<p>Given a string <code>s</code>, partition <code>s</code> such that every <span data-keyword="substring-nonempty">substring</span> of the partition is a <span data-keyword="palindrome-string"><strong>palindrome</strong></span>. Return <em>all possible palindrome partitioning of </em><code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "aab"
<strong>Output:</strong> [["a","a","b"],["aa","b"]]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = "a"
<strong>Output:</strong> [["a"]]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 16</code></li>
	<li><code>s</code> contains only lowercase English letters.</li>
</ul>

class Solution {
public:
    vector<vector<string>> partition(string s) {
        int n = s.length();
        vector<vector<bool>> palindromes(n, vector<bool>(n, false));
        for (int end = 0; end < n; end++) {
            for (int start = 0; start <= end; start++) {
                if (s[start] == s[end]) {
                    if (end - start <= 1) {
                        palindromes[start][end] = true;
                    } else {
                        palindromes[start][end] = palindromes[start + 1][end - 1];
                    }
                }
            }
        }

        vector<vector<vector<string>>> palindromeParts(n, vector<vector<string>>());

        vector<vector<int>> edges(n, vector<int>());
        for (int start = 0; start < n; start++) {
            for (int end = start; end < n; end++) {
                if (palindromes[start][end]) {
                    edges[start].push_back(end);
                }
            }
        }

        for (int start = n - 1; start >= 0; start--) {
            for (int end : edges[start]) {
                string curr = s.substr(start, end - start + 1);
                if (end == n - 1) {
                    palindromeParts[start].push_back(vector<string>(1, curr));
                } else {
                    for (vector<string> parts : palindromeParts[end + 1]) {
                        parts.insert(parts.begin(), curr);
                        palindromeParts[start].push_back(parts);
                    }
                }
            }
        }

        return palindromeParts[0];
    }
};
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