LeetCode知识点总结 - 89

LeetCode 89. Gray Code

题目

An n-bit gray code sequence is a sequence of 2^n 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.

思路

start: [0]
i = 0:          [0]
i = 1:          [0, 1]
                  nums[1] = nums[0] + 1
i = 2:          [0, 1, 3, 2]
                  nums[2:4] = nums[1: : -1] + 2
i = 3:          [0, 1, 3, 2, 6, 7, 5 ,4]
                 nums[4:8] = nums[3:: -1] + 4
similarly, we have nums[2**(i-1):2**i] =  nums[2**(i-1)-1::-1] + 2**(i-1)
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答案

class Solution:
    def grayCode(self, n):
        results = [0]
        for i in range(n):
            results += [x + pow(2, i) for x in reversed(results)]
        return results
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