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# Solve the Linear Equation of Single Variable

• Difficulty Level : Hard
• Last Updated : 01 Aug, 2022

Given a linear equation, task is to find the value of variable used. The equation contains only ‘+’, ‘-‘ operation, the variable and its coefficient.

1. If there is no solution for the equation, return “No solution”.
2. If there are infinite solutions for the equation, return “Infinite solutions”.
3. If there is exactly one solution for the equation, ensure that the value of x is an integer.

Examples :

```Input : "x + 5 - 3 + x = 6 + x - 2"
Output : "x = 2"

Input : "x = x"
Output : "Infinite solutions"

Input: "2x = x"
Output: "x = 0"

Input: "x = x + 2"
Output: "No solution"```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach : The idea is to use two pointers to update two parameters: the coefficient of variable used and the total sum. On the left and right side of ‘=’, use opposite signs for each numbers which is taken care of by a sign variable, which will flip once ‘=’ is seen. Now, in case of a unique solution, the ratio of the effective total and coefficient gives the required result. In case of infinite solutions, both the effective total and coefficient turns out to be zero e.g. x + 1 = x + 1. In case of no solution, the coefficient of x turns out to be zero, but the effective total is non-zero.

## C++

 `// CPP program to solve the given equation``#include ``using` `namespace` `std;` `// Function to solve the given equation``string solveEquation(string equation)``{``    ``int` `n = equation.size(), sign = 1, coeff = 0;``    ``int` `total = 0, i = 0;` `    ``// Traverse the equation``    ``for` `(``int` `j = 0; j < n; j++) {``        ``if` `(equation[j] == ``'+'` `|| equation[j] == ``'-'``) {``            ``if` `(j > i)``                ``total += sign * stoi(equation.substr(i, j - i));``            ``i = j;``        ``}` `        ``// For cases such as: x, -x, +x``        ``else` `if` `(equation[j] == ``'x'``) {``            ``if` `((i == j) || equation[j - 1] == ``'+'``)``                ``coeff += sign;``            ``else` `if` `(equation[j - 1] == ``'-'``)``                ``coeff -= sign;``            ``else``                ``coeff += sign * stoi(equation.substr(i, j - i));``            ``i = j + 1;``        ``}` `        ``// Flip sign once '=' is seen``        ``else` `if` `(equation[j] == ``'='``) {``            ``if` `(j > i)``                ``total += sign * stoi(equation.substr(i, j - i));``            ``sign = -1;``            ``i = j + 1;``        ``}``    ``}` `    ``// There may be a number left in the end``    ``if` `(i < n)``        ``total += sign * stoi(equation.substr(i));` `    ``// For infinite solutions``    ``if` `(coeff == 0 && total == 0)``        ``return` `"Infinite solutions"``;` `    ``// For no solution``    ``if` `(coeff == 0 && total)``        ``return` `"No solution"``;` `    ``// x = total sum / coeff of x``    ``// '-' sign indicates moving``    ``// numeric value to right hand side``    ``int` `ans = -total / coeff;``    ``return` `"x="` `+ to_string(ans);``}` `// Driver code``int` `main()``{``    ``string equation = ``"x+5-3+x=6+x-2"``;``    ``cout << solveEquation(equation);``    ``return` `0;``}`

