Check for balanced parentheses in an expression | O(1) space

Given a string of length n having parentheses in it, your task is to find whether given string has balanced parentheses or not. Please note there is constraint on space i.e. we are allowed to use only O(1) extra space.

Also See : Check for balanced parentheses

Examples:



Input : (())[]
Output : Yes

Input : ))(({}{
Output : No

If k = 1, then we will simply keep a count variable c = 0, whenever we encounter an opening parentheses we will increment c and whenever we encounter a closing parentheses we will reduce the count of c, At any stage we shouldn’t have c < 0 and at the end we must have c = 0 for string to be balanced.
Following is the idea of our algorithm for this problem. For any opening bracket say ‘[‘ we find its matching closing bracket ‘]’. Let’s say index of ‘[‘ was i and index of ‘]’ was j then following conditions must be true:

  1. i < j
  2. for all k such that i < k < j, for all the opening parentheses(index-k) it's matching closing parentheses x must satisfy k < x < j and for all the closing parentheses(index-k) it's matching opening parentheses x must satisfy i < x < k

C++

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// C++ code to check balanced parentheses with
// O(1) space. 
#include <stdio.h>
#include <stdlib.h>
  
// Function1 to match closing bracket
int matchClosing(char X[], int start,
                int end, char open, char close)
{
    int c = 1;
    int i = start + 1;
    while (i <= end) {
        if (X[i] == open)
            c++;
        else if (X[i] == close)
            c--;
        if (c == 0)
            return i;
        i++;
    }
    return i;
}
  
// Function1 to match opening bracket
int matchingOpening(char X[], int start,
                    int end, char open, char close)
{
    int c = -1;
    int i = end - 1;
  
    while (i >= start) {
        if (X[i] == open)
            c++;
        else if (X[i] == close)
            c--;
        if (c == 0)
            return i;
        i--;
    }
    return -1;
}
  
// Function to check balanced parentheses
bool isBalanced(char X[], int n)
{
    // helper variables
    int i, j, k, x, start, end;
  
    for (i = 0; i < n; i++) {
        // Handling case of opening parentheses
        if (X[i] == '(')
            j = matchClosing(X, i, n - 1, '(', ')');
        else if (X[i] == '{')
            j = matchClosing(X, i, n - 1, '{', '}');
        else if (X[i] == '[')
            j = matchClosing(X, i, n - 1, '[', ']');
  
        // Handling case of closing parentheses
        else {
            if (X[i] == ')')
                j = matchingOpening(X, 0, i, '(', ')');
            else if (X[i] == '}')
                j = matchingOpening(X, 0, i, '{', '}');
            else if (X[i] == ']')
                j = matchingOpening(X, 0, i, '[', ']');
  
            // If corresponsing matching
            // opening parentheses doesn't
            // lie in given interval return 0
            if (j < 0 || j >= i)
                return false;
  
            // else continue
            continue;
        }
  
        // If corresponding closing parentheses
        // doesn't lie in given interval
        // return 0
        if (j >= n || j < 0)
            return false;
  
        // if found, now check for each
        // opening and closing parentheses
        // in this interval
        start = i;
        end = j;
  
        for (k = start + 1; k < end; k++) {
            if (X[k] == '(') {
                x = matchClosing(X, k, end, '(', ')');
                if (!(k < x && x < end)) {
                    return false;
                }
            }
            else if (X[k] == ')') {
                x = matchingOpening(X, start, k, '(', ')');
                if (!(start < x && x < k)) {
                    return false;
                }
            }
  
            if (X[k] == '{') {
                x = matchClosing(X, k, end, '{', '}');
                if (!(k < x && x < end)) {
                    return false;
                }
            }
  
