## 640. Solve the Equation

Solve a given equation and return the value of x in the form of string "x=#value". The equation contains only '+', '-' operation, the variable x and its coefficient.

If there is no solution for the equation, return "No solution".

If there are infinite solutions for the equation, return "Infinite solutions".

If there is exactly one solution for the equation, we ensure that the value of x is an integer.

Example 1:

Input: "x+5-3+x=6+x-2"
Output: "x=2"

Example 2:

Input: "x=x"
Output: "Infinite solutions"

Example 3:

Input: "2x=x"
Output: "x=0"

Example 4:

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

Example 5:

Input: "x=x+2"
Output: "No solution"

## Rust Solution

struct Solution;

impl Solution {
fn solve_equation(equation: String) -> String {
let mut it = equation.split('=');
let left = it.next().unwrap();
let right = it.next().unwrap();
let (a, b) = Self::parse(left);
let (c, d) = Self::parse(right);
if a == c {
if b == d {
"Infinite solutions".to_string()
} else {
"No solution".to_string()
}
} else {
format!("x={}", (d - b) / (a - c))
}
}
fn parse(s: &str) -> (i32, i32) {
let mut sign = 1;
let mut x = false;
let mut val = None;
let mut a = 0;
let mut b = 0;
for c in s.chars() {
match c {
'x' => {
if val.is_none() {
val = Some(1);
}
x = true;
}
'+' => {
if let Some(v) = val {
if x {
a += sign * v;
} else {
b += sign * v;
}
}
val = None;
x = false;
sign = 1;
}
'-' => {
if let Some(v) = val {
if x {
a += sign * v;
} else {
b += sign * v;
}
}
val = None;
x = false;
sign = -1;
}
_ => {
val = if let Some(mut v) = val {
v *= 10;
v += (c as u8 - b'0') as i32;
Some(v)
} else {
Some((c as u8 - b'0') as i32)
};
}
}
}
if x {
if val.is_none() {
val = Some(1);
}
a += sign * val.unwrap();
} else {
b += sign * val.unwrap();
}
(a, b)
}
}

#[test]
fn test() {
let equation = "x+5-3+x=6+x-2".to_string();
let res = "x=2".to_string();
assert_eq!(Solution::solve_equation(equation), res);
let equation = "x=x".to_string();
let res = "Infinite solutions".to_string();
assert_eq!(Solution::solve_equation(equation), res);
let equation = "2x=x".to_string();
let res = "x=0".to_string();
assert_eq!(Solution::solve_equation(equation), res);
let equation = "2x+3x-6x=x+2".to_string();
let res = "x=-1".to_string();
assert_eq!(Solution::solve_equation(equation), res);
let equation = "x=x+2".to_string();
let res = "No solution".to_string();
assert_eq!(Solution::solve_equation(equation), res);
let equation = "0x=0".to_string();
let res = "Infinite solutions".to_string();
assert_eq!(Solution::solve_equation(equation), res);
let equation = "-x=-1".to_string();
let res = "x=1".to_string();
assert_eq!(Solution::solve_equation(equation), res);
}

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