LeetCode Interview Question 17.01. Addition without a plus sign

1. Title

  Design a function to add two numbers. + or other arithmetic operators may not be used.

Example:

Input: a = 1, b = 1
Output: 2

hint:

• a, b may be negative or 0
• The result will not overflow as a 32-bit integer

  Click here to jump to the question.

2. C# problem solution

  Perform binary addition of a and b, ai and bi represent the value of the i-th bit of a and b (0 or 1), and ci represents the carry of the i-th bit (0 or 1). Use ans to represent the calculation result. In the initial case, all bits of ans are 0.

1. ci = 0
   • ai = bi: ai and bi are either 0 or 1, so the result of the bit after addition is 0, and ans does not process it.
     • ai = bi = 0, then the bit is carried to 0 after calculation;
     • ai = bi = 1, then the bit is carried by 1 after calculation.
       Therefore ci = ai.
   • ai != bi: One of ai and bi is 0, and the other is 1. There will be no carry after adding. Considering ci = 0, ci is not processed, and the position of ans is 1.
2. ci = 1
   • ai = bi: ai is either 0 or 1, so the bit result after addition is 1, set ans to 1.
     • ai = bi = 0, then the bit is carried to 0 after calculation;
     • ai = bi = 1, then the bit is carried by 1 after calculation.
       Therefore ci = ai.
   • ai != bi: One of ai and bi is 0, and the other is 1, so the bit results after addition are both 0, and a carry is generated. Therefore ans is not processed and ci becomes 1. Considering that the premise of this branch is that ci is already 1, this situation can be skipped.

public class Solution {
    
    
    public int Add(int a, int b) {
    
    
        int ai, bi, ci = 0, i = 1, ans = 0;
        do {
    
    
            ai = (a & i) == 0 ? 0 : 1; // 获取 a 的每一位
            bi = (b & i) == 0 ? 0 : 1; // 获取 b 的每一位
            if (ci == 0) {
    
                 // 进位为 0
                if (ai == bi) ci = ai;
                else ans |= i;
            }
            else if (ai == bi) {
    
     // 进位为 1
                ci = ai;
                ans |= i;
            }
            i <<= 1; // 左移 i
        } while (i != 0);
        return ans;
    }
}

• Time: 20 ms, beats 77.78% of users using C#
• Memory: 25.95 MB, beats 94.44% of users using C#