## Gray Code

07/07/2016 Backtracking

## Question

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

Result: Accepted Time: 0 ms

Here should be some explanations.

/**
* Return an array of size *returnSize.
* Note: The returned array must be malloced, assume caller calls free().
*/
int* grayCode(int n, int* returnSize) {
int * ans = malloc(sizeof(int) * (1<<n));
*returnSize = 1 << n;
for(int i = 0; i < (1<<n); i++)
ans[i] = 0;
for(int i = 0; i < n; i++)
{
int t = 0;
int bit = 1 << i;
for(int j = 0 ; j < (1<<n); j+=bit)
{

if(t == 1 || t == 2)
for(int k = 0; k < bit; k++)
ans[j + k] |= bit;
t++;
t &= 3;
}
}
return ans;
}


Complexity Analytics

• Time Complexity: $O(n*log(n))$
• Space Complexity: $O(n)$