Daily practice (34): Addition without addition, subtraction, multiplication and division

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title: Daily practice (34): Addition without addition, subtraction, multiplication and division

categories:[Swords offer]

tags:[Daily practice]

date: 2022/03/09

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Daily practice (34): Addition without addition, subtraction, multiplication and division

Write a function to calculate the sum of two integers. It is required that the four operators "+", "-", "*" and "/" should not be used in the function body.

Example:

Input: a = 1, b = 1

Output: 2

hint:

a, b can both be negative or 0

The result will not overflow a 32-bit integer

Source: LeetCode

Link: https://leetcode-cn.com/problems/bu-yong-jia-jian-cheng-chu-zuo-jia-fa-lcof

Method 1: Bit Operations

Algorithm flow:

a ^ b calculates the base of each bit in the binary of the 2 addends

a & b Calculate the carry of each digit in the binary of the 2 addends

(a & b) << 1 carry for carry logic, that is, * 2

int add(int a, int b) {
    while (b != 0) {
        int carry = a & b ;     // 计算 进位
        a ^= b;                // 计算 本位
        b = (unsigned)c << 1;    
    }
    return a;
}

Method 2: Recursion

Addition = carry + non-carry part

Use XOR bit operation to represent the case of no carry 00=0 11=0 10=1 01=1

Use AND operation and left shift operation to represent the case of carry 11=10

Also perform a left shift operation in the loop

int add(int a, int b) {
    // 后续用a表示非进位和，b表示进位，当进位为0，则表示计算结束
    return b ? add(a ^ b, (unsigned)(a & b) << 1) : a;
}