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 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 code 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].

Solutions (Rust)

1. Mathematical

impl Solution {
    pub fn gray_code(n: i32) -> Vec<i32> {
        let mut x = 1;
        let mut ret = vec![0];

        for _ in 0..n {
            let mut rev = ret.iter().rev().map(|&num| num + x).collect();
            ret.append(&mut rev);
            x *= 2;
        }

        ret
    }
}

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