<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:
	// issecword denotes if it is the second word (the part after the decimal)
    bool check(string s, bool issecword)
    {
        int n=s.length();
		// Logic explained above
        if(issecword){
            if(n>0 && s[n-1]=='0') return false;
        }
        else{
            if(n>1 && s[0]=='0') return false;
        }
        return true;
    }

    vector<string> ambiguousCoordinates(string S) {
        vector<string> res;
        S=S.substr(1,S.length()-2);  // Remove the brackets
        int n=S.length();

        for(int i=1;i<n;i++){
            string s1=S.substr(0,i);
            string s2=S.substr(i);
            vector<string> res1, res2;
			
			// The full string without any decimal point can also be a coordinate.
			// But '01' or '001' is not possible.
            if(check(s1, false)) res1.push_back(s1);
            if(check(s2, false)) res2.push_back(s2);
			
			// First co-ordinate
            for(int j=1;j<s1.length();j++){
                string first=s1.substr(0,j);
                string second=s1.substr(j);
                if(check(first, false) && check(second, true)) res1.push_back(first+"."+second);
            }
			
			// Second co-ordinate
            for(int j=1;j<s2.length();j++){
                string first=s2.substr(0,j);
                string second=s2.substr(j);
                if(check(first, false) && check(second, true)) res2.push_back(first+"."+second);
            }
			
			// Combine all the results
            for(auto left:res1){
                for(auto right:res2){
                    res.push_back("(" + left + ", "+ right + ")");
                }
            }
        }
        return res;
    }
};
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