1680. Concatenation of Consecutive Binary Numbers

Description

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

 

Solutions

Solution: Bit Manipulation

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number} n
 * @return {number}
 */
const concatenatedBinary = function (n) {
  const MODULO = 10 ** 9 + 7;
  let result = 0;

  for (let value = 1; value <= n; value++) {
    result *= 1 << value.toString(2).length;
    result = (result + value) % MODULO;
  }
  return result;
};