Ambiguous Coordinates
<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>
String; Backtracking; Enumeration
class Solution {
public:
    vector<string> ambiguousCoordinates(string s) {
        int n = s.size();
        vector<string> ans;
        auto f = [&](int i, int j) {
            vector<string> res;
            for (int k = 1; k <= j - i; ++k) {
                string l = s.substr(i, k);
                string r = s.substr(i + k, j - i - k);
                bool ok = (l == "0" || l[0] != '0') && r.back() != '0';
                if (ok) {
                    res.push_back(l + (k < j - i ? "." : "") + r);
                }
            }
            return res;
        };
        for (int i = 2; i < n - 1; ++i) {
            for (auto& x : f(1, i)) {
                for (auto& y : f(i, n - 1)) {
                    ans.emplace_back("(" + x + ", " + y + ")");
                }
            }
        }
        return ans;
    }
};