We had some 2-dimensional coordinates, like "(1, 3)" or "(2, 0.5)". Then, we removed all commas, decimal points, and spaces and ended up with the string s.
"(1, 3)" becomes s = "(13)" and "(2, 0.5)" becomes s = "(205)".Return a list of strings representing all possibilities for what our original coordinates could have been.
Our original representation never had extraneous zeroes, so we never started with numbers like "00", "0.0", "0.00", "1.0", "001", "00.01", or any other number that can be represented with fewer digits. Also, a decimal point within a number never occurs without at least one digit occurring before it, so we never started with numbers like ".1".
The final answer list can be returned in any order. All coordinates in the final answer have exactly one space between them (occurring after the comma.)
Example 1:
Input: s = "(123)" Output: ["(1, 2.3)","(1, 23)","(1.2, 3)","(12, 3)"]
Example 2:
Input: s = "(0123)" Output: ["(0, 1.23)","(0, 12.3)","(0, 123)","(0.1, 2.3)","(0.1, 23)","(0.12, 3)"] Explanation: 0.0, 00, 0001 or 00.01 are not allowed.
Example 3:
Input: s = "(00011)" Output: ["(0, 0.011)","(0.001, 1)"]
Constraints:
4 <= s.length <= 12s[0] == '(' and s[s.length - 1] == ')'.s are digits.In #816 Ambiguous Coordinates, the input is a string representing digits inside parentheses. The task is to reconstruct all valid coordinate pairs by inserting a comma and optional decimal points while respecting number formatting rules.
The key idea is to enumerate every possible split of the string into two parts representing the x and y coordinates. For each part, generate all valid numeric representations by optionally inserting a decimal point. While doing so, enforce constraints such as no leading zeros for integers (except "0") and no trailing zeros in the fractional portion.
Using backtracking or enumeration, build valid numbers for each half and combine them into coordinate pairs. This approach systematically explores all placements while filtering invalid formats early.
The algorithm mainly iterates over string splits and decimal placements, giving a time complexity around O(n^3) in the worst case, with space used for storing valid coordinate combinations.
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Enumeration with Valid Decimal Generation | O(n^3) | O(n^2) |
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Problems similar to Ambiguous Coordinates can appear in FAANG-style interviews because they test string manipulation, enumeration, and edge-case handling. Interviewers often use such problems to evaluate careful implementation and reasoning about constraints.
The optimal approach enumerates every possible split of the string into two coordinate parts and then generates valid numeric formats for each part. By validating decimal placement rules early, invalid candidates are pruned efficiently. This systematic enumeration ensures all valid coordinate pairs are found.
Strings and dynamic lists are the main data structures used. Strings help create candidate numbers with decimal placements, while lists store valid coordinate combinations during enumeration. No complex data structures are required beyond careful string manipulation.
These rules ensure that generated numbers follow valid numeric formatting. Integers cannot have leading zeros unless the number is exactly '0', and decimals cannot end with trailing zeros. Enforcing these constraints prevents invalid coordinate representations from being included.