Ambiguous Coordinates - Leetcode Solution

The Ambiguous Coordinates problem on LeetCode asks us to take a string of digits and find all possible ways to represent it as a pair of valid coordinates.

For example, if we are given the input "123", we need to find all possible transformations to coordinates, which are valid decimal expressions.

We can approach this problem by splitting the input string into two parts, where the first part represents the x-coordinate and the second part represents the y-coordinate. We need to find all possible combinations of decimals that can form valid coordinates.

To simplify the problem, we can consider a helper function that takes a single string input and returns all possible decimal combinations that can be formed from it. This helper function can start by checking if the input is a single digit number, in which case it is a valid decimal by default. If the input is more than one digit, it can iterate over different positions to split the string, and recursively call itself on the two resulting substrings. It can then combine all possible combinations of the resulting decimals to return all possible valid decimals.

Once we have this helper function, we can use it to find all possible combinations for each part of the input string. We can then combine these coordinates in all possible ways using a nested loop and insert the decimal point appropriately to form valid coordinate strings.

Here is a python implementation of this approach:

def ambiguousCoordinates(s: str) -> List[str]:
    def valid_decimals(s: str) -> List[str]:
        n = len(s)
        if n == 1:
            return [s]
        if s[0] == "0":
            if s[-1] == "0":
                return []
            else:
                return ["0." + s[1:]]
        if s[-1] == "0":
            return [s]
        res = [s]
        for i in range(1, n):
            dec = s[:i] + "." + s[i:]
            if (dec[0] != "0" or dec[1] == ".") and (dec[-1] != "0"):
                res.append(dec)
        return res
    
    n = len(s)
    res = []
    for i in range(1, n):
        x = s[:i]
        y = s[i:]
        x_decimals = valid_decimals(x)
        y_decimals = valid_decimals(y)
        for x_dec in x_decimals:
            for y_dec in y_decimals:
                res.append("(" + x_dec + ", " + y_dec + ")")
    return res

In this implementation, the valid_decimals function returns a list of all valid decimal combinations for a given string. The main function ambiguousCoordinates iterates over all possible splits of the input string and uses the helper function to find all valid decimal combinations for each part. It then combines these decimals using a nested loop to form valid coordinate strings, which are stored in the res list and returned at the end of the function.

This solution has a time complexity of O(n^4), where n is the length of the input string, because we iterate over all possible splits and call the valid_decimals function for each part. However, the actual time complexity may be lower in practice, since the valid_decimals function only needs to be called for strings of length 2 or more, and it can skip some iterations based on the rules for valid decimals.

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