1680. 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

Rust Solution

struct Solution;

const MOD: i64 = 1_000_000_007;

impl Solution {
    fn concatenated_binary(n: i32) -> i32 {
        let mut res = 0;
        let mut stack: Vec<i64> = vec![];
        for i in 1..=n {
            let mut j = i;
            while j > 0 {
                stack.push((j % 2) as i64);
                j >>= 1;
            }
            while let Some(top) = stack.pop() {
                res <<= 1;
                res += top;
            }
            res %= MOD;
        }
        res as i32
    }
}

#[test]
fn test() {
    let n = 1;
    let res = 1;
    assert_eq!(Solution::concatenated_binary(n), res);
    let n = 3;
    let res = 27;
    assert_eq!(Solution::concatenated_binary(n), res);
    let n = 12;
    let res = 505379714;
    assert_eq!(Solution::concatenated_binary(n), res);
}

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