89. Gray Code

Problem

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.

Solution 1

/**
 * @param {number} n
 * @return {number[]}
 */
var grayCode = function(n) {
  var res = [0];
  helper(n, res, 0);
  return res;
};

var helper = function (n, res, num) {
  if (num >= n) return;
  var len = res.length;
  for (var i = len - 1; i >= 0; i--) {
    res.push(res[i] + len);
  }
  helper(n, res, num + 1);
};

Explain:

nope.

Complexity:

• Time complexity : O(2^n).
• Space complexity : O(2^n).

Solution 2

/**
 * @param {number} n
 * @return {number[]}
 */
var grayCode = function(n) {
  var res = [0];
  var len = 1;

  for (var i = 0; i < n; i++) {
    len = res.length;
    for (var j = len - 1; j >= 0; j--) {
      res.push(res[j] + len);
    }
  }

  return res;
};

Explain:

nope.

Complexity:

• Time complexity : O(2^n).
• Space complexity : O(2^n).