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# 0640. Solve the Equation

<https://leetcode.com/problems/solve-the-equation>

## Description

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"
```

**Example 4:**

```
**Input:** equation = "2x+3x-6x=x+2"
**Output:** "x=-1"
```

**Example 5:**

```
**Input:** equation = "x=x+2"
**Output:** "No solution"
```

**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'`.

## ac

```java
class Solution {
    public String solveEquation(String equation) {
        String[] strs = equation.split("=");
        int[] l = extract(strs[0]);
        int[] r = extract(strs[1]);

        int right = r[0] - l[0];
        int left = l[1] - r[1];

        if (left == 0 && right == 0) {
            return "Infinite solutions";
        } else if (left == 0 && right != 0) {
            return "No solution";
        } else {
            return "x=" + (int)(right / left);
        }
    }

    public int[] extract(String s) {
        String[] strs = s.split("-");
        int val = 0, xval = 0;
        for (int i = 0; i < strs.length; i++) {
            if (strs[i].length() == 0) continue; // skip empty
            String[] vals = strs[i].split("\\+");
            for (int j = 0; j < vals.length; j++) {
                int sign = i != 0 && j == 0 ? -1 : 1;
                if (vals[j].indexOf("x") < 0) { // normal value
                    val += sign * Integer.parseInt(vals[j]);
                } else if ("x".equals(vals[j])) {
                    xval += sign * 1;
                } else {
                    xval += sign * Integer.parseInt(vals[j].replace("x", ""));
                }
            }
        }

        return new int[]{val, xval};
    }
}

/*
1) extract the formula, return {normalVal, x-val}; 2) judge left part and right part
*/
```