779 K-th Symbol in Grammar

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17

class Solution:
    def kthGrammar(self, n: int, k: int) -> int:
        if n == 1:
            return 0

        if k % 2 == 0:
            # current is right child
            if self.kthGrammar(n - 1, k // 2) == 0:
                # parent is 0, then right child is 1
                return 1
            return 0
        else:
            # current is left child
            if self.kthGrammar(n - 1, (k+1) // 2) == 0:
                # parent is 0, then left child is 0
                return 0
            return 1