k-th-symbol-in-grammar

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779. K-th Symbol in Grammar (Medium)

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

Example 4:

Input: n = 3, k = 1
Output: 0
Explanation:
row 1: 0
row 2: 01
row 3: 0110

 

Constraints:

• 1 <= n <= 30
• 1 <= k <= 2n - 1

Related Topics

[Bit Manipulation] [Recursion] [Math]

Hints

Hint 1

Try to represent the current (N, K) in terms of some (N-1, prevK). What is prevK ?