<p>We had some 2-dimensional coordinates, like <code>&quot;(1, 3)&quot;</code> or <code>&quot;(2, 0.5)&quot;</code>. Then, we removed all commas, decimal points, and spaces and ended up with the string s.</p>

<ul>
	<li>For example, <code>&quot;(1, 3)&quot;</code> becomes <code>s = &quot;(13)&quot;</code> and <code>&quot;(2, 0.5)&quot;</code> becomes <code>s = &quot;(205)&quot;</code>.</li>
</ul>

<p>Return <em>a list of strings representing all possibilities for what our original coordinates could have been</em>.</p>

<p>Our original representation never had extraneous zeroes, so we never started with numbers like <code>&quot;00&quot;</code>, <code>&quot;0.0&quot;</code>, <code>&quot;0.00&quot;</code>, <code>&quot;1.0&quot;</code>, <code>&quot;001&quot;</code>, <code>&quot;00.01&quot;</code>, or any other number that can be represented with fewer digits. Also, a decimal point within a number never occurs without at least one digit occurring before it, so we never started with numbers like <code>&quot;.1&quot;</code>.</p>

<p>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.)</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;(123)&quot;
<strong>Output:</strong> [&quot;(1, 2.3)&quot;,&quot;(1, 23)&quot;,&quot;(1.2, 3)&quot;,&quot;(12, 3)&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;(0123)&quot;
<strong>Output:</strong> [&quot;(0, 1.23)&quot;,&quot;(0, 12.3)&quot;,&quot;(0, 123)&quot;,&quot;(0.1, 2.3)&quot;,&quot;(0.1, 23)&quot;,&quot;(0.12, 3)&quot;]
<strong>Explanation:</strong> 0.0, 00, 0001 or 00.01 are not allowed.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;(00011)&quot;
<strong>Output:</strong> [&quot;(0, 0.011)&quot;,&quot;(0.001, 1)&quot;]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>4 &lt;= s.length &lt;= 12</code></li>
	<li><code>s[0] == &#39;(&#39;</code> and <code>s[s.length - 1] == &#39;)&#39;</code>.</li>
	<li>The rest of <code>s</code> are digits.</li>
</ul>

class Solution
{
public:
    vector<string> ambiguousCoordinates(string s)
    {
        split(s);
        return res;
    }

protected:
    vector<string> res;
    void split(string &s)
    {
        string rs = s;
        rs.pop_back();
        reverse(rs.begin(), rs.end());
        rs.pop_back();
        string first;
        for (int i = 1; i < s.length() - 2; ++i)
        {
            vector<string> first_half, last_half;
            first += s[i];
            rs.pop_back();
            string second = rs;
            reverse(second.begin(), second.end());
            cout << first << " - " << second << endl;
            bt(first, first_half);
            bt(second, last_half);
            // cout << first_half << endl;
            // cout << last_half << endl;
            for (const string &sub1 : first_half)
            {
                for (const string &sub2 : last_half)
                    res.emplace_back('(' + sub1 + ", " + sub2 + ')');
            }
        }
    }
    void bt(const string &s, vector<string> &result)
    {
        for (int i = 1; i <= s.length(); ++i)
        {
            string first = s.substr(0, i);
            string second = s.substr(i);
            string merge = first + (second.empty() ? "" : '.' + second);
            if (isValid(first, second) == false)
                continue;
            cout << merge << endl;
            result.emplace_back(first + (second.empty() ? "" : '.' + second));
        }
    }

    bool isValid(const string &first, const string &second)
    {
        if (first.size() != 1 && first[0] == '0' || (!second.empty() && second.back() == '0'))
            return false;
        return true;
    }
};
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