Solve the Equation

Solve the Equation

What is this problem about?

The "Solve the Equation" problem is a string parsing and algebraic challenge. You are given a string representing a linear equation in the form "x+5-3+x=6+x-2", and you need to find the value of 'x'. The equation can have three types of results: a specific value (e.g., "x=2"), "No solution", or "Infinite solutions".

The problem requires you to carefully parse the string, handle signs (+ and -), consolidate all 'x' terms on one side and all constant terms on the other, and finally solve for 'x'. It's a test of your ability to handle complex string manipulation and mathematical logic.

Why is this asked in interviews?

Amazon and other tech firms use this interview question to check a candidate's parsing skills. String parsing is a common task in software engineering, whether it's processing logs, interpreting configuration files, or building compilers. This problem specifically tests how you handle edge cases like "-x", "+x", "0x", and "x" without a coefficient. It also evaluates your ability to structure code cleanly by breaking the problem into logical steps: parsing, simplifying, and solving.

Algorithmic pattern used

The algorithmic pattern used here is Simulation and String Parsing. You can split the equation into two halves (left and right of the '='). For each half, you iterate through the terms, identifying whether each term is a constant or a coefficient of 'x'. You sum up all 'x' coefficients and all constants for both sides. Finally, you transform the equation into the form $Ax = B$.

• If $A \neq 0$, $x = B/A$.
• If $A = 0$ and $B = 0$, Infinite solutions.
• If $A = 0$ and $B \neq 0$, No solution.

Example explanation

Take the equation "x+5-2x=6-3".

1. Left side: x + 5 - 2x.
   • Coefficients: $1 - 2 = -1$.
   • Constants: $5$.
2. Right side: 6 - 3.
   • Coefficients: $0$.
   • Constants: $3$.
3. Equation: $-1x + 5 = 3 \Rightarrow -1x = 3 - 5 \Rightarrow -1x = -2 \Rightarrow x = 2$. The output for this solve the equation coding problem would be "x=2".

Common mistakes candidates make

One very common mistake is failing to handle the "x" term correctly when there is no explicit number (treating "x" as $1x$ and "-x" as $-1x$). Another mistake is incorrect sign handling when moving terms across the '=' sign. Parsing the numbers themselves can also be tricky if you don't correctly identify the boundaries between terms. Finally, failing to distinguish between the two "A=0" cases (Infinite vs. No solution) is a frequent logic error.

Interview preparation tip

When tackling the "Solve the Equation interview question," a great strategy is to use a helper function that parses a single side of the equation and returns a pair (x_coeff, constant). You can make parsing easier by pre-processing the string—for example, replacing all '-' with '+-' to make splitting by '+' simpler. This reduces the number of cases you have to handle in your main logic loop and makes the code more robust.