem of checking balance parenthesis. It is because by nature parenthesis must occur in pairs and in the correct order and the stack LIFO property is best to handle such patterns.

Algorithm Steps to Validate Parenthesis:

Step 1: Initialize an empty stack to hold the opening parenthesis.

Step 2: Iterate through each character of the expression:

If the character is an opening parenthesis ('(', '{', '['), push it onto the stack.
If the character is a closing parenthesis (')', '}', ']') then check if the stack is empty then return false (unbalanced) else pop the top element and check if it matches with the closing parenthesis.
If the closing parenthesis does not match with the top element of the stack then return false.

Step 3: After iteration, check if the stack is empty (balanced) and return true, else return false (unbalanced).

Example Illustration.

Below is the code implementation of the above approach:

C++ Java Python C#

// C++ code implementation to check balanced parenthesis
#include<iostream>
#include<stack>
using namespace std;

//function to check balance parenthesis
bool validParenthesis(string str){
    stack<char> st;

    for(int i = 0; i < str.size(); i++){
        //opening parenthesis, push into the stack
        if(str[i] == '{' || str[i] == '[' || str[i] == '(') {
            st.push(str[i]);    
        }else if(str[i] == '}' || str[i] == ']' || str[i] == ')') {
            
            //empty stack
            if(st.empty())
               return false;
            
            //check if stack top contain a matching opening bracket
            //pop the top element if matching is found
            if((st.top() == '{' && str[i] == '}') 
            || (st.top() == '[' && str[i] == ']') 
            || (st.top() == '(' && str[i] == ')')) {
                st.pop();
            }
            else{
                return false;
            } 
        }
    }
    //stack is empty after complete iteration
    if(st.empty()) 
       return true;
    
    return false;   
}
int main() {
    string str = "[{(){()}}]";

    if(validParenthesis(str)){
        cout<<"Balance Parenthesis"<<endl;
    }else{
        cout<<"Unbalance Parenthesis"<<endl;
    }
    return 0;
}

// Java Code Implementation to check balanced parenthesis
import java.util.Stack;

public class ParenthesisChecker {
    public static boolean isValidParenthesis(String str) {
        Stack<Character> stack = new Stack<>();
        //push the char in stack if they are opening brackets
        for (char ch : str.toCharArray()) {
            if (ch == '{' || ch == '[' || ch == '(') {
                stack.push(ch);
            } else if (ch == '}' || ch == ']' || ch == ')') {
                if (stack.isEmpty()) return false;
                
             
              //pop the top element if matching bracket is found
                char top = stack.pop();
                if ((top == '{' && ch == '}') || (top == '[' && ch == ']') 
                || (top == '(' && ch == ')')) {
                    continue;
                } else {
                    return false; // Mismatched brackets
                }
            }
        }

        return stack.isEmpty();
    }

    public static void main(String[] args) {
        String str = "[{(){()}}]";

        if (isValidParenthesis(str)) {
            System.out.println("Balanced Parenthesis");
        } else {
            System.out.println("Unbalanced Parenthesis");
        }
    }
}

# Python code to check balanced parenthesis
def is_valid_parenthesis(s):
stack = []

for char in s:
    # checking for open brackets
    if char in '{[(':
        stack.append(char)
    # checking for closing brackets    
    elif char in '})]':
        if not stack:
            return False
        
        # pop the top char from stack if matching pair is found
        top = stack.pop()
        if (top == '{' and char == '}') or (top == '[' and char == ']') or (top == '(' and char == ')'):
            pass
        else:
            return False  # Mismatched brackets

return not stack


# Example usage
parenthesis_str = "[{(){()}}]"
if is_valid_parenthesis(parenthesis_str):
print("Balanced Parenthesis")
else:
print("Unbalanced Parenthesis")

// C# code to check balanced parenthesis
using System;
using System.Collections.Generic;

class ParenthesisChecker
{
    static bool IsValidParenthesis(string str)
    {
        Stack<char> stack = new Stack<char>();

        foreach (char ch in str)
        {   // push the char in stack if it is opening bracket
            if (ch == '{' || ch == '[' || ch == '(')
            {
                stack.Push(ch);
            }
            // pop the top char from stack if it is matching pair of closing bracket 
            else if (ch == '}' || ch == ']' || ch == ')')
            {
                if (stack.Count == 0) return false;

                char top = stack.Pop();
                if ((top == '{' && ch == '}') || (top == '[' && ch == ']') 
                  || (top == '(' && ch == ')'))
                {
                    continue;// Matching brackets, continue
                }
                else
                {
                    return false; // Mismatched brackets
                }
            }
        }

        return stack.Count == 0;
    }

    static void Main()
    {
        string str = "[{(){()}}]";

        if (IsValidParenthesis(str))
        {
            Console.WriteLine("Balanced Parenthesis");
        }
        else
        {
            Console.WriteLine("Unbalanced Parenthesis");
        }
    }
}

Output:

Balanced Parenthesis

Time Complexity: The algorithm iterates through each character in the expression once, resulting in a time complexity of O(n), where n is the length of the expression.
Space Complexity: The space complexity is O(n), where n is the length of the expression. This is due to the stack storing opening parentheses, and in the worst case, the stack may contain all opening parentheses before encountering the corresponding closing ones.

Check Balanced Parenthesis Without Using Stack.

While the stack is a convenient data structure for checking balanced parentheses, it's possible to achieve the same goal without using a stack.

Algorithm Steps:

Step 1: Initialize an integer variable i to -1. This variable will be used to track the top of the stack.

Step 2: Iterate through the expression:

If ch is an opening parenthesis ('(', '{', '[') then increase the value of i by 1 and replace the character at index i in the expression with the opening bracket.
If ch is a closing parenthesis (')', '}', ']') check if i is greater than or equal to 0. Check if the current closing bracket matches the corresponding opening bracket at index i: If yes, decrement i by 1 else returns false.

Step 3: After completing the iteration check if i is equal to -1 return true else return false.