Ambiguous Coordinates

Ambiguous Coordinates

What is this problem about?

The "Ambiguous Coordinates interview question" is a string manipulation and enumeration problem. You are given a string representing coordinates like (1234), but the commas and decimal points have been removed. You need to return all possible valid coordinate pairs $(x, y)$ that could have formed this string. A "valid" number cannot have unnecessary leading or trailing zeros (e.g., "0.0" is okay, "01" is not, and "1.0" is not).

Why is this asked in interviews?

Google uses the "Ambiguous Coordinates coding problem" to test a candidate's ability to handle complex string formatting rules and nested iterations. It evaluates "Enumeration interview pattern" skills—specifically, how to systematically explore all ways to split a string into two parts and then all ways to insert decimal points into each part.

Algorithmic pattern used

This is an Exhaustive Enumeration and Validation problem.

1. Split the String: Iterate through all possible ways to split the input string into two non-empty substrings, $L$ and $R$.
2. Generate Valid Numbers: For each substring, find all possible ways to insert a decimal point to create a valid number.
   • A string is valid as an integer if it doesn't have leading zeros (unless it's just "0").
   • A string is valid as a decimal if the integer part doesn't have leading zeros and the decimal part doesn't have trailing zeros.
3. Cartesian Product: For every valid number derived from $L$ and every valid number derived from $R$, combine them into a coordinate pair.

Example explanation

Input: "(123)"

• Split into 1 and 23.
  • 1 can only be 1.
  • 23 can be 23 or 2.3.
  • Pairs: (1, 23), (1, 2.3).
• Split into 12 and 3.
  • 12 can be 12 or 1.2.
  • 3 can only be 3.
  • Pairs: (12, 3), (1.2, 3).

Common mistakes candidates make

• Ignoring Zero Rules: Allowing numbers like "01" (leading zero) or "1.0" (trailing zero in decimal), which are usually prohibited by the problem constraints.
• Missing splits: Forgetting that "0.001" is a valid split if the original string was "0001".
• Complexity management: Not breaking the problem into a helper function (e.g., getValidDecimals(s)) makes the code very messy and hard to debug.

Interview preparation tip

Practice breaking down "Generation" problems into smaller steps. First, solve "how to split," then solve "how to validate a single part," and finally combine them. This modular approach is much easier to explain to an interviewer.