0 ⊕ A = A //A为任意数
A ⊕ A = 0
即,任意数与0相与都等于其自身,任意数与其自身异或都为0
补充:
(A ⊕ B) ⊕ C = A ⊕ (B ⊕ C) //结合律
(A ⊕ B) ⊕ (C ⊕ D) = A ⊕ B ⊕ C ⊕ D //可以去掉括号
A ⊕ B ⊕ C ⊕ D = A ⊕ C ⊕ B ⊕ D //可以随意交换
即,只要参与异或运算的成员不变,任意交换异或顺序,结果都一样
同理:
若f ⊕ m = G,则:
f ⊕ G = m //推导: f ⊕ G = f ⊕ (f ⊕ m) = f ⊕ f ⊕ m = 0 ⊕ m = m)
m ⊕ G = f //同上
//cpp
int singleNumber(vector<int>& nums) {
for (int i = 1; i < nums.size(); i++) { //遍历数组
nums[0] ^= nums[i]; //直接用第0号存储异或结果,节省空间
}
return nums[0];
}
#py
class Solution:
def singleNumber(self, nums: List[int]) -> int:
res = nums[0]
for i in range(1, len(nums)):
res ^= nums[i]
return res