Ruairí O'Brien

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# Day 27 - Concatenation of Consecutive Binary Numbers

## The Problem

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 `10^9 + 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`

## Tests

``````import pytest
from .Day27_ConcatenationOfConsecutiveBinaryNumbers import Solution

s = Solution()

@pytest.mark.parametrize(
"n,expected",
[
(1, 1),
(3, 27),
(12, 505379714),
],
)
def test_concatenated_binary(n, expected):
assert s.concatenatedBinary(n) == expected
``````

## Solution

``````class Solution:
def concatenatedBinary(self, n: int) -> int:
l = 0
ans = 0
for i in range(1, n + 1):
if i & (i - 1) == 0:
l += 1
ans = ((ans << l) | i) % (10 ** 9 + 7)
return ans
``````