            else if (X[k] == '}') {
                x = matchingOpening(X, start, k, '{', '}');
                if (!(start < x && x < k)) {
                    return false;
                }
            }
            if (X[k] == '[') {
                x = matchClosing(X, k, end, '[', ']');
                if (!(k < x && x < end)) {
                    return false;
                }
            }
            else if (X[k] == ']') {
                x = matchingOpening(X, start, k, '[', ']');
                if (!(start < x && x < k)) {
                    return false;
                }
            }
        }
    }
  
    return true;
}
  
// Driver Code
int main()
{
    char X[] = "[()]()";
    int n = 6;
    if (isBalanced(X, n))
        printf("Yes\n");
    else
        printf("No\n");
  
    char Y[] = "[[()]])";
    n = 7;
    if (isBalanced(Y, n))
        printf("Yes\n");
    else
        printf("No\n");
  
    return 0;
}

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Java

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// Java code to check balanced parentheses with
// O(1) space.
  
class GFG {
  
// Function1 to match closing bracket
    static int matchClosing(char X[], int start,
            int end, char open, char close) {
        int c = 1;
        int i = start + 1;
        while (i <= end) {
            if (X[i] == open) {
                c++;
            } else if (X[i] == close) {
                c--;
            }
            if (c == 0) {
                return i;
            }
            i++;
        }
        return i;
    }
  
// Function1 to match opening bracket
    static int matchingOpening(char X[], int start,
            int end, char open, char close) {
        int c = -1;
        int i = end - 1;
  
        while (i >= start) {
            if (X[i] == open) {
                c++;
            } else if (X[i] == close) {
                c--;
            }
            if (c == 0) {
                return i;
            }
            i--;
        }
        return -1;
    }
  
// Function to check balanced parentheses
    static boolean isBalanced(char X[], int n) {
        // helper variables
        int i, j = 0, k, x, start, end;
  
        for (i = 0; i < n; i++) {
            // Handling case of opening parentheses
            if (X[i] == '(') {
                j = matchClosing(X, i, n - 1, '(', ')');
            } else if (X[i] == '{') {
                j = matchClosing(X, i, n - 1, '{', '}');
            } else if (X[i] == '[') {
                j = matchClosing(X, i, n - 1, '[', ']');
            } // Handling case of closing parentheses
            else {
                if (X[i] == ')') {
                    j = matchingOpening(X, 0, i, '(', ')');
                } else if (X[i] == '}') {
                    j = matchingOpening(X, 0, i, '{', '}');
                } else if (X[i] == ']') {
                    j = matchingOpening(X, 0, i, '[', ']');
                }
  
                // If corresponsing matching
                // opening parentheses doesn't
                // lie in given interval return 0
                if (j < 0 || j >= i) {
                    return false;
                }
  
                // else continue
                continue;
            }
  
            // If corresponding closing parentheses
            // doesn't lie in given interval
            // return 0
            if (j >= n || j < 0) {
                return false;
            }
  
            // if found, now check for each
            // opening and closing parentheses
            // in this interval
            start = i;
            end = j;
  
            for (k = start + 1; k < end; k++) {
                if (X[k] == '(') {
                    x = matchClosing(X, k, end, '(', ')');
                    if (!(k < x && x < end)) {
                        return false;
                    }
                } else if (X[k] == ')') {
                    x = matchingOpening(X, start, k, '(', ')');
                    if (!(start < x && x < k)) {
                        return false;
                    }
                }
  
                if (X[k] == '{') {
                    x = matchClosing(X, k, end, '{', '}');
                    if (!(k < x && x < end)) {
                        return false;
                    }
                } else if (X[k] == '}') {
                    x = matchingOpening(X, start, k, '{', '}');
                    if (!(start < x && x < k)) {
                        return false;
                    }
                }
                if (X[k] == '[') {
                    x = matchClosing(X, k, end, '[', ']');
                    if (!(k < x && x < end)) {
                        return false;
                    }
                } else if (X[k] == ']') {
                    x = matchingOpening(X, start, k, '[', ']');
                    if (!(start < x && x < k)) {
                        return false;
                    }
                }
            }
        }
  
        return true;
    }
  
// Driver Code
    public static void main(String[] args) {
          
    char X[] = "[()]()".toCharArray();
    int n = 6;
    if (isBalanced(X, n))
        System.out.printf("Yes\n");
    else
        System.out.printf("No\n");
   
    char Y[] = "[[()]])".toCharArray();
    n = 7;
    if (isBalanced(Y, n))
        System.out.printf("Yes\n");
    else
        System.out.printf("No\n");
    }
}
//this code contributed by Rajput-Ji

