How do you solve Solve the Equation on LeetCode?

Solve the Equation (LeetCode #640) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding how to parse and manipulate strings is crucial for solving equations.

What is the time complexity of Solve the Equation?

The optimal solution for Solve the Equation runs in O(n) time and uses O(1) space. The complexity is O(n) because we only make a single pass through the equation to compute the coefficients and constants.

What is the brute force solution for Solve the Equation?

The brute force approach for Solve the Equation is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we can simulate the equation by trying to isolate 'x' on one side. This involves parsing the equation, separating the left and right sides, and then manually calculating the coefficients of 'x' and the constant terms. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Solve the Equation?

Solve the Equation uses the following concepts: Math, String, Simulation. The recommended patterns to study are: String Manipulation, Mathematical Equations.

What are the interview tips for Solve the Equation?

Always clarify the problem statement and constraints before jumping into coding. Think aloud during the interview to show your thought process. Test your solution with different edge cases to ensure robustness.

What are common mistakes when solving Solve the Equation?

Failing to account for signs when parsing terms. Not considering edge cases like 'x=x' which leads to infinite solutions.

#640

Solve the Equation

Medium

MathStringSimulationString ManipulationMathematical Equations

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal solution involves a single pass through the equation to calculate the coefficients of 'x' and the constant terms. This approach is efficient as it avoids unnecessary iterations and directly computes the result.

⚙️

Algorithm

4 steps

1Step 1: Split the equation into left and right parts using '='.
2Step 2: Initialize variables to track the coefficients of 'x' and the constant terms for both sides.
3Step 3: Iterate through the equation once, updating the coefficients and constants based on the current character and its sign.
4Step 4: Calculate the total coefficients and constants, and determine the solution based on their values.

solution.py26 lines

1def solveEquation(equation):
2    left, right = equation.split('=')
3    coeff, const = 0, 0
4    sign = 1
5    for side in [left, right]:
6        i = 0
7        while i < len(side):
8            if side[i] == '+':
9                sign = 1
10                i += 1
11            elif side[i] == '-':
12                sign = -1
13                i += 1
14            num = 0
15            while i < len(side) and side[i].isdigit():
16                num = num * 10 + int(side[i])
17                i += 1
18            if i < len(side) and side[i] == 'x':
19                coeff += sign * (num if num else 1)
20                i += 1
21            else:
22                const += sign * num
23        const *= -1  # Reverse sign for right side
24    if coeff == 0:
25        return 'Infinite solutions' if const == 0 else 'No solution'
26    return f'x={const // coeff}'

ℹ

Complexity note: The complexity is O(n) because we only make a single pass through the equation to compute the coefficients and constants.

1Understanding how to parse and manipulate strings is crucial for solving equations.
2Recognizing that coefficients and constants can be separated helps in simplifying the problem.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.