<p>Given a string&nbsp;<code>s</code><var>,</var>&nbsp;return <em>the maximum&nbsp;number of unique substrings that the given string can be split into</em>.</p>

<p>You can split string&nbsp;<code>s</code> into any list of&nbsp;<strong>non-empty substrings</strong>, where the concatenation of the substrings forms the original string.&nbsp;However, you must split the substrings such that all of them are <strong>unique</strong>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;ababccc&quot;
<strong>Output:</strong> 5
<strong>Explanation</strong>: One way to split maximally is [&#39;a&#39;, &#39;b&#39;, &#39;ab&#39;, &#39;c&#39;, &#39;cc&#39;]. Splitting like [&#39;a&#39;, &#39;b&#39;, &#39;a&#39;, &#39;b&#39;, &#39;c&#39;, &#39;cc&#39;] is not valid as you have &#39;a&#39; and &#39;b&#39; multiple times.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aba&quot;
<strong>Output:</strong> 2
<strong>Explanation</strong>: One way to split maximally is [&#39;a&#39;, &#39;ba&#39;].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aa&quot;
<strong>Output:</strong> 1
<strong>Explanation</strong>: It is impossible to split the string any further.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>
	<p><code>1 &lt;= s.length&nbsp;&lt;= 16</code></p>
	</li>
	<li>
	<p><code>s</code> contains&nbsp;only lower case English letters.</p>
	</li>
</ul>

class Solution {
    vector<vector<int>> getCombs(int n, int k) {
        if (k == 0 || n < k) return {};
        if (k == 1) return {{n}};


        vector<vector<int>> res;

        for (int size = 1; n - size >= k-1; ++size) {
            auto subCombs = getCombs(n-size, k-1);

            for (auto sub: subCombs) {
                sub.insert(sub.begin(), size);
                res.push_back(sub);
            }
        }

        return res;
    }
public:
    int maxUniqueSplit(string s) {
        for (int k = s.size(); k >= 2; --k) {
            vector<vector<int>> combs = getCombs(s.size(), k);

            for (auto comb : combs) {
                unordered_set<string> substrs;

                for (int i = 0, start = 0; i < comb.size(); ++i) {
                    string cur = s.substr(start, comb[i]);
                    substrs.insert(cur);
                    start += comb[i];                    
                }

                if (substrs.size() == k) return k;
            }
        }

        return 1;
    }
};
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