<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) {
        for (int i = 2; i < S.size() - 1; i++) {
            string strs[2] = {S.substr(1,i-1), S.substr(i,S.size()-i-1)};
            xPoss.clear();
            for (int j = 0; j < 2; j++)
                if (xPoss.size() || !j) parse(strs[j], j);
        }
        return ans;
    }
private:
    vector<string> ans, xPoss;
    void parse(string str, int xy) {
        if (str.size() == 1 || str.front() != '0')
            process(str, xy);
        if (str.size() > 1 && str.back() != '0')
            process(str.substr(0,1) + "." + str.substr(1), xy);
        if (str.size() > 2 && str.front() != '0' && str.back() != '0')
            for (int i = 2; i < str.size(); i++)
                process(str.substr(0,i) + "." + str.substr(i), xy);
    }
    void process(string str, int xy) {
        if (xy)
            for (auto x : xPoss)
                ans.push_back("(" + x + ", " + str + ")");
        else xPoss.push_back(str);
    }
};
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