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.

#816

Medium

auto_awesome回溯·pruning

LeetCode 题解工作台

模糊坐标

我们有一些二维坐标，如 "(1, 3)" 或 "(2, 0.5)" ，然后我们移除所有逗号，小数点和空格，得到一个字符串 S 。返回所有可能的原始字符串到一个列表中。原始的坐标表示法不会存在多余的零，所以不会出现类似于"00", "0.0", "0.00", "1.0", "001", "00.0…

字符串回溯枚举

题目描述

我们有一些二维坐标，如 "(1, 3)" 或 "(2, 0.5)"，然后我们移除所有逗号，小数点和空格，得到一个字符串S。返回所有可能的原始字符串到一个列表中。

原始的坐标表示法不会存在多余的零，所以不会出现类似于"00", "0.0", "0.00", "1.0", "001", "00.01"或一些其他更小的数来表示坐标。此外，一个小数点前至少存在一个数，所以也不会出现“.1”形式的数字。

最后返回的列表可以是任意顺序的。而且注意返回的两个数字中间（逗号之后）都有一个空格。

示例 1:
输入: "(123)"
输出: ["(1, 23)", "(12, 3)", "(1.2, 3)", "(1, 2.3)"]

示例 2:
输入: "(00011)"
输出:  ["(0.001, 1)", "(0, 0.011)"]
解释: 
0.0, 00, 0001 或 00.01 是不被允许的。

示例 3:
输入: "(0123)"
输出: ["(0, 123)", "(0, 12.3)", "(0, 1.23)", "(0.1, 23)", "(0.1, 2.3)", "(0.12, 3)"]

示例 4:
输入: "(100)"
输出: [(10, 0)]
解释: 
1.0 是不被允许的。

提示:

4 <= S.length <= 12.
S[0] = "(", S[S.length - 1] = ")", 且字符串 S 中的其他元素都是数字。

lightbulb

解题思路

方法一：暴力模拟

枚举纵坐标的起始位置，然后分别获取横、纵坐标的所有可能的表示形式，最后将横、纵坐标的所有可能的表示形式组合起来。

我们将一个坐标值 $x$ 或 $y$ 按照小数点的位置分成左右两部分，那么两部分应该满足以下条件：

左半部分不能以 0 开头，除非左半部分只有 0；
右半部分不能以 0 结尾。

时间复杂度 $O(n^3)$ ，其中 $n$ 为字符串 $S$ 的长度。

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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)
        ]

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

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

warning

常见陷阱

外企场景

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

swap_horiz

进阶变体

外企场景

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

help

常见问题

外企场景

继续练习

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