K-th Symbol in Grammar — LeetCode 779 Python Solution

The problem

We build a table of n rows (1-indexed). We start by writing 0 in the 1st row.

Example

Input

n = 1, k = 1

Output

0

Explanation

row 1: 0

Python solution

class Solution:
    def kthGrammar(self, n: int, k: int) -> int:
        if n == 1:
            return 0
        if k <= (1 << (n - 2)):
            return self.kthGrammar(n - 1, k)
        return self.kthGrammar(n - 1, k - (1 << (n - 2))) ^ 1

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 779. K-th Symbol in Grammar is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Bit Manipulation.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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