<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) {
        vector<string> res;

        if (s.size() <= 3) return std::move(res);
        int n = s.size();
        // divide [1, i), [i, n-1)
        for (int i = 2; i < n-1; i++) {
            vector<string> left(stringCombine(s.substr(1, i-1)));
            vector<string> right(stringCombine(s.substr(i, n-i-1)));
            if (left.size() == 0 || right.size() == 0) {
                continue;
            }
            for (int l = 0; l < left.size(); l++) {
                for (int r = 0; r < right.size(); r++) {
                    string tmp = "(";
                    tmp += left[l];
                    tmp += ", ";
                    tmp += right[r];
                    tmp += ")";
                    res.push_back(tmp);
                }
            }
        }
        
        return res;
    }

    vector<string> stringCombine(string s) {
        vector<string> res;

        if (s.size() == 1)  {
            res.push_back(s);
            return move(res);
        }



        for (int i = 1; i < s.size(); i++) {
            string left = s.substr(0, i);
            string right = s.substr(i, s.size());
            if (validBeforePoint(left) && validAfterPoint(right)) {
                string tmp = "";
                tmp += left;
                tmp += '.';
                tmp += right;
                res.push_back(tmp);
            }
        }
                if (validBeforePoint(s)) res.push_back(s);
        return move(res);

    }

    bool validBeforePoint(string& s) {
        if (s.size() == 1) return true;
        return *s.begin() != '0';
    }
    bool validAfterPoint(string& s) {
        return *s.rbegin() != '0';
    }
};
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