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Python 3

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# Python 3 code to check balanced 
# parentheses with O(1) space. 
  
# Function1 to match closing bracket
def matchClosing(X, start, end, 
                   open, close):
  
    c = 1
    i = start + 1
    while (i <= end):
        if (X[i] == open):
            c += 1
        elif (X[i] == close):
            c -= 1
        if (c == 0):
            return i
        i += 1
    return i
  
# Function1 to match opening bracket
def matchingOpening(X, start, end, 
                      open, close):
  
    c = -1
    i = end - 1
  
    while (i >= start):
        if (X[i] == open):
            c += 1
        elif (X[i] == close):
            c -= 1
        if (c == 0):
            return i
        i -= 1
  
    return -1
  
# Function to check balanced 
# parentheses
def isBalanced(X, n):
  
    for i in range(n):
          
        # Handling case of opening 
        # parentheses
        if (X[i] == '('):
            j = matchClosing(X, i, n - 1, '(', ')')
        elif (X[i] == '{'):
            j = matchClosing(X, i, n - 1, '{', '}')
        elif (X[i] == '['):
            j = matchClosing(X, i, n - 1, '[', ']')
  
        # Handling case of closing
        # parentheses
        else :
            if (X[i] == ')'):
                j = matchingOpening(X, 0, i, '(', ')')
            elif (X[i] == '}'):
                j = matchingOpening(X, 0, i, '{', '}')
            elif (X[i] == ']'):
                j = matchingOpening(X, 0, i, '[', ']')
  
            # If corresponsing matching opening 
            # parentheses doesn't lie in given 
            # interval return 0
            if (j < 0 or j >= i):
                return False
  
            # else continue
            continue
  
        # If corresponding closing parentheses
        # doesn't lie in given interval, return 0
        if (j >= n or j < 0):
            return False
  
        # if found, now check for each opening and 
        # closing parentheses in this interval
        start = i
        end = j
  
        for k in range(start + 1, end) :
            if (X[k] == '(') :
                x = matchClosing(X, k, end, '(', ')')
                if (not(k < x and x < end)):
                    return False
              
            elif (X[k] == ')'):
                x = matchingOpening(X, start, k, '(', ')')
                if (not(start < x and x < k)):
                    return False
  
            if (X[k] == '{'):
                x = matchClosing(X, k, end, '{', '}')
                if (not(k < x and x < end)):
                    return False
  
            elif (X[k] == '}'):
                x = matchingOpening(X, start, k, '{', '}')
                if (not(start < x and x < k)):
                    return False
                  
            if (X[k] == '['):
                x = matchClosing(X, k, end, '[', ']')
                if (not(k < x and x < end)):
                    return False
                  
            elif (X[k] == ']'):
                x = matchingOpening(X, start, k, '[', ']')
                if (not(start < x and x < k)):
                    return False
  
    return True
  
# Driver Code
if __name__ == "__main__":
      
    X = "[()]()"
    n = 6
    if (isBalanced(X, n)):
        print("Yes")
    else:
        print("No")
  
    Y = "[[()]])"
    n = 7
    if (isBalanced(Y, n)):
        print("Yes")
    else:
        print("No")
  
# This code is contributed by ita_c

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C#

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// C# code to check balanced parentheses with
// O(1) space.
using System;
public class GFG {
   
