Encode Number

Encode Number

What is this problem about?

The Encode Number interview question defines a specific encoding scheme for non-negative integers. The encoding follows a binary-like pattern where numbers are mapped to strings of '0's and '1's. The mapping starts as follows: 0 -> "", 1 -> "0", 2 -> "1", 3 -> "00", 4 -> "01", 5 -> "10", 6 -> "11", and so on. Your goal is to find the encoded string for a given integer n.

Why is this asked in interviews?

Companies like Quora ask the Encode Number coding problem to test a candidate's ability to recognize mathematical mappings and work with different number bases. It’s a twist on the standard decimal-to-binary conversion. It evaluates whether a candidate can identify that the encoding for n is related to the binary representation of n + 1 by removing the leading '1'.

Algorithmic pattern used

The problem uses a Math and Bit Manipulation pattern.

1. Observe that the number of strings of length L is 2^L.
2. The encoding for n is essentially the binary representation of n + 1, but with the most significant bit removed.
3. Steps:
   • Add 1 to the input number: n = n + 1.
   • Convert n to its binary string.
   • Remove the first character (which is always '1') from the binary string.
   • Return the result.

Example explanation

Suppose n = 3.

1. n + 1 = 4.
2. Binary representation of 4 is 100.
3. Remove the leading '1': 00. Result for 3 is "00".

Suppose n = 6.

1. n + 1 = 7.
2. Binary of 7 is 111.
3. Remove the leading '1': 11. Result for 6 is "11".

Common mistakes candidates make

• Direct Binary Conversion: Thinking the answer is just the binary of n, which doesn't account for the empty string at 0 or the length transitions.
• Handling 0: Forgetting that 0 should return an empty string.
• Inefficient concatenation: Building the string character by character in a loop instead of using built-in binary conversion functions.

Interview preparation tip

When you see a sequence like this (0, 1, 1, 2, 2, 2, 2...), always write down the binary equivalents of the numbers and their neighbors. Often, shifting or adding a constant reveals the underlying mapping immediately.