问题摘要:计算两个整数的和并且避免使用(+)
思路:1.使用位运算(& ^)。
2.回想int类型整数的表达形式:2's complement
3.方法模拟全加器
答案:
//sum = carry_bit + sum_bit
int add(int a, int b){
//I will store carry_bit in "b"
while(b != 0){
//only when the bits from two numbers are both 1 will carry_bit be generated.
int carry = a & b;
//calculate the sum of a certain bit without considering carry
a = a ^ b;
//make b carry_bit so that we will continuously calculate "carry + sum"
//notice that i_th carry is for i+1_th bit
b = carry << 1;
}
return a;
}
算法正确性解释:
1. 本算法一定会截至:
每一次b = carry << 1; carry = a & b; 且b的位数固定,所以经过一定次数的循环后b一定会变为0;
2. 二进制数字之和=本位之和+本位右方的进位(例:00001010 + 00001100, 本为和0000 0110,右方进位1000,sum=00010110),所以只需递归求"本位之和+本位右方的进位"。