## Java

 `// Java program to solve``// the given equation``import` `java.io.*;` `class` `GFG``{``// Function to solve``// the given equation``static` `String solveEquation(String equation)``{``    ``int` `n = equation.length(),``        ``sign = ``1``, coeff = ``0``;``    ``int` `total = ``0``, i = ``0``;` `    ``// Traverse the equation``    ``for` `(``int` `j = ``0``; j < n; j++)``    ``{``        ``if` `(equation.charAt(j) == ``'+'` `||``            ``equation.charAt(j) == ``'-'``)``        ``{``            ``if` `(j > i)``                ``total += sign *``                         ``Integer.parseInt(``                                 ``equation.substring(i, j));``            ``i = j;``        ``}` `        ``// For cases such``        ``// as: x, -x, +x``        ``else` `if` `(equation.charAt(j) == ``'x'``)``        ``{``            ``if` `((i == j) ||``                 ``equation.charAt(j - ``1``) == ``'+'``)``                ``coeff += sign;``                ` `            ``else` `if` `(equation.charAt(j - ``1``) == ``'-'``)``                ``coeff -= sign;``                ` `            ``else``                ``coeff += sign *``                         ``Integer.parseInt(``                                 ``equation.substring(i, j));``            ``i = j + ``1``;``        ``}` `        ``// Flip sign once``        ``// '=' is seen``        ``else` `if` `(equation.charAt(j) == ``'='``)``        ``{``            ``if` `(j > i)``                ``total += sign *``                         ``Integer.parseInt(``                                 ``equation.substring(i, j));``            ``sign = -``1``;``            ``i = j + ``1``;``        ``}``    ``}` `    ``// There may be a``    ``// number left in the end``    ``if` `(i < n)``        ``total = total +``                ``sign *``                ``Integer.parseInt(``                        ``equation.substring(i));` `    ``// For infinite``    ``// solutions``    ``if` `(coeff == ``0` `&&``        ``total == ``0``)``        ``return` `"Infinite solutions"``;` `    ``// For no solution``    ``if` `(coeff == ``0` `&&``        ``total != ``0``)``        ``return` `"No solution"``;` `    ``// x = total sum / coeff``    ``// of x '-' sign indicates``    ``// moving numeric value to``    ``// right hand side``    ``int` `ans = -total / coeff;``    ``return` `(Integer.toString(ans));``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``String equation = ``new` `String(``"x+5-3+x=6+x-2"``);``    ``System.out.print(``"x = "` `+``                      ``solveEquation(equation));``}``}` `// This code is contributed by``// Manish Shaw(manishshaw1)`

## Python3

 `# Python program to solve``# the given equation` `# def to solve``# the given equation``def` `solveEquation(equation) :` `    ``n ``=` `len``(equation)``    ``sign ``=` `1``    ``coeff ``=` `0``    ``total ``=` `0``    ``i ``=` `0` `    ``# Traverse the equation``    ``for` `j ``in` `range``(``0``, n) :``    ` `        ``if` `(equation[j] ``=``=` `'+'` `or``            ``equation[j] ``=``=` `'-'``) :``        ` `            ``if` `(j > i) :``                ``total ``=` `(total ``+` `sign ``*``                         ``int``(equation[i: j]))``            ``i ``=` `j``        ` `        ``# For cases such``        ``# as: x, -x, +x``        ``elif` `(equation[j] ``=``=` `'x'``) :``        ` `            ``if` `((i ``=``=` `j) ``or``                ``equation[j ``-` `1``] ``=``=` `'+'``) :``                ``coeff ``+``=` `sign``            ``elif` `(equation[j ``-` `1``] ``=``=` `'-'``) :``                ``coeff ``=` `coeff ``-` `sign``            ``else` `:``                ``coeff ``=` `(coeff ``+` `sign ``*``                         ``int``(equation[i: j]))``            ``i ``=` `j ``+` `1``        ` `        ``# Flip sign once``        ``# '=' is seen``        ``elif` `(equation[j] ``=``=` `'='``) :``        ` `            ``if` `(j > i) :``                ``total ``=` `(total ``+` `sign ``*``                         ``int``(equation[i: j]))``            ``sign ``=` `-``1``            ``i ``=` `j ``+` `1``        ` `    ``# There may be a number``    ``# left in the end``    ``if` `(i < n) :``        ``total ``=` `(total ``+` `sign ``*``                 ``int``(equation[i: ``len``(equation)]))` `    ``# For infinite solutions``    ``if` `(coeff ``=``=` `0` `and``        ``total ``=``=` `0``) :``        ``return` `"Infinite solutions"` `    ``# For no solution``    ``if` `(coeff ``=``=` `0` `and` `total) :``        ``return` `"No solution"` `    ``# x = total sum / coeff of x``    ``# '-' sign indicates moving``    ``# numeric value to right hand side``    ``ans ``=` `-``total ``/` `coeff``    ``return` `int``(ans)` `# Driver code``equation ``=` `"x+5-3+x=6+x-2"``print` `(``"x = {}"` `.