Remove brackets from an algebraic string containing + and - operators
Last Updated :
11 May, 2025
Given an algebraic expression as a string s containing operands (letters), + and - operators, and parentheses, simplify the expression by removing all parentheses and correctly applying the operators. Return the simplified expression without parentheses.
Examples:
Input:"(a - (b + c) + d)"
Output: "a- b - c + d"
Explanation: a - (b + c) + d simplifies to a - b - c + d
Input:"a - (b - c - (d + e )) - f"
Output: "a - b + c + d + e - f"
Explanation: c - (d + e), to get (c - d - e) The outer - flips the signs, resulting in a - b + c + d + e - f
The approach uses a stack to track the sign context while processing the expression. Initially, the stack is set to 1 (positive context). When encountering a - before a parenthesis, the sign inside the parentheses is toggled by pushing -1 onto the stack. For each operator (+ or -), the stack’s top determines if the operator should be flipped. When encountering operands, they are directly appended to the result. After processing the entire string, the simplified expression is returned without parentheses and with correct signs.
C++
#include <iostream>
#include <stack>
#include <string>
using namespace std;
string simplify(string s)
{
int len = s.length();
string res = "";
stack<int> st;
// Initially, we assume the sign is positive
st.push(1);
for (int i = 0; i < len; i++)
{
if (s[i] == '(')
{
// If the previous character is '-',
// we flip the sign inside parentheses
if (i > 0 && s[i - 1] == '-')
{
st.push(-st.top());
}
else
{
st.push(st.top());
}
}
else if (s[i] == ')')
{
// Pop when we encounter a
// closing parenthesis
st.pop();
}
else if (s[i] == '+')
{
// Add '+' or '-' based on the current sign
if (st.top() == 1)
res += '+';
else
res += '-';
}
else if (s[i] == '-')
{
// Add '+' or '-' based on the current sign
if (st.top() == 1)
res += '-';
else
res += '+';
}
else
{
// If it's an operand
// (variable), add it directly
res += s[i];
}
}
return res;
}
int main()
{
string s = "(a-(d-(b-c))+d)";
cout << simplify(s) << endl;
return 0;
}
import java.util.Stack;
public class GfG {
public static String simplify(String s) {
int len = s.length();
StringBuilder res = new StringBuilder();
Stack<Integer> st = new Stack<>();
// Initially, we assume the sign is positive
st.push(1);
for (int i = 0; i < len; i++) {
if (s.charAt(i) == '(') {
// If the previous character is '-', we
// flip the sign inside parentheses
if (i > 0 && s.charAt(i - 1) == '-') {
st.push(-st.peek());
} else {
st.push(st.peek());
}
} else if (s.charAt(i) == ')') {
// Pop when we encounter a closing parenthesis
st.pop();
} else if (s.charAt(i) == '+') {
// Add '+' or '-' based on the current sign
if (st.peek() == 1)
res.append('+');
else
res.append('-');
} else if (s.charAt(i) == '-') {
// Add '+' or '-' based on the current sign
if (st.peek() == 1)
res.append('-');
else
res.append('+');
} else {
// If it's an operand (variable), add it directly
res.append(s.charAt(i));
}
}
return res.toString();
}
public static void main(String[] args) {
String s = "(a-(d-(b-c))+d)";
System.out.println(simplify(s));
}
}
def simplify(s):
length = len(s)
res = ""
st = []
# Initially, we assume the sign is positive
st.append(1)
for i in range(length):
if s[i] == '(':
# If the previous character is '-',
# we flip the sign inside parentheses
if i > 0 and s[i - 1] == '-':
st.append(-st[-1])
else:
st.append(st[-1])
elif s[i] == ')':
# Pop when we encounter a closing parenthesis
st.pop()
elif s[i] == '+':
# Add '+' or '-' based on the current sign
if st[-1] == 1:
res += '+'
else:
res += '-'
elif s[i] == '-':
# Add '+' or '-' based on the current sign
if st[-1] == 1:
res += '-'
else:
res += '+'
else:
# If it's an operand (variable), add it directly
res += s[i]
return res
s = '(a-(d-(b-c))+d)'
print(simplify(s))
using System;
using System.Collections.Generic;
class GfG {
public static string Simplify(string s) {
int len = s.Length;
string res = "";
Stack<int> st = new Stack<int>();
// Initially, we assume the sign is positive
st.Push(1);
for (int i = 0; i < len; i++) {
if (s[i] == '(') {
// If the previous character is '-', we flip the sign inside parentheses
if (i > 0 && s[i - 1] == '-') {
st.Push(-st.Peek());
} else {
st.Push(st.Peek());
}
} else if (s[i] == ')') {
// Pop when we encounter a closing parenthesis
st.Pop();
} else if (s[i] == '+') {
// Add '+' or '-' based on the current sign
if (st.Peek() == 1)
res += '+';
else
res += '-';
} else if (s[i] == '-') {
// Add '+' or '-' based on the current sign
if (st.Peek() == 1)
res += '-';
else
res += '+';
} else {
// If it's an operand (variable), add it directly
res += s[i];
}
}
return res;
}
static void Main() {
string s = "(a-(d-(b-c))+d)";
Console.WriteLine(Simplify(s));
}
}
function simplify(s) {
let len = s.length;
let res = '';
let st = [];
// Initially, we assume the sign is positive
st.push(1);
for (let i = 0; i < len; i++) {
if (s[i] === '(') {
// If the previous character is '-', we flip the sign inside parentheses
if (i > 0 && s[i - 1] === '-') {
st.push(-st[st.length - 1]);
} else {
st.push(st[st.length - 1]);
}
} else if (s[i] === ')') {
// Pop when we encounter a closing parenthesis
st.pop();
} else if (s[i] === '+') {
// Add '+' or '-' based on the current sign
if (st[st.length - 1] === 1)
res += '+';
else
res += '-';
} else if (s[i] === '-') {
// Add '+' or '-' based on the current sign
if (st[st.length - 1] === 1)
res += '-';
else
res += '+';
} else {
// If it's an operand (variable), add it directly
res += s[i];
}
}
return res;
}
let s = '(a-(d-(b-c))+d)';
console.log(simplify(s));
Time Complexity: O(n), Where n is the length of the given string.
Auxiliary Space: O(n)
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