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1680. Concatenation of Consecutive Binary Numbers

Difficulty Topics

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

Solution

concatenation-of-consecutive-binary-numbers.py
class Solution:
    def concatenatedBinary(self, n: int) -> int:
        M = 10 ** 9 + 7

        total = 0
        for x in range(1, n + 1):
            total *= pow(2, x.bit_length())
            total += x
            total %= M

        return total