algoadvance

Problem Statement

You are given a string s representing coordinates with some format issues. The valid format for coordinates is (x, y), where x and y are valid numbers. Your task is to return all possible valid coordinates obtained from the given string s.

The input string s will always be of the form "(abc)", where a, b, and c are digits, and there are no commas, spaces, or additional parentheses.

Example

Input: s = "(123)"
Output: ["(1, 23)", "(12, 3)", "(1.2, 3)", "(1, 2.3)"]

Clarifying Questions

1. Q: Are the digits in the string always non-zero? A: No, the digits can include zero. The function needs to handle the correct placement of decimal points, especially considering leading zeros.

2. Q: How long can the input string be? A: The input string is always guaranteed to be enclosed within a single pair of parentheses and will contain at least two digits.

3. Q: Are floating point numbers allowed as coordinates, and how should they be formatted? A: Yes, floating point numbers are allowed. Decimal points should not appear at the start or end of the number and there shouldn’t be any leading zeros unless the number is “0”.

Strategy

The strategy to solve this problem involves:

1. Parsing the Input: Remove the outer parentheses to extract the numeric string content.
2. Generating Possible Coordinates: For each possible split of the string into two parts, generate all valid representations for both the x and y parts.
3. Validating Coordinates:
   • For each part of the split, determine all valid ways to insert a decimal point (if applicable).
   • Ensure that numbers do not start or end with a decimal point and handle zeros correctly.
4. Creating Pairs: Combine valid representations of the x and y parts to generate the full coordinate pairs in the required format.

Code

def ambiguousCoordinates(s):
    def valid_with_decimal(s):
        res = []
        if s[0] != '0' or s == "0":  # can be "123" -> "123" or "0"
            res.append(s)
        for i in range(1, len(s)):
            left, right = s[:i], s[i:]
            if (left[0] != '0' or left == '0') and right[-1] != '0':
                res.append(left + '.' + right)
        return res

    s = s[1:-1]  # remove the parentheses
    result = []

    for i in range(1, len(s)):
        left, right = s[:i], s[i:]
        left_options = valid_with_decimal(left)
        right_options = valid_with_decimal(right)
        for l in left_options:
            for r in right_options:
                result.append(f"({l}, {r})")

    return result

# Example usage:
s = "(123)"
print(ambiguousCoordinates(s))  # ["(1, 23)", "(12, 3)", "(1.2, 3)", "(1, 2.3)"]

Time Complexity

• Parsing Input: O(n) where n is the length of the string.
• Generating Split and Decimal Validations: For each of the n splits, validating each segment requires essentially linear scans for valid decimal placement.
  • Combined, this is O(n^2) considering all possible splits and valid placements.

Thus, the overall time complexity is O(n^2), which should be efficient for reasonable input sizes given coordinate problem constraints.

I hope this provides a clear and concise solution to the problem. Let me know if you have any further questions!

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