Is Solve the Equation easy or hard?

Solve the Equation is rated Medium difficulty on LeetCode with an acceptance rate around 46%. The challenge is not advanced math but careful string parsing, handling implicit coefficients like 'x' or '-x', and correctly detecting infinite or impossible equations.

Solve the Equation Python/Java solution

Python and Java implementations typically scan the equation character by character, parse numbers, and update coefficient and constant accumulators. Both languages achieve O(n) time and O(1) space by avoiding extra arrays and computing the simplified equation directly during traversal.

How to solve Solve the Equation in O(n)?

Scan the string and track two values: the total coefficient of x and the total constant value. When crossing the '=' sign, flip the sign of subsequent terms so they effectively move to the left side. After the scan, solve the reduced equation ax + b = 0 using x = -b / a, with checks for zero coefficients to handle infinite or no solutions.

What is the best approach for Solve the Equation?

The most efficient approach parses the equation once and aggregates the coefficient of x and the constant terms. By treating the equation as ax + b = 0 after moving terms across the '=' sign, you can directly compute x = -b / a. This solution runs in O(n) time and O(1) space and is the method most interviewers expect.

Is Solve the Equation asked at Google/Amazon/Meta?

String parsing and equation simulation problems appear in interviews at companies like Amazon, Google, and Meta because they test careful parsing, edge-case handling, and algebraic reasoning. Variants of this problem often appear in online assessments and coding rounds.

What data structure is used in Solve the Equation?

The problem mainly uses string traversal and integer counters rather than complex data structures. You maintain variables for the coefficient of x and the constant sum while parsing tokens from the string. This makes it a lightweight combination of string processing and math simulation.

What is the time complexity of Solve the Equation?

The optimal solution runs in O(n) time where n is the length of the equation string. Each character is processed once while parsing numbers, signs, and x terms. Space complexity is O(1) since only a few counters for coefficients and constants are maintained.

Description Solution Video 10:00

640. Solve the Equation

Medium46.7% acceptance2 companies

Solve a given equation and return the value of 'x' in the form of a string "x=#value". The equation contains only '+', '-' operation, the variable 'x' and its coefficient. You should return "No solution" if there is no solution for the equation, or "Infinite solutions" if there are infinite solutions for the equation.

If there is exactly one solution for the equation, we ensure that the value of 'x' is an integer.

Example 1:

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

Example 2:

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

Example 3:

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

Constraints:

3 <= equation.length <= 1000
equation has exactly one '='.
equation consists of integers with an absolute value in the range [0, 100] without any leading zeros, and the variable 'x'.
The input is generated that if there is a single solution, it will be an integer.