題目
An n-bit gray code sequence is a sequence of 2n
integers where:
- Every integer is in the inclusive range
[0, 2n - 1]
, - The first integer is
0
, - An integer appears no more than once in the sequence,
- The binary representation of every pair of adjacent integers differs by exactly one bit, and
- The binary representation of the first and last integers differs by exactly one bit.
Given an integer n
, return any valid n-bit gray code sequence.
Example 1:
Input: n = 2
Output: [0,1,3,2]
Explanation:
The binary representation of [0,1,3,2] is [00,01,11,10].
- 00 and 01 differ by one bit
- 01 and 11 differ by one bit
- 11 and 10 differ by one bit
- 10 and 00 differ by one bit
[0,2,3,1] is also a valid gray code sequence, whose binary representation is [00,10,11,01].
- 00 and 10 differ by one bit
- 10 and 11 differ by one bit
- 11 and 01 differ by one bit
- 01 and 00 differ by one bit
Example 2:
Input: n = 1
Output: [0,1]
思路
- n = 0 [0]
- n = 1 [0, 1]
- n = 2 [0, 1, 3, 2]
- n = 3 [0, 1, 3, 2, 6, 7, 5, 4]
認真找尋規律,每一個都會是前一個的 reverse 再加上最大的 bit,也就是 2^(n - 1)
Solution
/**
* @param {number} n
* @return {number[]}
*/
var grayCode = function(n) {
var res = [0]
var count = 0
while(count < n) {
const offset = Math.pow(2, n - 1)
const temp = [...res].reverse().map(v => v + offset)
res = res.concat(temp)
n--
}
return res
};
Complexity
- Time complexity : O(n)
- Space complexity : O(1)