The problem requires solving equations with the variable 'x', using basic arithmetic operations. Your task is to parse the equation, isolate the value of 'x', and return it in the form of a string. You must handle edge cases such as no solution or infinite solutions based on the structure of the equation.
Problem Statement
Given an equation in the form of a string, solve for the variable 'x'. The equation will involve the addition and subtraction of integers, and the variable 'x'. You need to determine the value of 'x' or return specific outputs when there are no solutions or infinite solutions.
For equations with exactly one solution, return the result as "x=#value". If there is no solution, return "No solution", and if there are infinite solutions, return "Infinite solutions".
Examples
Example 1
Input: equation = "x+5-3+x=6+x-2"
Output: "x=2"
Example details omitted.
Example 2
Input: equation = "x=x"
Output: "Infinite solutions"
Example details omitted.
Example 3
Input: equation = "2x=x"
Output: "x=0"
Example details omitted.
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.
Solution Approach
Parse the Equation
Start by splitting the equation at the equals sign to create two parts. Each part will be processed separately to isolate terms involving 'x' on one side and constants on the other.
Balance the Equation
Convert all terms to one side of the equation, ensuring that terms involving 'x' are grouped together, and constants are isolated. Use basic arithmetic to move terms across the equals sign.
Solve for 'x'
After balancing, calculate the value of 'x' by dividing the sum of constants by the coefficient of 'x'. If the equation results in contradictions or identities, determine if there is no solution or infinite solutions.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time and space complexity depend on how you process the equation. Parsing the string and performing arithmetic operations both involve linear time complexity, O(n), where n is the length of the equation. Space complexity depends on how the equation is stored and split, typically O(n).
What Interviewers Usually Probe
- Look for candidates who can break down and parse the string effectively.
- Evaluate how well they handle edge cases, such as infinite solutions or no solutions.
- Assess if they can balance the equation systematically and solve for 'x' without skipping steps.
Common Pitfalls or Variants
Common pitfalls
- Overcomplicating the parsing process, leading to errors when extracting coefficients or constants.
- Failing to account for edge cases, such as when the equation simplifies to 'x=x' (infinite solutions).
- Mismanaging signs during the balancing step, which could lead to incorrect values for 'x'.
Follow-up variants
- Equations with only addition or subtraction operations.
- Handling more complex terms such as fractions or higher powers of 'x'.
- Expanding the problem to handle multiple variables or more complicated expressions.
How GhostInterview Helps
- GhostInterview assists by providing step-by-step guidance through parsing and solving equations, making it easier to spot errors early.
- The solver highlights edge cases and tricky pitfalls, ensuring you don't miss special conditions like infinite solutions or no solution.
- With its feedback system, GhostInterview helps you refine your solution by focusing on balancing the equation and handling all mathematical operations correctly.
Topic Pages
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- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How do I solve equations in the form 'x=5'?
Simply return the solution as 'x=5'. The equation is already balanced, so no further steps are necessary.
What if there is no 'x' in the equation?
If there is no 'x' and the constants do not balance, return 'No solution'. If the equation is always true, return 'Infinite solutions'.
What happens when the equation simplifies to 'x=x'?
This equation has infinite solutions. Return 'Infinite solutions' as the result.
Can the input equation contain terms with multiple variables?
No, this problem specifically deals with equations containing only one variable, 'x'.
How does GhostInterview help with solving this problem?
GhostInterview offers step-by-step assistance for parsing and balancing the equation, ensuring you handle all special cases, such as infinite or no solutions.
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