Is Concatenation of Consecutive Binary Numbers easy or hard?

The problem is rated Medium because the straightforward idea of concatenating binaries leads to inefficient solutions. The challenge is recognizing that binary concatenation can be simulated with bit shifts and detecting when the bit length increases.

Concatenation of Consecutive Binary Numbers Python/Java solution

Python and Java implementations both follow the same logic: iterate from 1 to n, detect when the bit length increases (power of two), left shift the current result, add the number, and take modulo 1e9+7. The algorithm remains O(n) time and O(1) space across languages.

How to solve Concatenation of Consecutive Binary Numbers in O(n)?

Iterate from 1 to n while maintaining a running result. When the current number is a power of two, increase the bit length counter. Left shift the result by this bit length, OR it with the current number, and apply modulo 1e9+7. This simulates binary concatenation using arithmetic instead of strings.

What is the best approach for Concatenation of Consecutive Binary Numbers?

The best approach uses bit manipulation with left shifts. Instead of building a binary string, maintain a running integer result. For each number i from 1 to n, shift the current result left by the number of bits in i and OR it with i. This runs in O(n) time and O(1) space.

Is Concatenation of Consecutive Binary Numbers asked at Google/Amazon/Meta?

Problems involving bit manipulation and binary representation frequently appear in interviews at companies like Google, Amazon, and Meta. This specific problem tests understanding of binary length growth, bit shifts, and modular arithmetic, which are common interview topics.

What data structure is used in Concatenation of Consecutive Binary Numbers?

The optimal solution does not rely on complex data structures. It uses integer variables and bit manipulation operations such as left shift and bitwise OR. The brute-force version may use a string builder to accumulate binary digits.

What is the time complexity of Concatenation of Consecutive Binary Numbers?

The optimal bit manipulation solution runs in O(n) time because each number from 1 to n is processed once with constant-time bit operations. Space complexity is O(1). A naive approach that concatenates binary strings takes O(n log n) time and space due to string growth.

Description Hints 1 Solution Video 15:29

1680. Concatenation of Consecutive Binary Numbers

Medium66.6% acceptance3 companies

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: