Introduction

In this blog post, we will explore how to solve the LeetCode problem "1680" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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. 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

Explanation

• Iterative Concatenation: Iterate from 1 to n. In each iteration, convert the current number to its binary representation.
  • Efficient Binary Shift: Instead of explicitly concatenating strings, simulate the concatenation by left-shifting the current result by the number of bits in the current number's binary representation and then adding the current number.
  • Modulo Arithmetic: Apply the modulo operator (10⁹ + 7) after each shift and addition to prevent overflow.

• Runtime Complexity: O(n log n), Storage Complexity: O(1)

Code

    def concatenatedBinary(n):
    MOD = 10**9 + 7
    result = 0
    for i in range(1, n + 1):
        bits = len(bin(i)) - 2  # Number of bits in binary representation of i
        result = ((result << bits) % MOD + i) % MOD
    return result