779. K-th Symbol in Grammar

Problem

We build a table of n rows (1-indexed). We start by writing 0 in the 1st row. Now in every subsequent row, we look at the previous row and replace each occurrence of 0 with 01, and each occurrence of 1 with 10.

• For example, for n = 3, the 1st row is 0, the 2nd row is 01, and the 3rd row is 0110.

Given two integer n and k, return the kth (1-indexed) symbol in the nth row of a table of n rows.

  Example 1:

Input: n = 1, k = 1
Output: 0
Explanation: row 1: 0

Example 2:

Input: n = 2, k = 1
Output: 0
Explanation: 
row 1: 0
row 2: 01

Example 3:

Input: n = 2, k = 2
Output: 1
Explanation: 
row 1: 0
row 2: 01

  Constraints:

• 1 <= n <= 30

• 1 <= k <= 2n - 1

Solution

/**
 * @param {number} n
 * @param {number} k
 * @return {number}
 */
var kthGrammar = function(n, k) {
    var op = 0;
    while (n > 1) {
        n--;
        if (k % 2 === 0) {
            op = op === 0 ? 1 : 0;
        }
        k = Math.ceil(k / 2);
    }
    return op;
};

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(1).