feat: add solutions to lc problem: No.2235 (#1467)

No.2235.Add Two Integers

Author: yanglbme

solution/2200-2299/2235.Add Two Integers/README.md

@@ -38,6 +38,36 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
+**方法一：使用加法运算符**
+
+我们可以直接使用加法运算符 `+` 来计算两个整数的和。
+
+时间复杂度 $O(1)$，空间复杂度 $O(1)$。
+
+**方法二：位运算（不使用加法运算符）**
+
+我们也可以在不使用加法运算符的前提下，使用位运算来计算两个整数的和。
+
+假设 $num1_i$ 和 $num2_i$ 分别表示 $num1$ 和 $num2$ 的第 $i$ 个二进制位。一共有 $4$ 种情况：
+
+| $num1_i$ | $num2_i$ | 不进位的和 | 进位 |
+| -------- | -------- | ---------- | ---- |
+| 0        | 0        | 0          | 0    |
+| 0        | 1        | 1          | 0    |
+| 1        | 0        | 1          | 0    |
+| 1        | 1        | 0          | 1    |
+
+观察可以发现，“不进位的和”与“异或运算”有相同规律，而进位则与“与”运算规律相同，并且需要左移一位。
+
+因此：
+
+-   对两数进行按位 `&` 与运算，然后左移一位，得到进位，记为 $carry$；
+-   对两数进行按位 `^` 异或运算，得到不进位的和；
+-   问题转换为求：“不进位的数 + 进位” 之和；
+-   循环，直至第二个数为 $0$，返回第一个数即可（也可以用递归实现）。
+
+时间复杂度 $O(\log M)$，其中 $M$ 为题目中数字的最大值。空间复杂度 $O(1)$。
+
 <!-- tabs:start -->
 
 ### **Python3**
@@ -50,6 +80,16 @@ class Solution:
         return num1 + num2
 ```
 
+```python
+class Solution:
+    def sum(self, num1: int, num2: int) -> int:
+        num1, num2 = num1 & 0xFFFFFFFF, num2 & 0xFFFFFFFF
+        while num2:
+            carry = ((num1 & num2) << 1) & 0xFFFFFFFF
+            num1, num2 = num1 ^ num2, carry
+        return num1 if num1 < 0x80000000 else ~(num1 ^ 0xFFFFFFFF)
+```
+
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
@@ -62,11 +102,16 @@ class Solution {
 }
 ```
 
-### **TypeScript**
-
-```ts
-function sum(num1: number, num2: number): number {
-    return num1 + num2;
+```java
+class Solution {
+    public int sum(int num1, int num2) {
+        while (num2 != 0) {
+            int carry = (num1 & num2) << 1;
+            num1 ^= num2;
+            num2 = carry;
+        }
+        return num1;
+    }
 }
 ```
 
@@ -81,6 +126,20 @@ public:
 };
 ```
 
+```cpp
+class Solution {
+public:
+    int sum(int num1, int num2) {
+        while (num2) {
+            unsigned int carry = (unsigned int) (num1 & num2) << 1;
+            num1 ^= num2;
+            num2 = carry;
+        }
+        return num1;
+    }
+};
+```
+
 ### **Go**
 
 ```go
@@ -89,6 +148,17 @@ func sum(num1 int, num2 int) int {
 }
 ```
 
+```go
+func sum(num1 int, num2 int) int {
+	for num2 != 0 {
+		carry := (num1 & num2) << 1
+		num1 ^= num2
+		num2 = carry
+	}
+	return num1
+}
+```
+
 ### **TypeScript**
 
 ```ts
@@ -97,6 +167,17 @@ function sum(num1: number, num2: number): number {
 }
 ```
 
+```ts
+function sum(num1: number, num2: number): number {
+    while (num2) {
+        const carry = (num1 & num2) << 1;
+        num1 ^= num2;
+        num2 = carry;
+    }
+    return num1;
+}
+```
+
 ### **Rust**
 
 ```rust
@@ -107,6 +188,21 @@ impl Solution {
 }
 ```
 
+```rust
+impl Solution {
+    pub fn sum(num1: i32, num2: i32) -> i32 {
+        let mut num1 = num1;
+        let mut num2 = num2;
+        while num2 != 0 {
+            let carry = (num1 & num2) << 1;
+            num1 ^= num2;
+            num2 = carry;
+        }
+        num1
+    }
+}
+```
+
 ### **C**
 
 ```c

solution/2200-2299/2235.Add Two Integers/README_EN.md

@@ -42,6 +42,16 @@ class Solution:
         return num1 + num2
 ```
 
+```python
+class Solution:
+    def sum(self, num1: int, num2: int) -> int:
+        num1, num2 = num1 & 0xFFFFFFFF, num2 & 0xFFFFFFFF
+        while num2:
+            carry = ((num1 & num2) << 1) & 0xFFFFFFFF
+            num1, num2 = num1 ^ num2, carry
+        return num1 if num1 < 0x80000000 else ~(num1 ^ 0xFFFFFFFF)
+```
+
 ### **Java**
 
 ```java
@@ -52,11 +62,16 @@ class Solution {
 }
 ```
 
-### **TypeScript**
-
-```ts
-function sum(num1: number, num2: number): number {
-    return num1 + num2;
+```java
+class Solution {
+    public int sum(int num1, int num2) {
+        while (num2 != 0) {
+            int carry = (num1 & num2) << 1;
+            num1 ^= num2;
+            num2 = carry;
+        }
+        return num1;
+    }
 }
 ```
 
@@ -71,6 +86,20 @@ public:
 };
 ```
 
+```cpp
+class Solution {
+public:
+    int sum(int num1, int num2) {
+        while (num2) {
+            unsigned int carry = (unsigned int) (num1 & num2) << 1;
+            num1 ^= num2;
+            num2 = carry;
+        }
+        return num1;
+    }
+};
+```
+
 ### **Go**
 
 ```go
@@ -79,6 +108,17 @@ func sum(num1 int, num2 int) int {
 }
 ```
 
+```go
+func sum(num1 int, num2 int) int {
+	for num2 != 0 {
+		carry := (num1 & num2) << 1
+		num1 ^= num2
+		num2 = carry
+	}
+	return num1
+}
+```
+
 ### **TypeScript**
 
 ```ts
@@ -87,6 +127,17 @@ function sum(num1: number, num2: number): number {
 }
 ```
 
+```ts
+function sum(num1: number, num2: number): number {
+    while (num2) {
+        const carry = (num1 & num2) << 1;
+        num1 ^= num2;
+        num2 = carry;
+    }
+    return num1;
+}
+```
+
 ### **Rust**
 
 ```rust
@@ -97,6 +148,21 @@ impl Solution {
 }
 ```
 
+```rust
+impl Solution {
+    pub fn sum(num1: i32, num2: i32) -> i32 {
+        let mut num1 = num1;
+        let mut num2 = num2;
+        while num2 != 0 {
+            let carry = (num1 & num2) << 1;
+            num1 ^= num2;
+            num2 = carry;
+        }
+        num1
+    }
+}
+```
+
 ### **C**
 
 ```c