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LeetCode_格雷编码_中等_89.格雷编码
2022-07-06 11:32:00 【小城老街】
1.题目
n 位格雷码序列是一个由 2n 个整数组成的序列,其中:
① 每个整数都在范围 [0, 2n - 1] 内(含 0 和 2n - 1)
② 第一个整数是 0
③ 一个整数在序列中出现不超过一次
④ 每对相邻整数的二进制表示恰好一位不同 ,且第一个和最后一个整数的二进制表示恰好一位不同
给你一个整数 n ,返回任一有效的 n 位格雷码序列 。
示例 1:
输入:n = 2
输出:[0,1,3,2]
解释:
[0,1,3,2] 的二进制表示是 [00,01,11,10] 。
- 00 和 01 有一位不同
- 01 和 11 有一位不同
- 11 和 10 有一位不同
- 10 和 00 有一位不同
[0,2,3,1] 也是一个有效的格雷码序列,其二进制表示是 [00,10,11,01] 。
- 00 和 10 有一位不同
- 10 和 11 有一位不同
- 11 和 01 有一位不同
- 01 和 00 有一位不同
示例 2:
输入:n = 1
输出:[0,1]
提示:
1 <= n <= 16
来源:力扣(LeetCode)
链接:https://leetcode.cn/problems/gray-code
著作权归领扣网络所有。商业转载请联系官方授权,非商业转载请注明出处。
2.思路
思路参考本题官方题解。
(1)对称生成
(2)二进制数转格雷码
3.代码实现(Java)
//思路1————对称生成
class Solution {
public List<Integer> grayCode(int n) {
List<Integer> res = new ArrayList<Integer>();
res.add(0);
for (int i = 1; i <= n; i++) {
int m = res.size();
for (int j = m - 1; j >= 0; j--) {
res.add(res.get(j) | (1 << (i - 1)));
}
}
return res;
}
}
//思路2————二进制数转格雷码
class Solution {
public List<Integer> grayCode(int n) {
List<Integer> res = new ArrayList<>();
for (int i = 0; i < (1 << n); i++) {
res.add((i >> 1) ^ i);
}
return res;
}
}
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