``        ``format``(solveEquation(equation)))` `# This code is contributed by``# Manish Shaw(manishshaw1)`

## C#

 `// C# program to solve``// the given equation``using` `System;` `class` `GFG``{``    ``// Function to solve``    ``// the given equation``    ``static` `string` `solveEquation(``string` `equation)``    ``{``        ``int` `n = equation.Length,``            ``sign = 1, coeff = 0;``        ``int` `total = 0, i = 0;``    ` `        ``// Traverse the equation``        ``for` `(``int` `j = 0; j < n; j++)``        ``{``            ``if` `(equation[j] == ``'+'` `||``                ``equation[j] == ``'-'``)``            ``{``                ``if` `(j > i)``                    ``total += sign *``                             ``Int32.Parse(``                             ``equation.Substring(i, j - i));``                ``i = j;``            ``}``    ` `            ``// For cases such``            ``// as: x, -x, +x``            ``else` `if` `(equation[j] == ``'x'``)``            ``{``                ``if` `((i == j) ||``                     ``equation[j - 1] == ``'+'``)``                    ``coeff += sign;``                    ` `                ``else` `if` `(equation[j - 1] == ``'-'``)``                    ``coeff -= sign;``                    ` `                ``else``                    ``coeff += sign *``                             ``Int32.Parse(``                             ``equation.Substring(i, j - i));``                ``i = j + 1;``            ``}``    ` `            ``// Flip sign once``            ``// '=' is seen``            ``else` `if` `(equation[j] == ``'='``)``            ``{``                ``if` `(j > i)``                    ``total += sign *``                             ``Int32.Parse(``                             ``equation.Substring(i, j - i));``                ``sign = -1;``                ``i = j + 1;``            ``}``        ``}``    ` `        ``// There may be a``        ``// number left in the end``        ``if` `(i < n)``            ``total += sign *``                     ``Int32.Parse(``                     ``equation.Substring(i));``    ` `        ``// For infinite``        ``// solutions``        ``if` `(coeff == 0 && total == 0)``            ``return` `"Infinite solutions"``;``    ` `        ``// For no solution``        ``if` `(coeff == 0 && total != 0)``            ``return` `"No solution"``;``    ` `        ``// x = total sum / coeff``        ``// of x '-' sign indicates``        ``// moving numeric value to``        ``// right hand side``        ``int` `ans = -total / coeff;``        ``return` `"x = "` `+ ans.ToString();``    ``}``    ` `    ``// Driver code``    ``static` `void` `Main()``    ``{``        ``string` `equation = ``"x+5-3+x=6+x-2"``;``        ``Console.Write(solveEquation(equation));``    ``}``}` `// This code is contributed by``// Manish Shaw(manishshaw1)`