// Function1 to match closing bracket
    static int matchClosing(char []X, int start,
            int end, char open, char close) {
        int c = 1;
        int i = start + 1;
        while (i <= end) {
            if (X[i] == open) {
                c++;
            } else if (X[i] == close) {
                c--;
            }
            if (c == 0) {
                return i;
            }
            i++;
        }
        return i;
    }
   
// Function1 to match opening bracket
    static int matchingOpening(char []X, int start,
            int end, char open, char close) {
        int c = -1;
        int i = end - 1;
   
        while (i >= start) {
            if (X[i] == open) {
                c++;
            } else if (X[i] == close) {
                c--;
            }
            if (c == 0) {
                return i;
            }
            i--;
        }
        return -1;
    }
   
// Function to check balanced parentheses
    static bool isBalanced(char []X, int n) {
        // helper variables
        int i, j = 0, k, x, start, end;
   
        for (i = 0; i < n; i++) {
            // Handling case of opening parentheses
            if (X[i] == '(') {
                j = matchClosing(X, i, n - 1, '(', ')');
            } else if (X[i] == '{') {
                j = matchClosing(X, i, n - 1, '{', '}');
            } else if (X[i] == '[') {
                j = matchClosing(X, i, n - 1, '[', ']');
            } // Handling case of closing parentheses
            else {
                if (X[i] == ')') {
                    j = matchingOpening(X, 0, i, '(', ')');
                } else if (X[i] == '}') {
                    j = matchingOpening(X, 0, i, '{', '}');
                } else if (X[i] == ']') {
                    j = matchingOpening(X, 0, i, '[', ']');
                }
   
                // If corresponsing matching
                // opening parentheses doesn't
                // lie in given interval return 0
                if (j < 0 || j >= i) {
                    return false;
                }
   
                // else continue
                continue;
            }
   
            // If corresponding closing parentheses
            // doesn't lie in given interval
            // return 0
            if (j >= n || j < 0) {
                return false;
            }
   
            // if found, now check for each
            // opening and closing parentheses
            // in this interval
            start = i;
            end = j;
   
            for (k = start + 1; k < end; k++) {
                if (X[k] == '(') {
                    x = matchClosing(X, k, end, '(', ')');
                    if (!(k < x && x < end)) {
                        return false;
                    }
                } else if (X[k] == ')') {
                    x = matchingOpening(X, start, k, '(', ')');
                    if (!(start < x && x < k)) {
                        return false;
                    }
                }
   
                if (X[k] == '{') {
                    x = matchClosing(X, k, end, '{', '}');
                    if (!(k < x && x < end)) {
                        return false;
                    }
                } else if (X[k] == '}') {
                    x = matchingOpening(X, start, k, '{', '}');
                    if (!(start < x && x < k)) {
                        return false;
                    }
                }
                if (X[k] == '[') {
                    x = matchClosing(X, k, end, '[', ']');
                    if (!(k < x && x < end)) {
                        return false;
                    }
                } else if (X[k] == ']') {
                    x = matchingOpening(X, start, k, '[', ']');
                    if (!(start < x && x < k)) {
                        return false;
                    }
                }
            }
        }
   
        return true;
    }
   
// Driver Code
    public static void Main() {
           
    char []X = "[()]()".ToCharArray();
    int n = 6;
    if (isBalanced(X, n))
        Console.Write("Yes\n");
    else
        Console.Write("No\n");
    
    char []Y = "[[()]])".ToCharArray();
    n = 7;
    if (isBalanced(Y, n))
        Console.Write("Yes\n");
    else
        Console.Write("No\n");
    }
}
// This code contributed by Rajput-Ji

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PHP

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<?php
// PHP code to check balanced parentheses 
// with O(1) space.
  
