Represent a number N in base -2

Given an integer N, the task is to find base -2 representation of the number N in the form of a string, such that S₀ * (- 2)⁰ + S₁ * (- 2)¹ + ... + S_k * (- 2)^k = N. The string should only consist of 0s and 1s and unless the string is equal to zero, the initial character should be 1.

Examples:

Input: N = -9
Output: 1011
Explanation: 1011 is -2 representation of -9
(-2)⁰+ (-2)¹+ (-2)³ = 1+ (-2) + (-8) = -9

Input: N = -7
Output: 1001

Approach: Follow the steps below to solve the problem:

• Initialize an empty string S.
• Iterate from N, until N is greater than zero.
  • If N is even, append '0' in front of S and divide N by -2.
  • Otherwise, append '1' in front of S, and decrement N by 1, and then divide N by -2.
• If the string S is empty, then return '0'
• Finally, return the string S.

Below is the implementation of the above approach:

1011

Time Complexity: O(N)
Auxiliary Space: O(1)