[LintCode] A + B 问题

Bit-by-Bit summation:

class Solution {
public:
    /*
     * @param a: The first integer
     * @param b: The second integer
     * @return: The sum of a and b
     */
    int aplusb(int a, int b) {
        // write your code here, try to do it without arithmetic operators.
        int res = 0, sum = 0, carry = 0;
        for (int i = 0; i < 32; i++, a >>= 1, b >>= 1){
            int d1 = a & 1, d2 = b & 1;
            sum = (d1 ^ d2 ^ carry);
            carry = max((d1 & d2), max((d1 & carry), (d2 & carry)));
            res ^= (sum << i);
        }
        return res;
    }
};

Treat a + b as two parts:

1. a + b without carry;
2. carry of a + b;
3. recursively plus part 1 and part 2 until no carry exists.

class Solution {
public:
    /*
     * @param a: The first integer
     * @param b: The second integer
     * @return: The sum of a and b
     */
    int aplusb(int a, int b) {
        // write your code here, try to do it without arithmetic operators.
        while (b) {
            int carry = a & b;  // carry
            a ^= b;             // plus without carry
            b = carry << 1;     // recursively plus the two parts
        }
        return a;
    }
};

The code can be further shortened by writing it recursively.

class Solution {
public:
    /*
     * @param a: The first integer
     * @param b: The second integer
     * @return: The sum of a and b
     */
    int aplusb(int a, int b) {
        // write your code here, try to do it without arithmetic operators.
        if (!b) return a;
        return aplusb(a ^ b, (a & b) << 1);
    }
};

Or just in one line :-) 

class Solution {
public:
    /*
     * @param a: The first integer
     * @param b: The second integer
     * @return: The sum of a and b
     */
    int aplusb(int a, int b) {
        // write your code here, try to do it without arithmetic operators.
        return (!b ? a : aplusb(a ^ b, (a & b) << 1));
    }
};