# 640.Solve-the-Equation

## 题目描述

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"

## 代码

### Approach 1: Partioning Coefficients

x = 右边/左边
• Time complexity : O(n)
• Space complexity : O(n)
class Solution {
public String solveEquation(String equation) {
String[] lr = equation.split("=");
int lhs = 0, rhs = 0;
for (String x: breakIt(lr[0])) {
if (x.indexOf("x") >= 0) {
lhs += Integer.parseInt(coeff(x));
} else {
rhs -= Integer.parseInt(x);
}
}
for (String x: breakIt(lr[1])) {
if (x.indexOf("x") >= 0)
lhs -= Integer.parseInt(coeff(x));
else
rhs += Integer.parseInt(x);
}
if (lhs == 0) {
if (rhs == 0) {
return "Infinite solutions";
} else {
return "No solution";
}
}
return "x=" + rhs / lhs;
}
public List<String> breakIt(String s) {
List<String> res = new ArrayList<>();
String r = "";
for (int i = 0; i < s.length(); i++) {
if (s.charAt(i) == '+' || s.charAt(i) == '-') {
if (r.length() > 0) { // 分割
}
r = "" + s.charAt(i);
} else {
r += s.charAt(i);
}
}
return res;
}
public String coeff(String x) {
if (x.length() > 1 && x.charAt(x.length() - 2) >= '0' && x.charAt(x.length() - 2) <= '9') {
return x.replace("x", "");
} else {
return x.replace("x", "1");
}
}
}

### Approach #2 Using regex for spliting

class Solution {
public String coeff(String x) {
if (x.length() > 1 && x.charAt(x.length() - 2) >= '0' && x.charAt(x.length() - 2) <= '9')
return x.replace("x", "");
return x.replace("x", "1");
}
public String solveEquation(String equation) {
String[] lr = equation.split("=");
int lhs = 0, rhs = 0;
for (String x: lr[0].split("(?=\\+)|(?=-)")) {
if (x.indexOf("x") >= 0) {
lhs += Integer.parseInt(coeff(x));
} else
rhs -= Integer.parseInt(x);
}
for (String x: lr[1].split("(?=\\+)|(?=-)")) {
if (x.indexOf("x") >= 0)
lhs -= Integer.parseInt(coeff(x));
else
rhs += Integer.parseInt(x);
}
if (lhs == 0) {
if (rhs == 0)
return "Infinite solutions";
else
return "No solution";
} else
return "x=" + rhs / lhs;
}
}