Modify a numeric string to a balanced parentheses by replacements
Last Updated :
08 Sep, 2021
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Given a numeric string S made up of characters '1', '2' and '3' only, the task is to replace characters with either an open bracket ( '(' ) or a closed bracket ( ')' ) such that the newly formed string becomes a balanced bracket sequence.
Note: All occurrences of a character must be replaced by the same parentheses.
Examples:
Input: S = "1123"
Output: Yes, (())
Explanation: Replacing occurrences of character '1' with '(', '2' with ')' and '3' with ')'. Therefore, the obtained bracket sequence is “(())”, which is balanced.Input: S = "1121"
Output: No
Approach: The given problem can be solved based on the following observations:
- For a balanced bracket sequence, it is necessary for the first and last characters to be open and closed brackets respectively. Therefore, the first and the last characters should be different.
- If the first and the last characters of a string are the same, then it is impossible to obtain a balanced bracket sequence.
- If the first and last characters of a string are different, then they are replaced by open and closed brackets respectively. The third character is replaced either by open or closed brackets.
- Check for both ways of replacements one by one for the remaining third character.
- If both replacements of the third remaining character can't make a balanced bracket sequence, then it is impossible to make a balanced bracket sequence.
Follow the steps below to solve the given problem:
- Check if the first and last characters of the string S are equal or not. If found to be true, then print "No" and return.
- Initialize two variables, say cntforOpen and cntforClose, to store the count of open and closed brackets.
- Iterate over the characters of the string and perform the following operations:
- If the current character is the same as the first character of the string, increment cntforOpen.
- If the current character is the same as the last character of the string, decrement cntforOpen.
- For the remaining third character, increment cntforOpen, i.e. replacing that character with '('.
- If at any instant, cntforOpen is found to be negative, then a balanced bracket sequence cannot be obtained.
- Similarly, check using cntforClose variable, i.e. replacing the third character with ')'.
- If none of the above two methods generates a balanced bracket sequence, then print "No". Otherwise, print "Yes".
Below is the implementation of the above approach:
// C++ program for the above approach
#include <iostream>
using namespace std;
// Function to check if the given
// string can be converted to a
// balanced bracket sequence or not
void balBracketSequence(string str)
{
int n = str.size();
// Check if the first and
// last characters are equal
if (str[0]
== str[n - 1])
{
cout << "No" << endl;
}
else {
// Initialize two variables to store
// the count of open and closed brackets
int cntForOpen = 0, cntForClose = 0;
int check = 1;
for (int i = 0; i < n; i++) {
// If the current character is
// same as the first character
if (str[i] == str[0])
cntForOpen++;
// If the current character is
// same as the last character
else if (str[i] == str[n - 1])
cntForOpen--;
else
cntForOpen++;
// If count of open brackets
// becomes less than 0
if (cntForOpen < 0) {
check = 0;
break;
}
}
if (check && cntForOpen == 0) {
cout << "Yes, ";
// Print the new string
for (int i = 0; i < n; i++) {
if (str[i] == str[n - 1])
cout << ')';
else
cout << '(';
}
return;
}
else {
for (int i = 0; i < n; i++) {
// If the current character is
// same as the first character
if (str[i] == str[0])
cntForClose++;
else
cntForClose--;
// If bracket sequence
// is not balanced
if (cntForClose
< 0) {
check = 0;
break;
}
}
// Check for unbalanced
// bracket sequence
if (check
&& cntForClose
== 0) {
cout << "Yes, ";
// Print the sequence
for (int i = 0; i < n;
i++) {
if (str[i] == str[0])
cout << '(';
else
cout << ')';
}
return;
}
}
cout << "No";
}
}
// Driver Code
int main()
{
// Given Input
string str = "123122";
// Function Call
balBracketSequence(str);
return 0;
}
// Java program for the above approach
import java.util.*;
class GFG{
// Function to check if the given
// string can be converted to a
// balanced bracket sequence or not
static void balBracketSequence(String str)
{
int n = str.length();
// Check if the first and
// last characters are equal
if (str.charAt(0)
== str.charAt(n - 1))
{
System.out.println("No");
}
else {
// Initialize two variables to store
// the count of open and closed brackets
int cntForOpen = 0, cntForClose = 0;
int check = 1;
for (int i = 0; i < n; i++) {
// If the current character is
// same as the first character
if (str.charAt(i) == str.charAt(0))
cntForOpen++;
// If the current character is
// same as the last character
else if (str.charAt(i) == str.charAt(n - 1))
cntForOpen -= 1;
else
cntForOpen += 1;
// If count of open brackets
// becomes less than 0
if (cntForOpen < 0) {
check = 0;
break;
}
}
if (check != 0 && cntForOpen == 0) {
System.out.print("Yes, ");
// Print the new string
for (int i = 0; i < n; i++) {
if (str.charAt(i) == str.charAt(n - 1))
System.out.print(')');
else
System.out.print('(');
}
return;
}
else {
for (int i = 0; i < n; i++) {
// If the current character is
// same as the first character
if (str.charAt(i) == str.charAt(0))
cntForClose++;
else
cntForClose--;
// If bracket sequence
// is not balanced
if (cntForClose
< 0) {
check = 0;
break;
}
}
// Check for unbalanced
// bracket sequence
if (check != 0
&& cntForClose
== 0) {
System.out.print("Yes, ");
// Print the sequence
for (int i = 0; i < n;
i++) {
if (str.charAt(i) == str.charAt(0))
System.out.print('(');
else
System.out.print(')');
}
return;
}
}
System.out.print("No");
}
}
// Driver Code
public static void main(String args[])
{
// Given Input
String str = "123122";
// Function Call
balBracketSequence(str);
}
}
// This code is contributed by ipg2016107.
