Gray Code.js

/**
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.
*/
/**
 * @param {number} n
 * @return {number[]}
 * 
 * 例举grey code序列，并找规律 :
n = 0: 0
n = 1: 0, 1
n = 2: 00, 01, 11, 10  (0, 1, 3, 2)
n = 3: 000, 001, 011, 010, 110, 111, 101, 100 (0, 1, 3, 2, 6, 7, 5, 4)
以n = 3为例，grey code中前4个包括了n = 2的所有gray code。后4个则是前4个逆序后加上2^2。

推广：n = i的grey code的前一半包括了n = i-1的所有grey code，而后一半则为前一半逆序后家上2^(i-1)
 */
var grayCode = function(n) {
    var result = [],
        cur,
        i,
        j;
    
    result [0] = 0;
    
    if (n === 0) {
        return result;
    }
    
    for (i = 1; i <= n; i++) {
        for (j = Math.pow(2, i - 1); j > 0; j--) {
            result.push(result[j - 1] + (1 << (i - 1)));
        }
    }
    
    return result;
};