[LeetCode 89] Gray Code (格雷码问题)

题目链接：gray-code

import java.util.ArrayList;
import java.util.List;

/**
 * 
		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.
		
		For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:
		
		00 - 0
		01 - 1
		11 - 3
		10 - 2
		Note:
		For a given n, a gray code sequence is not uniquely defined.
		
		For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.
		
		For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.
 *
 */

public class GrayCode {

//	12 / 12 test cases passed.
//	Status: Accepted
//	Runtime: 188 ms
//	Submitted: 3 minutes ago

	//时间复杂度O(2 ^ n) ,空间复杂度 O(1)
	
    public List<Integer> grayCode(int n) {
		List<Integer> graycode = new ArrayList<Integer>();
		int total = 1 << n;    	
    	for (int i = 0; i < total; i++) {
			graycode.add(i ^ (i >> 1));			//格雷码公式 ：n ^ (n / 2)
		}    	
    	return graycode;
    }    
	public static void main(String[] args) {
		GrayCode codes = new GrayCode();
		System.out.println(codes.grayCode(4));

	}

}