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feat: add solutions to lc problem: No.0640
No.0640.Solve the Equation
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‎solution/0600-0699/0640.Solve the Equation/README.md

Lines changed: 124 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -51,22 +51,145 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：数学**
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将方程 $equation$ 按照等号 “=” 切分为左右两个式子，分别算出左右两个式子中 "x" 的系数 $x_i$，以及常数的值 $y_i$。
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那么方程转换为等式 $x_1 \times x + y_1 = x_2 \times x + y_2$。
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- 当 $x_1 = x_2$：若 $y_1 \neq y_2$，方程无解；若 $y_1=y_2$，方程有无限解。
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- 当 $x_1 \neq x_2$：方程有唯一解 $x=\frac{y_2-y_1}{x_1-x_2}$。
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相似题目：[592. 分数加减运算](/solution/0500-0599/0592.Fraction%20Addition%20and%20Subtraction/README.md)
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
61-
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class Solution:
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def solveEquation(self, equation: str) -> str:
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def f(s):
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x = y = 0
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if s[0] != '-':
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s = '+' + s
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i, n = 0, len(s)
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while i < n:
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sign = 1 if s[i] == '+' else -1
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i += 1
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j = i
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while j < n and s[j] not in '+-':
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j += 1
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v = s[i: j]
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if v[-1] == 'x':
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x += sign * (int(v[:-1]) if len(v) > 1 else 1)
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else:
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y += sign * int(v)
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i = j
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return x, y
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a, b = equation.split('=')
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x1, y1 = f(a)
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x2, y2 = f(b)
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if x1 == x2:
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return 'Infinite solutions' if y1 == y2 else 'No solution'
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return f'x={(y2 - y1) // (x1 - x2)}'
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public String solveEquation(String equation) {
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String[] es = equation.split("=");
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int[] a = f(es[0]), b = f(es[1]);
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int x1 = a[0], y1 = a[1];
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int x2 = b[0], y2 = b[1];
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if (x1 == x2) {
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return y1 == y2 ? "Infinite solutions" : "No solution";
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}
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return "x=" + (y2 - y1) / (x1 - x2);
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}
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private int[] f(String s) {
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int x = 0, y = 0;
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if (s.charAt(0) != '-') {
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s = "+" + s;
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}
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int i = 0, n = s.length();
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while (i < n) {
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int sign = s.charAt(i) == '+' ? 1 : -1;
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++i;
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int j = i;
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while (j < n && s.charAt(j) != '+' && s.charAt(j) != '-') {
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++j;
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}
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String v = s.substring(i, j);
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if (s.charAt(j - 1) == 'x') {
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x += sign * (v.length() > 1 ? Integer.parseInt(v.substring(0, v.length() - 1)) : 1);
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} else {
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y += sign * Integer.parseInt(v);
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}
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i = j;
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}
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return new int[]{x, y};
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}
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}
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```
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### **Go**
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```go
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func solveEquation(equation string) string {
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f := func(s string) []int {
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x, y := 0, 0
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if s[0] != '-' {
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s = "+" + s
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}
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i, n := 0, len(s)
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for i < n {
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sign := 1
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if s[i] == '-' {
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sign = -1
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}
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i++
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j := i
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for j < n && s[j] != '+' && s[j] != '-' {
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j++
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}
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v := s[i:j]
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if s[j-1] == 'x' {
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a := 1
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if len(v) > 1 {
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a, _ = strconv.Atoi(v[:len(v)-1])
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}
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x += sign * a
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} else {
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a, _ := strconv.Atoi(v)
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y += sign * a
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}
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i = j
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}
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return []int{x, y}
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}
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es := strings.Split(equation, "=")
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a, b := f(es[0]), f(es[1])
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x1, y1 := a[0], a[1]
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x2, y2 := b[0], b[1]
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if x1 == x2 {
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if y1 == y2 {
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return "Infinite solutions"
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} else {
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return "No solution"
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}
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}
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return fmt.Sprintf("x=%d", (y2-y1)/(x1-x2))
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}
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```
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### **...**

