Leetcode #1680: Concatenation of Consecutive Binary Numbers
In this guide, we solve Leetcode #1680 Concatenation of Consecutive Binary Numbers in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Bit Manipulation, Math, Simulation
Intuition
The problem structure lets us track state with bitwise operations.
Bit operations are constant time and avoid extra memory.
Approach
Apply XOR/AND/OR and shifts to maintain the required invariant.
Aggregate the result in a single pass.
Steps:
- Identify a bitwise invariant.
- Combine values with bit operations.
- Return the aggregated result.
Example
Input: n = 1
Output: 1
Explanation: "1" in binary corresponds to the decimal value 1.
Python Solution
class Solution:
def concatenatedBinary(self, n: int) -> int:
mod = 10**9 + 7
ans = 0
for i in range(1, n + 1):
ans = (ans << i.bit_length() | i) % mod
return ans
Complexity
The time complexity is , where is the given integer. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.