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 code 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].
Solution: DP
dp[0] = 0
dp[i] = dp[i – 1] + [x | 1 << (i – 1) for x in reversed(dp[i – 1])]
Time complexity: O(2^n)
Space complexity: O(2^n)
C++
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// Author: Huahua class Solution { public: vector<int> grayCode(int n) { vector<vector<int>> dp(n + 1); dp[0] = {0}; for (int i = 1; i <= n; ++i) { dp[i] = dp[i - 1]; for (int j = dp[i - 1].size() - 1; j >= 0; --j) dp[i].push_back(dp[i - 1][j] | (1 << (i - 1))); } return dp[n]; } }; |
Python3
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# Author: Huahua class Solution: def grayCode(self, n: int) -> List[int]: dp = [0] for i in range(n): dp = dp + [x | 1 << i for x in reversed(dp)] return dp |
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