1800 Concatenation Of Consecutive Binary Numbers

Concatenation of Consecutive Binary Numbers

Given an integer n, return the decimal value of the binary string formed by concatenating the binary representations of *1 to n in order, *modulo **109 + 7.

 

Example 1:

**Input:** n = 1
**Output:** 1
**Explanation: **"1" in binary corresponds to the decimal value 1. 

Example 2:

**Input:** n = 3
**Output:** 27
**Explanation: **In binary, 1, 2, and 3 corresponds to "1", "10", and "11".
After concatenating them, we have "11011", which corresponds to the decimal value 27.

Example 3:

**Input:** n = 12
**Output:** 505379714
**Explanation**: The concatenation results in "1101110010111011110001001101010111100".
The decimal value of that is 118505380540.
After modulo 109 + 7, the result is 505379714.

 

Constraints:

1 <= n <= 105

impl Solution {
    pub fn concatenated_binary(n: i32) -> i32 {
        let mut result: i64 = 0;
        let modulo: i64 = 1_000_000_007;
        let mut bit_length = 0;

        for i in 1..=n {
            // If i is power of 2, increase bit length
            if (i & (i - 1)) == 0 {
                bit_length += 1;
            }

            result = ((result << bit_length) + i as i64) % modulo;
        }

        result as i32
    }
}