#816

Medium

auto_awesomeBacktracking search with pruning

LeetCode Problem Workspace

Ambiguous Coordinates

Find all valid 2D coordinate possibilities for an ambiguous input string using backtracking and pruning techniques.

Problem Statement

You are given a string s that represents a 2-dimensional coordinate in a compressed format without spaces, commas, or decimal points. The string starts with ( and ends with ), and the content between them consists solely of digits. Your task is to determine all valid possibilities for what the original coordinate pairs could have been before compression.

The valid coordinate pairs must meet the following criteria: each component of the pair (x or y) cannot have extraneous leading zeroes (e.g., no 00, 0.0, or 001). Additionally, any decimal point within a number must be preceded by at least one digit (e.g., .1 is invalid). The solution should output all valid combinations as a list of strings.

Examples

Example 1

Input: s = "(123)"

Output: ["(1, 2.3)","(1, 23)","(1.2, 3)","(12, 3)"]

Example details omitted.

Example 2

Input: s = "(0123)"

Output: ["(0, 1.23)","(0, 12.3)","(0, 123)","(0.1, 2.3)","(0.1, 23)","(0.12, 3)"]

0.0, 00, 0001 or 00.01 are not allowed.

Example 3

Input: s = "(00011)"

Output: ["(0, 0.011)","(0.001, 1)"]

Example details omitted.

Constraints

4 <= s.length <= 12
s[0] == '(' and s[s.length - 1] == ')'.
The rest of s are digits.

Solution Approach

Backtracking with Pruning

The core approach is to perform a backtracking search for all potential splits in the input string. For each split, check if the resulting segments satisfy the constraints for valid numbers. If any of the splits result in invalid numbers, prune that branch of the search early to save computation time.

String Enumeration

Each coordinate component (x or y) must be checked for validity. During the search, test different placements for the decimal point and ensure that all generated numbers are valid without leading zeroes or unnecessary decimals. This step leverages string manipulation and enumeration to explore all potential valid splits.

Efficient Pruning

Given the constraints, pruning is essential to prevent the search from generating too many invalid combinations. Early rejection of invalid splits (like those with multiple leading zeroes or improper decimal placement) ensures the algorithm remains efficient, even with longer input strings.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on how the backtracking is implemented, with pruning reducing the search space. Each split requires checking two components of the string, and the pruning ensures the algorithm avoids generating unnecessary invalid combinations. Space complexity primarily depends on the number of valid coordinate combinations stored during the search.

What Interviewers Usually Probe

The candidate demonstrates a solid understanding of backtracking principles and pruning techniques.
The solution correctly handles string manipulation and checks for number validity during the backtracking process.
The candidate is able to optimize the search process, ensuring that invalid paths are pruned early.

Common Pitfalls or Variants

Common pitfalls

Forgetting to prune invalid paths early, leading to unnecessary computation and inefficiency.
Handling invalid cases like leading zeroes or misplaced decimal points improperly.
Not considering edge cases where the number may be too long to fit in the coordinate format.

Follow-up variants

Modify the input format by including additional constraints on the length of the coordinate components.
Increase the length of the string, forcing the backtracking solution to handle longer inputs and potentially explore more combinations.
Introduce a requirement where one of the coordinates must always contain a decimal point, adding an additional constraint to the search process.

FAQ

What is the main challenge of solving the Ambiguous Coordinates problem?

The main challenge is to correctly implement a backtracking search with pruning to handle the numerous valid and invalid coordinate combinations efficiently.

How does pruning help in the Ambiguous Coordinates problem?

Pruning helps by eliminating invalid coordinate combinations early, reducing the number of potential solutions and improving algorithm performance.

What should I consider when splitting the input string in Ambiguous Coordinates?

When splitting, you must ensure that neither of the coordinate components has leading zeroes or is improperly formatted (e.g., misplaced decimal points).

Can the Ambiguous Coordinates problem be solved without backtracking?

Backtracking is the most efficient approach for this problem, as it allows for pruning invalid paths during the search, preventing unnecessary computation.

How do I ensure all valid combinations are generated in the Ambiguous Coordinates problem?

By exploring all possible decimal placements and validating the resulting coordinates, you can ensure that all valid combinations are considered during the backtracking process.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def ambiguousCoordinates(self, s: str) -> List[str]:
        def f(i, j):
            res = []
            for k in range(1, j - i + 1):
                l, r = s[i : i + k], s[i + k : j]
                ok = (l == '0' or not l.startswith('0')) and not r.endswith('0')
                if ok:
                    res.append(l + ('.' if k < j - i else '') + r)
            return res

        n = len(s)
        return [
            f'({x}, {y})' for i in range(2, n - 1) for x in f(1, i) for y in f(i, n - 1)
        ]

Continue Practicing

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