[LintCode] A + B Problem（位运算）

Problem

Write a function that add two numbers A and B. You should not use + or any arithmetic operators.

Example

Given a=1 and b=2 return 3

Challenge

Of course you can just return a + b to get accepted. But Can you challenge not do it like that?

Note

**位运算笔记
Bit Manipulation Notes:**

加法：

1. ^异或运算：求和；

2. &与运算：进位。

减法：

1. 将负数化为正：~i, +1，两步完成取反

2. 做加法

乘法：

1. a * b: if (b & 1) ans += a //b的最后一位是1，则结果+a

2. 每次循环后a << 1, b >> 1; //b始终判断最后一位，a进位累加（小学生算式做乘法）

除法：（不赘述，O(log n)）

http://blog.csdn.net/ojshilu/article/details/11179911

Solution

class Solution {
    public int aplusb(int a, int b) {
        // write your code here, try to do it without arithmetic operators.
        if (b == 0) return a;
        int sum = a^b;
        int carry = (a&b) << 1;
        return aplusb(sum, carry);
    }
}