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Ambiguous Coordinates

Difficulty: Medium

Problem Description

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. Return a list of strings representing all possibilities for what our original coordinates could have been. Our original representation never had extraneous zeroes, and 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).

Key Insights

  • The input string contains digits that need to be partitioned into two valid numbers representing x and y coordinates.
  • Each coordinate can be a whole number or a decimal, but must not have leading zeros unless it is '0'.
  • We can generate all possible combinations of valid coordinates by enumerating all possible splits of the string and validating each segment.

Space and Time Complexity

Time Complexity: O(n^2) - where n is the length of the input string. We may check each possible split and validate each segment. Space Complexity: O(m) - where m is the number of valid coordinate combinations generated.

Solution

To solve this problem, we will use a backtracking approach to generate all possible pairs of coordinates from the input string. The string will be split in various ways to form valid x and y coordinates. We will employ checks to ensure that each coordinate adheres to the specified formatting rules (e.g., no leading zeros, valid decimal placements). We store each valid coordinate pair in a list and return that list as the final result.

Code Solutions

def ambiguousCoordinates(s):
    s = s[1:-1]  # Remove the parentheses
    res = []

    # Function to generate valid numbers from a string
    def generate_numbers(s):
        numbers = []
        n = len(s)
        for i in range(n):
            # Whole number case
            if s[:i+1] and (s[0] != '0' or i == 0):
                numbers.append(s[:i+1])
            # Decimal case
            if i < n - 1:
                if s[0] != '0':
                    numbers.append(s[:i+1] + '.' + s[i+1:])
                elif s[i+1] != '0':  # Only allow decimals if there's a non-zero after the point
                    numbers.append(s[:i+1] + '.' + s[i+1:])
        return numbers

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

    return res
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