## PHP

 ` ``\$i``)``                ``\$total` `+= ``\$sign` `*``                          ``intval``(``substr``(``\$equation``,``                                        ``\$i``, ``\$j` `- ``\$i``));``            ``\$i` `= ``\$j``;``        ``}` `        ``// For cases such``        ``// as: x, -x, +x``        ``else` `if` `(``\$equation``[``\$j``] == ``'x'``)``        ``{``            ``if` `((``\$i` `== ``\$j``) ||``                 ``\$equation``[``\$j` `- 1] == ``'+'``)``                ``\$coeff` `+= ``\$sign``;``            ``else` `if` `(``\$equation``[``\$j` `- 1] == ``'-'``)``                ``\$coeff` `-= ``\$sign``;``            ``else``                ``\$coeff` `+= ``\$sign` `*``                          ``intval``(``substr``(``\$equation``,``                                        ``\$i``, ``\$j` `- ``\$i``));``            ``\$i` `= ``\$j` `+ 1;``        ``}` `        ``// Flip sign once``        ``// '=' is seen``        ``else` `if` `(``\$equation``[``\$j``] == ``'='``)``        ``{``            ``if` `(``\$j` `> ``\$i``)``                ``\$total` `+= ``\$sign` `*``                          ``intval``(``substr``(``\$equation``,``                                        ``\$i``, ``\$j` `- ``\$i``));``            ``\$sign` `= -1;``            ``\$i` `= ``\$j` `+ 1;``        ``}``    ``}` `    ``// There may be a number``    ``// left in the end``    ``if` `(``\$i` `< ``\$n``)``        ``\$total` `+= ``\$sign` `*``                  ``intval``(``substr``(``\$equation``, ``\$i``));` `    ``// For infinite solutions``    ``if` `(``\$coeff` `== 0 &&``        ``\$total` `== 0)``        ``return` `"Infinite solutions"``;` `    ``// For no solution``    ``if` `(``\$coeff` `== 0 && ``\$total``)``        ``return` `"No solution"``;` `    ``// x = total sum / coeff of x``    ``// '-' sign indicates moving``    ``// numeric value to right hand side``    ``\$ans` `= -``\$total` `/ ``\$coeff``;``    ``return` `"x = "` `. ``\$ans``;``}` `// Driver code``\$equation` `= ``"x+5-3+x=6+x-2"``;``echo` `(solveEquation(``\$equation``));` `// This code is contributed by``// Manish Shaw(manishshaw1)``?>`

## Javascript

 `// JavaScript program to solve the given equation` `// Function to solve the given equation``function` `solveEquation(equation)``{``    ``let n = equation.length, sign = 1, coeff = 0;``    ``let total = 0, i = 0;` `    ``// Traverse the equation``    ``for` `(let j = 0; j < n; j++) {``        ``if` `(equation[j] == ``'+'` `|| equation[j] == ``'-'``) {``            ``if` `(j > i)``                ``total += sign * parseInt(equation.substr(i, j - i));``            ``i = j;``        ``}` `        ``// For cases such as: x, -x, +x``        ``else` `if` `(equation[j] == ``'x'``) {``            ``if` `((i == j) || equation[j - 1] == ``'+'``)``                ``coeff += sign;``            ``else` `if` `(equation[j - 1] == ``'-'``)``                ``coeff -= sign;``            ``else``                ``coeff += sign * parseInt(equation.substr(i, j - i));``            ``i = j + 1;``        ``}` `        ``// Flip sign once '=' is seen``        ``else` `if` `(equation[j] == ``'='``) {``            ``if` `(j > i)``                ``total += sign * parseInt(equation.substr(i, j - i));``            ``sign = -1;``            ``i = j + 1;``        ``}``    ``}` `    ``// There may be a number left in the end``    ``if` `(i < n)``        ``total += sign * parseInt(equation.substr(i));` `    ``// For infinite solutions``    ``if` `(coeff == 0 && total == 0)``        ``return` `"Infinite solutions"``;` `    ``// For no solution``    ``if` `(coeff == 0 && total)``        ``return` `"No solution"``;` `    ``// x = total sum / coeff of x``    ``// '-' sign indicates moving``    ``// numeric value to right hand side``    ``let ans = -Math.floor(total / coeff);``    ``return` `"x="` `+ ans.toString();``}` `// Driver code``let equation = ``"x+5-3+x=6+x-2"``;``console.log(solveEquation(equation));` `// This code is contributed by phasing17`

Output:

`x = 2`

Time complexity : O(n), where n is the length of equation string. Auxiliary Space : O(1)

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