<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:
    bool validOrNot(string &s, int j)
    {
        // no decimal point
        if(j == 0)
        {
            if(s[0] == '0' && s.size() > 1)
            {
                return false;
            }
        }
        // decimal at jth positon in s1
        else
        {
            if(s[s.size() - 1] == '0')
                    return false;
            if(s[0] == '0' && j != 1)
                return false;
            
        }
        return true;
    }
    vector<string> ambiguousCoordinates(string s) {
        s = s.substr(1, s.size()-2);
        int n = s.size();
        vector<string> ans;
        for(int i=1; i<n; i++)
        {
            string first = s.substr(0, i);
            string second = s.substr(i);
            
            for(int j=0; j<first.size(); j++)
            {
                for(int k=0; k<second.size(); k++)
                {
                    bool x;
                    if(first.size() == 1)
                    {
                        x = true;
                    }
                    else 
                    {
                        x = validOrNot(first, j);
                        if(!x) continue;
                    }
                    if(second.size() != 1)
                    {
                        x = x && validOrNot(second, k);
                    }
                    
                    if(x)
                    {
                        string s1, s2;
                        if(j)
                        {
                            s1 = first.substr(0, j) + "." + first.substr(j);
                        }
                        else
                        {
                            s1 = first;
                        }
                        if(k)
                        {
                            s2 = second.substr(0, k) + "." + second.substr(k);
                        }
                        else
                        {
                            s2 = second;
                        }
                        
                        ans.push_back("(" + s1 + ", " + s2 + ")");
                    }
                }
            }
        }
        return ans;
    }
};
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