// Function1 to match closing bracket
function matchClosing($X, $start, $end
                          $open, $close)
{
    $c = 1;
    $i = $start + 1;
    while ($i <= $end
    {
        if ($X[$i] == $open
        {
            $c++;
        
        else if ($X[$i] == $close
        {
            $c--;
        }
        if ($c == 0) 
        {
            return $i;
        }
        $i++;
    }
    return $i;
}
  
// Function1 to match opening bracket
function matchingOpening($X, $start, $end
                             $open, $close
{
    $c = -1;
    $i = $end - 1;
  
    while ($i >= $start
    {
        if ($X[$i] == $open)
        {
            $c++;
        
        else if ($X[$i] == $close
        {
            $c--;
        }
        if ($c == 0)
        {
            return $i;
        }
        $i--;
    }
    return -1;
}
  
// Function to check balanced parentheses
function isBalanced($X, $n
{
    // helper variables
    $i; $j = 0; $k; $x; $start; $end;
  
    for ($i = 0; $i < $n; $i++) 
    {
        // Handling case of opening parentheses
        if ($X[$i] == '(')
        {
            $j = matchClosing($X, $i, $n - 1, '(', ')');
        
        else if ($X[$i] == '{'
        {
            $j = matchClosing($X, $i, $n - 1, '{', '}');
        
        else if ($X[$i] == '['
        {
            $j = matchClosing($X, $i, $n - 1, '[', ']');
        }
          
        // Handling case of closing parentheses
        else 
        {
            if ($X[$i] == ')')
            {
                $j = matchingOpening($X, 0, $i, '(', ')');
            
            else if ($X[$i] == '}'
            {
                $j = matchingOpening($X, 0, $i, '{', '}');
            
            else if ($X[$i] == ']')
            {
                $j = matchingOpening($X, 0, $i, '[', ']');
            }
  
            // If corresponsing matching opening parentheses 
            // doesn't lie in given interval return 0
            if ($j < 0 || $j >= $i
            {
                return false;
            }
  
            // else continue
            continue;
        }
  
        // If corresponding closing parentheses
        // doesn't lie in given interval
        // return 0
        if ($j >= $n || $j < 0) 
        {
            return false;
        }
  
        // if found, now check for each opening 
        // and closing parentheses in this interval
        $start = $i;
        $end = $j;
  
        for ($k = $start + 1; $k < $end; $k++)
        {
            if ($X[$k] == '('
            {
                $x = matchClosing($X, $k, $end, '(', ')');
                if (!($k < $x && $x < $end)) 
                {
                    return false;
                }
            
            else if ($X[$k] == ')')
            {
                $x = matchingOpening($X, $start, $k, '(', ')');
                if (!($start < $x && $x < $k)) 
                {
                    return false;
                }
            }
  
            if ($X[$k] == '{')
            {
                $x = matchClosing($X, $k, $end, '{', '}');
                if (!($k < $x && $x < $end))
                {
                    return false;
                }
            
            else if ($X[$k] == '}')
            {
                $x = matchingOpening($X, $start, $k, '{', '}');
                if (!($start < $x && $x < $k))
                {
                    return false;
                }
            }
            if ($X[$k] == '['
            {
                $x = matchClosing($X, $k, $end, '[', ']');
                if (!($k < $x && $x < $end))
                {
                    return false;
                }
            
            else if ($X[$k] == ']')
            {
                $x = matchingOpening($X, $start, $k, '[', ']');
                if (!($start < $x && $x < $k))
                {
                    return false;
                }
            }
        }
    }
  
    return true;
}
  
// Driver Code
$X = str_split("[()]()");
$n = 6;
if (isBalanced($X, $n))
    echo("Yes\n");
else
    echo("No\n");
  
$Y = str_split("[[()]])");
$n = 7;
if (isBalanced($Y, $n))
    echo("Yes\n");
else
    echo("No\n");
  
// This code contributed by Mukul Singh
?>

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Output:

Yes
No

Time Complexity: O(n3)

Auxiliary Space: O(1)



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