[LeetCode] 89. Gray Code 格雷码

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;
    }
};

  

    

原文地址:https://www.cnblogs.com/lightwindy/p/9678749.html

时间: 2024-09-30 16:51:27

[LeetCode] 89. Gray Code 格雷码的相关文章

LeetCode --- 89. Gray Code

题目链接:Gray Code 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 b

算法学习 - Gray Code(格雷码)的解释和c++实现

Gray Code(格雷码) 典型的二进制格雷码(Binary Gray Code)简称格雷码.当初是为了通信,现在则常用于模拟-数字转换和位置-数字转换中. 特点是:一组数的编码中,若任意两个相邻的代码只有一位二进制数不同,则称这种编码为格雷码. 格雷码属于可靠性编码,是一种错误最小化的编码方式. 格雷码是一种绝对编码方式. 由于格雷码是一种变权码. 格雷码的十进制数奇偶性与其码字中1的个数的奇偶性相同. 十进制转换为格雷码 好的上面我们已经介绍那么多了,那么我来说下如何把一个十进制的数字转换

leetCode 89.Gray Code (格雷码) 解题思路和方法

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. Fo

LeetCode Gray Code 格雷码

题意:提供一个数字n,代表二进制的个数,那么就有2的n次方个可能性了,从0到2^n-1.将其转成格雷码,再直接将二进制的格雷码按二进制的读法变成整数,装在vector容器中返回,要有序(否则你直接将0-2^n-1返回算了). 思路:咋一看!什么是格雷码?假设有1个整数,是二进制形式的,将其最高位的1提出来,其他的每一位等于该位上的数字与该数字的前一位之异或. 好像很复杂的样子?举例: 整数 21 = 0001 0101 二进制 ,格雷码前4位是这样的0001,这就是将二进制的最高位的1提出来啦,

leetcode 89 Gray Code ----- java

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. Fo

gray code 格雷码 递归

格雷码 the n-1 bit code, with 0 prepended to each word, followd by the n-1 bit code in reverse order, with 1 prepended to each word. public class GrayCode{ public static void gray(int n, String prefix) { if(n == 0) System.out.println(prefix); else { gra

LeetCode:Gray Code

1.题目名称 Gray Code(格雷码) 2.题目地址 https://leetcode.com/problems/gray-code/ 3.题目内容 英文: 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

89. Gray Code

89. Gray Code 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 be

[C++]LeetCode: 86 Gray Code (格雷码)

题目: 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