Introduction

In this blog post, we will explore how to solve the LeetCode problem "1611" 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, you must transform it into 0 using the following operations any number of times: Change the rightmost (0th) bit in the binary representation of n. Change the ith bit in the binary representation of n if the (i-1)th bit is set to 1 and the (i-2)th through 0th bits are set to 0. Return the minimum number of operations to transform n into 0. Example 1: Input: n = 3 Output: 2 Explanation: The binary representation of 3 is "11". "11" -> "01" with the 2nd operation since the 0th bit is 1. "01" -> "00" with the 1st operation. Example 2: Input: n = 6 Output: 4 Explanation: The binary representation of 6 is "110". "110" -> "010" with the 2nd operation since the 1st bit is 1 and 0th through 0th bits are 0. "010" -> "011" with the 1st operation. "011" -> "001" with the 2nd operation since the 0th bit is 1. "001" -> "000" with the 1st operation. Constraints: 0 <= n <= 109

Explanation

Here's an efficient solution to determine the minimum operations to transform an integer n to 0 using the given operations.

• Gray Code Connection: The core idea is to recognize that the given operations are closely related to the Gray code sequence. The minimum number of operations to transform n to 0 is equivalent to converting the binary representation of n to its corresponding Gray code and then interpreting that Gray code as an integer. The Gray code has the property that adjacent numbers differ by only one bit, and this maps directly to the allowed operations.

• Iterative Gray Code Calculation: We can calculate the Gray code representation efficiently using the formula gray_code = n ^ (n >> 1). This XOR operation effectively implements the Gray code conversion.

• Return Gray Code: The Gray code obtained is the number of operations needed to transform n to 0.

• Time & Space Complexity:

  • Runtime Complexity: O(1)
  • Storage Complexity: O(1)

Code

    def solve():
    n = int(input())
    gray_code = n ^ (n >> 1)
    print(gray_code)
solve()