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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.
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.
1function solveEquation(equation) {
2 const parse = (s) => {
3 let parts = { x_coef: 0, const: 0 };
4 let num = '';
5 let sign = 1;
6 for (let i = 0; i <= s.length; i++) {
7 if (i < s.length && (s[i] === '+' || s[i] === '-')) {
8 if (num) parts.const += sign * parseInt(num, 10);
9 num = '';
10 sign = s[i] === '+' ? 1 : -1;
11 } else if (i < s.length && s[i].match(/[0-9]/)) {
12 num += s[i];
13 } else {
14 if (s[i] === 'x') {
15 if (num === '') num = '1';
16 parts.x_coef += sign * parseInt(num, 10);
17 } else if (num) {
18 parts.const += sign * parseInt(num, 10);
19 }
20 num = '';
21 }
22 }
23 return parts;
24 };
25
26 const [left, right] = equation.split('=');
27 const leftParts = parse(left + '+');
28 const rightParts = parse(right + '+');
29
30 const x_coef = leftParts.x_coef - rightParts.x_coef;
31 const constant = rightParts.const - leftParts.const;
32
33 if (x_coef === 0) {
34 return constant === 0 ? 'Infinite solutions' : 'No solution';
35 } else {
36 return `x=${constant / x_coef}`;
37 }
38}We parse through both sides of the equation, isolating numerical values and coefficients of 'x'. This JavaScript solution efficiently separates constants from 'x' coefficients, checks their relation, and forms a resultant string based on the coefficient conditions.
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.
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.
1class Solution {
2 public String solveEquation
This Java solution employs a procedural methodology to enact a clear separation between the parsing of numeric and 'x' terms. Each section of the equation is handled independently to derive an organized result, promoting calculation flow integrity and variable isolation for results.