‎solution/0600-0699/0640.Solve the Equation/README_EN.md

Lines changed: 113 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -46,13 +46,125 @@
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### **Python3**
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```python
49-
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class Solution:
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def solveEquation(self, equation: str) -> str:
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def f(s):
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x = y = 0
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if s[0] != '-':
54+
s = '+' + s
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i, n = 0, len(s)
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while i < n:
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sign = 1 if s[i] == '+' else -1
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i += 1
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j = i
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while j < n and s[j] not in '+-':
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j += 1
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v = s[i: j]
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if v[-1] == 'x':
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x += sign * (int(v[:-1]) if len(v) > 1 else 1)
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else:
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y += sign * int(v)
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i = j
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return x, y
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a, b = equation.split('=')
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x1, y1 = f(a)
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x2, y2 = f(b)
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if x1 == x2:
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return 'Infinite solutions' if y1 == y2 else 'No solution'
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return f'x={(y2 - y1) // (x1 - x2)}'
5076
```
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### **Java**
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```java
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class Solution {
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public String solveEquation(String equation) {
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String[] es = equation.split("=");
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int[] a = f(es[0]), b = f(es[1]);
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int x1 = a[0], y1 = a[1];
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int x2 = b[0], y2 = b[1];
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if (x1 == x2) {
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return y1 == y2 ? "Infinite solutions" : "No solution";
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}
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return "x=" + (y2 - y1) / (x1 - x2);
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}
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private int[] f(String s) {
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int x = 0, y = 0;
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if (s.charAt(0) != '-') {
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s = "+" + s;
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}
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int i = 0, n = s.length();
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while (i < n) {
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int sign = s.charAt(i) == '+' ? 1 : -1;
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++i;
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int j = i;
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while (j < n && s.charAt(j) != '+' && s.charAt(j) != '-') {
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++j;
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}
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String v = s.substring(i, j);
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if (s.charAt(j - 1) == 'x') {
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x += sign * (v.length() > 1 ? Integer.parseInt(v.substring(0, v.length() - 1)) : 1);
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} else {
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y += sign * Integer.parseInt(v);
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}
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i = j;
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}
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return new int[]{x, y};
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}
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}
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```
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### **Go**
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```go
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func solveEquation(equation string) string {
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f := func(s string) []int {
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x, y := 0, 0
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if s[0] != '-' {
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s = "+" + s
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}
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i, n := 0, len(s)
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for i < n {
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sign := 1
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if s[i] == '-' {
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sign = -1
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}
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i++
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j := i
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for j < n && s[j] != '+' && s[j] != '-' {
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j++
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}
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v := s[i:j]
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if s[j-1] == 'x' {
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a := 1
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if len(v) > 1 {
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a, _ = strconv.Atoi(v[:len(v)-1])
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}
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x += sign * a
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} else {
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a, _ := strconv.Atoi(v)
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y += sign * a
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}
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i = j
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}
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return []int{x, y}
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}
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es := strings.Split(equation, "=")
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a, b := f(es[0]), f(es[1])
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x1, y1 := a[0], a[1]
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x2, y2 := b[0], b[1]
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if x1 == x2 {
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if y1 == y2 {
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return "Infinite solutions"
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} else {
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return "No solution"
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}
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}
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return fmt.Sprintf("x=%d", (y2-y1)/(x1-x2))
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}
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```
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### **...**

‎solution/0600-0699/0640.Solve the Equation/Solution.go

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,46 @@
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func solveEquation(equation string) string {
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f := func(s string) []int {
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x, y := 0, 0
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if s[0] != '-' {
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s = "+" + s
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}
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i, n := 0, len(s)
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for i < n {
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sign := 1
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if s[i] == '-' {
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sign = -1
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}
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i++
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j := i
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for j < n && s[j] != '+' && s[j] != '-' {
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j++
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}
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v := s[i:j]
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if s[j-1] == 'x' {
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a := 1
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if len(v) > 1 {
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a, _ = strconv.Atoi(v[:len(v)-1])
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}
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x += sign * a
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} else {
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a, _ := strconv.Atoi(v)
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y += sign * a
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}
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i = j
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}
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return []int{x, y}
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}
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es := strings.Split(equation, "=")
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a, b := f(es[0]), f(es[1])
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x1, y1 := a[0], a[1]
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x2, y2 := b[0], b[1]
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if x1 == x2 {
39+
if y1 == y2 {
40+
return "Infinite solutions"
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} else {
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return "No solution"
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}
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}
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return fmt.Sprintf("x=%d", (y2-y1)/(x1-x2))
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}

‎solution/0600-0699/0640.Solve the Equation/Solution.java

Lines changed: 36 additions & 0 deletions
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class Solution {
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public String solveEquation(String equation) {
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String[] es = equation.split("=");
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int[] a = f(es[0]), b = f(es[1]);
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int x1 = a[0], y1 = a[1];
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int x2 = b[0], y2 = b[1];
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if (x1 == x2) {
8+
return y1 == y2 ? "Infinite solutions" : "No solution";
9+
}
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return "x=" + (y2 - y1) / (x1 - x2);
11+
}
12+
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private int[] f(String s) {
14+
int x = 0, y = 0;
15+
if (s.charAt(0) != '-') {
16+
s = "+" + s;
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}
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int i = 0, n = s.length();
19+
while (i < n) {
20+
int sign = s.charAt(i) == '+' ? 1 : -1;
21+
++i;
22+
int j = i;
23+
while (j < n && s.charAt(j) != '+' && s.charAt(j) != '-') {
24+
++j;
25+
}
26+
String v = s.substring(i, j);
27+
if (s.charAt(j - 1) == 'x') {
28+
x += sign * (v.length() > 1 ? Integer.parseInt(v.substring(0, v.length() - 1)) : 1);
29+
} else {
30+
y += sign * Integer.parseInt(v);
31+
}
32+
i = j;
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}
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return new int[]{x, y};
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}
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}

‎solution/0600-0699/0640.Solve the Equation/Solution.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,27 @@
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class Solution:
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def solveEquation(self, equation: str) -> str:
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def f(s):
4+
x = y = 0
5+
if s[0] != '-':
6+
s = '+' + s
7+
i, n = 0, len(s)
8+
while i < n:
9+
sign = 1 if s[i] == '+' else -1
10+
i += 1
11+
j = i
12+
while j < n and s[j] not in '+-':
13+
j += 1
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v = s[i: j]
15+
if v[-1] == 'x':
16+
x += sign * (int(v[:-1]) if len(v) > 1 else 1)
17+
else:
18+
y += sign * int(v)
19+
i = j
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return x, y
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22+
a, b = equation.split('=')
23+
x1, y1 = f(a)
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x2, y2 = f(b)
25+
if x1 == x2:
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return 'Infinite solutions' if y1 == y2 else 'No solution'
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return f'x={(y2 - y1) // (x1 - x2)}'

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