# Python program for the above approach;
# Function to check if the given
# string can be converted to a
# balanced bracket sequence or not
def balBracketSequence(str):
n = len(str)
# Check if the first and
# last characters are equal
if (str[0] == str[n - 1]):
print("No", end="")
else:
# Initialize two variables to store
# the count of open and closed brackets
cntForOpen = 0
cntForClose = 0
check = 1
for i in range(n):
# If the current character is
# same as the first character
if (str[i] == str[0]):
cntForOpen += 1
# If the current character is
# same as the last character
elif str[i] == str[n - 1] :
cntForOpen -= 1
else:
cntForOpen += 1
# If count of open brackets
# becomes less than 0
if (cntForOpen < 0):
check = 0
break
if (check and cntForOpen == 0):
print("Yes, ", end="")
# Print the new string
for i in range(n):
if (str[i] == str[n - 1]):
print(')', end="")
else:
print('(', end="")
return
else:
for i in range(n):
# If the current character is
# same as the first character
if (str[i] == str[0]):
cntForClose += 1
else:
cntForClose -= 1
# If bracket sequence
# is not balanced
if (cntForClose < 0):
check = 0
break
# Check for unbalanced
# bracket sequence
if (check and cntForClose == 0):
print("Yes, ", end="")
# Print the sequence
for i in range(n):
if (str[i] == str[0]):
print('(', end="")
else:
print(')', end="")
return
print("NO", end="")
# Driver Code
# Given Input
str = "123122"
# Function Call
balBracketSequence(str)
# This code is contributed by gfgking
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
// Function to check if the given
// string can be converted to a
// balanced bracket sequence or not
static void balBracketSequence(string str)
{
int n = str.Length;
// Check if the first and
// last characters are equal
if (str[0] == str[n - 1])
{
Console.Write("No");
}
else
{
// Initialize two variables to store
// the count of open and closed brackets
int cntForOpen = 0, cntForClose = 0;
int check = 1;
for(int i = 0; i < n; i++)
{
// If the current character is
// same as the first character
if (str[i] == str[0])
cntForOpen++;
// If the current character is
// same as the last character
else if (str[i] == str[n - 1])
cntForOpen--;
else
cntForOpen++;
// If count of open brackets
// becomes less than 0
if (cntForOpen < 0)
{
check = 0;
break;
}
}
if (check != 0 && cntForOpen == 0)
{
Console.Write("Yes, ");
// Print the new string
for(int i = 0; i < n; i++)
{
if (str[i] == str[n - 1])
Console.Write(')');
else
Console.Write('(');
}
return;
}
else
{
for(int i = 0; i < n; i++)
{
// If the current character is
// same as the first character
if (str[i] == str[0])
cntForClose++;
else
cntForClose--;
// If bracket sequence
// is not balanced
if (cntForClose < 0)
{
check = 0;
break;
}
}
// Check for unbalanced
// bracket sequence
if (check != 0 && cntForClose == 0)
{
Console.Write("Yes, ");
// Print the sequence
for(int i = 0; i < n; i++)
{
if (str[i] == str[0])
Console.Write('(');
else
Console.Write(')');
}
return;
}
}
Console.Write("No");
}
}
// Driver Code
public static void Main()
{
// Given Input
string str = "123122";
// Function Call
balBracketSequence(str);
}
}
// This code is contributed by sanjoy_62
<script>
// JavaScript program for the above approach;
// Function to check if the given
// string can be converted to a
// balanced bracket sequence or not
function balBracketSequence(str)
{
let n = str.length;
// Check if the first and
// last characters are equal
if (str[0]
== str[n - 1])
{
document.write( "No");
}
else {
// Initialize two variables to store
// the count of open and closed brackets
let cntForOpen = 0, cntForClose = 0;
let check = 1;
for (let i = 0; i < n; i++) {
// If the current character is
// same as the first character
if (str[i] == str[0])
cntForOpen++;
// If the current character is
// same as the last character
else if (str[i] == str[n - 1])
cntForOpen--;
else
cntForOpen++;
// If count of open brackets
// becomes less than 0
if (cntForOpen < 0) {
check = 0;
break;
}
}
if (check && cntForOpen == 0) {
document.write("Yes, ");
// Print the new string
for (let i = 0; i < n; i++) {
if (str[i] == str[n - 1])
document.write(')');
else
document.write('(');
}
return;
}
else {
for (let i = 0; i < n; i++) {
// If the current character is
// same as the first character
if (str[i] == str[0])
cntForClose++;
else
cntForClose--;
// If bracket sequence
// is not balanced
if (cntForClose
< 0) {
check = 0;
break;
}
}
// Check for unbalanced
// bracket sequence
if (check
&& cntForClose
== 0) {
document.write("Yes, ");
// Print the sequence
for (let i = 0; i < n;
i++) {
if (str[i] == str[0])
document.write('(');
else
document.write(')');
}
return;
}
}
document.write("NO") ;
}
}
// Driver Code
// Given Input
let str = "123122";
// Function Call
balBracketSequence(str);
// This code is contributed by Potta Lokesh
</script>
Output:
Yes, ()(())
Time Complexity: O(N)
Auxiliary Space: O(1)
