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 <= 1000equation has exactly one '='.equation consists of integers with an absolute value in the range [0, 100] without any leading zeros, and the variable 'x'.This approach involves rearranging the equation to separate the terms involving 'x' from the constant terms. We ensure that all terms involving 'x' are on one side of the equation and all constant terms on the other side. This allows us to solve for 'x' by simplifying both sides to isolated 'x' terms versus numerical constants.
We split the equation at the equal sign and process both sides to calculate the total coefficients for 'x' and any constant. By comparing these totals, we determine if the equation has no solution, infinite solutions, or exactly one solution. Parsing involves iterating through each character of the string, summing coefficients and constants.
JavaScript
Time Complexity: O(n), where n is the length of the equation string. Space Complexity: O(1), as we use a constant amount of extra space.
This approach focuses on scanning the equation and simplifying terms by combining all instances of the variable 'x' and the constant terms separately. After combining, we analyze the coefficients to deduce the solution.
In this C# solution, we further enhance parsing by leveraging tuples for clean coefficient and constant extraction. This method helps standardize processing by treating everything as terms to be added or subtracted from a total, revealing a systematic deduction path for solutions or infinite cases.
Java
Time Complexity: O(n), where n represents the number of characters in the input string. Space Complexity: O(1), since only fixed-space variables are utilized.
| Approach | Complexity |
|---|---|
| Balancing Equation Terms | Time Complexity: O(n), where n is the length of the equation string. Space Complexity: O(1), as we use a constant amount of extra space. |
| Combining and Simplifying Terms | Time Complexity: O(n), where n represents the number of characters in the input string. Space Complexity: O(1), since only fixed-space variables are utilized. |
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