[LeetCode] 89. Gray Code 格雷码
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The gray code is a binary numeral system where two successive values differ in only one bit.
Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.
Example 1:
Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2
For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.
00 - 0
10 - 2
11 - 3
01 - 1
Example 2:
Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
A gray sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
Therefore, for n = 0 the gray code sequence is [0].
首先要清楚什么是格雷码，然后用位操作来处理。
Java:
public List<Integer> grayCode(int n) {
List<Integer> result = new LinkedList<>();
for (int i = 0; i < 1<<n; i++) result.add(i ^ i>>1);
return result;
}
Java:
public List<Integer> grayCode(int n) {
List<Integer> rs=new ArrayList<Integer>();
rs.add(0);
for(int i=0;i<n;i++){
int size=rs.size();
for(int k=size-1;k>=0;k--)
rs.add(rs.get(k) | 1<<i);
}
return rs;
}
Python:
class Solution(object):
def grayCode(self, n):
"""
:type n: int
:rtype: List[int]
"""
result = [0]
for i in xrange(n):
for n in reversed(result):
result.append(1 << i | n)
return result
Python:
# Proof of closed form formula could be found here:
# http://math.stackexchange.com/questions/425894/proof-of-closed-form-formula-to-convert-a-binary-number-to-its-gray-code
class Solution2(object):
def grayCode(self, n):
"""
:type n: int
:rtype: List[int]
"""
return [i >> 1 ^ i for i in xrange(1 << n)]
C++:
// Time: (2^n)
// Space: O(1)
class Solution {
public:
vector<int> grayCode(int n) {
vector<int> result = {0};
for (int i = 0; i < n; ++i) {
for (int j = result.size() - 1; j >= 0; --j) {
result.emplace_back(1 << i | result[j]);
}
}
return result;
}
};
C++:
// Time: (2^n)
// Space: O(1)
// Proof of closed form formula could be found here:
// http://math.stackexchange.com/questions/425894/proof-of-closed-form-formula-to-convert-a-binary-number-to-its-gray-code
class Solution2 {
public:
vector<int> grayCode(int n) {
vector<int> result;
for (int i = 0; i < 1 << n; ++i) {
result.emplace_back(i >> 1 ^ i);
}
return result;
}
};
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