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Ruairí O'Brien
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. 
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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.
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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.
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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
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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
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Analysis

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