## Algorithm

Hacker rank Problem Name: 10 Days of JavaScript - Day 6: Bitwise Operators

# Day 6: Bitwise Operators

## Objective

Today, we’re practicing bitwise operations. Check the attached tutorial for more details.

We define S to be a sequence of distinct sequential integers from 1 to n; in other words, S = {1,2,3,…,n}. We want to know the maximum bitwise AND value of any two integers, a and b (where (a < b)), in sequence S that is also less than a given integer, k.

Complete the function in the editor so that given n and k, it returns the maximum a & b < k.

Note: The & symbol represents the bitwise AND operator.

## Input Format

The first line contains an integer, q, denoting the number of function calls.
Each of the q subsequent lines defines a dataset for a function call in the form of two space-separated integers describing the respective values of n and k.

## Constraints

• 1 <= q <= 10^3
• 2 <= n <= 10^3
• 2 <= k <= n

## Output Format

Return the maximum possible value of a & b < k for any a < b in sequence S.

## Explanation 0

We perform the following q = 3 function calls:

1. When n = 5 and k = 2, we have the following possible a and b values in set S = {1,2,3,4,5}:
a b a & b
1 2 001 & 010 = (000)^2 => (0)
1 3 001 & 011 = (001)^2 => (1)
1 4 001 & 100 = (000)^2 => (0)
1 5 001 & 101 = (001)^2 => (1)
2 3 010 & 011 = (010)^2 => (2)
2 4 010 & 100 = (000)^2 => (0)
2 5 010 & 101 = (000)^2 => (0)
3 4 011 & 100 = (000)^2 => (0)
3 5 011 & 101 = (001)^2 => (1)
4 5 100 & 101 = (100)^2 => (4)
• The maximum of any a & b that is also < k is 1, so we return 1.
1. When n = 8 and k = 5, the maximum of any a & b < k in set S = {1,2,3,4,5,6,7,8} is 4 (see table above), so we return 4.
2. When n = 2 and k = 2, the maximum of any a & b < k in set S = {1,2} is 0 (see table above), so we return 0.

## Explanation 1

We perform the following q = 2 function calls:

1. When n = 9 and k = 2, we have the following possible a and b values in set S = {1,2,3,4,5,6,7,8,9}** is 1 (see table above), so we return 1.
2. When n = 8 and k = 3, the maximum of any a & b < k in set S = {1,2,3,4,5,6,7,8} is 2 (see table above), so we return 2.

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
'use strict';

process.stdin.resume();
process.stdin.setEncoding('utf-8');

let inputString = '';
let currentLine = 0;

process.stdin.on('data', inputStdin => {
inputString += inputStdin;
});

process.stdin.on('end', _ => {
inputString = inputString.trim().split('\n').map(string => {
return string.trim();
});

main();
});

return inputString[currentLine++];
}
function getMaxLessThanK(n, k) {

var mx = -1;

for(var i=1; i < =n; i++){
for(var j=i+1; j < =n; j++){
var res = i & j;
if(res > mx && res < k>{
mx = res;
}
}
}
return mx;

};
``````
Copy The Code &

Input

cmd
3 5 2 8 5 2 2

Output

cmd
1 4 0