371. Sum of Two Integers
Calculate the sum of two integers a and b, but you are not allowed to use the operator + and -. Example: Given a = 1 and b = 2, return 3. Credits: Special thanks to @fujiaozhu for adding this problem and creating all test cases.
这道题让我们实现两数相加,但是不能用加号或者其他什么数学运算符号,那么我们只能回归计算机运算的本质,位操作Bit Manipulation,我们在做加法运算的时候,每位相加之后可能会有进位Carry产生,然后在下一位计算时需要加上进位一起运算,那么我们能不能将两部分拆开呢,我们来看一个例子759+674
1. 如果我们不考虑进位,可以得到323
2. 如果我们只考虑进位,可以得到1110
3. 我们把上面两个数字假期323+1110=1433就是最终结果了
然后我们进一步分析,如果得到上面的第一第二种情况,我们在二进制下来看,不考虑进位的加,0+0=0, 0+1=1, 1+0=1, 1+1=0,这就是异或的运算规则,如果只考虑进位的加0+0=0, 0+1=0, 1+0=0, 1+1=1,而这其实这就是与的运算,而第三步在将两者相加时,我们再递归调用这个算法,终止条件是当进位为0时,我们直接返回第一步的结果,参见代码如下:
For this, problem, for example, we have a = 1, b = 3,
In bit representation, a = 0001, b = 0011,
First, we can use "and"("&") operation between a and b to find a carry.
carry = a & b, then carry = 0001
Second, we can use "xor" ("^") operation between a and b to find the different bit, and assign it to a,
Then, we shift carry one position left and assign it to b, b = 0010.
Iterate until there is no carry (or b == 0)
// Iterative public int getSum(int a, int b) { if (a == 0) return b; if (b == 0) return a; while (b != 0) { int carry = a & b; a = a ^ b; b = carry << 1; } return a; } // Iterative public int getSubtract(int a, int b) { while (b != 0) { int borrow = (~a) & b; a = a ^ b; b = borrow << 1; } return a; } // Recursive public int getSum(int a, int b) { return (b == 0) ? a : getSum(a ^ b, (a & b) << 1); } // Recursive public int getSubtract(int a, int b) { return (b == 0) ? a : getSubtract(a ^ b, (~a & b) << 1); } // Get negative number public int negate(int x) { return ~x + 1; }