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Problem

Submissions

K-th Symbol in Grammar

Contributed by

Yash_5830

Medium

0/80

Avg time to solve 20 mins

Success Rate 80 %

3 upvotes

Problem Statement

You are given two integers, ‘N’ and ‘K’. Your task is to return the ‘K-th’ bit in row ‘N’ of the given sequence.

Sequence: The first row contains a single bit ‘1’. In each subsequent row, we look at the previous row and replace each ‘1’ with ‘10’ and each ‘0’ with ‘01’.

Example:

N = 4, K = 5

Given sequence:
The previous row’s ‘1’ becomes ‘10’, and ‘0’ becomes ‘01’ for each subsequent row. The contents of each row are:
Row 1: 1
As, ‘1’ => ‘10’, So ‘1’ (row 1) => ‘10’ (row 2)

Row 2: 10
As ‘1’ => ‘10’& ‘0’ => ‘01’,So ‘10’ (row 2) => ‘1001’ (row 3)

Row 3: 1001
As ‘10’ => ‘1001’ & ‘01’ => ‘0110’, So ‘1001’ (row 3) => ‘10010110’ (row 4)

Row 4: 10010110
The ‘5-th’ bit in row ‘4’ is ‘0’. Return ‘0’ as the answer.

Note:

Both ‘K’ and ‘N’ have 1-based indexing.

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input format:

The first line of input contains an integer ‘T’ which denotes the number of test cases. Then, the ‘T’ test cases follow.

The first and only line of each test case contains two space-separated integers, ‘N’ and ‘K’, denoting the row number and index of the bit you need to return.

Output format:

For every test case, print a single line containing a single integer (0 or 1) representing the ‘K-th’ bit in the row ‘N’.

Note:

You do not need to input or print anything, as it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10 ^ 4
1 <= N <= 30
1 <= K <= 2 ^ (N - 1)

Where ‘T’ is the number of test cases, ‘N’ is the row number, and ‘K’ is the bit index.

Time limit: 1 second.

Sample input 1:

2
3 4
5 8

Sample output 1:

1
0

Explanation of sample input 1:

Test Case 1:
N = 3, K = 4

Given sequence:
Row 1: 1
Row 2: 10
Row 3: 1001
The ‘4-th’ bit in row ‘3’ is 1. Return ‘1’ as the answer.

Test Case 2:
N = 5, K = 8

Given sequence:
Row 1: 1
Row 2: 10
Row 3: 1001
Row 4: 10010110
Row 5: 1001011001101001
The ‘8-th’ bit in row ‘5’ is ‘0’. Return ‘0’ as the answer.

Sample input 2:

2
3 2
2 1

Sample output 2:

0
1

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