<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">palindrome</span>.</p>

<p>Return <em>the <strong>minimum</strong> cuts needed for a palindrome partitioning of</em> <code>s</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;aab&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> The palindrome partitioning [&quot;aa&quot;,&quot;b&quot;] could be produced using 1 cut.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;a&quot;
<strong>Output:</strong> 0
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;ab&quot;
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 2000</code></li>
	<li><code>s</code> consists of lowercase English letters only.</li>
</ul>

class Solution {
public:
    int minCut(string s) {
        std::unordered_map<int, int> memo;
        return minCutRecursive(s, 0, memo) - 1;
    }

    int minCutRecursive(std::string& s, int start_index, std::unordered_map<int, int>& memo)
    {
        if (start_index == s.length())
        {
            return 0;
        }
        else if (memo.find(start_index) != memo.end())
        {
            return memo[start_index];
        }

        int min_count = INT_MAX;

        for (int end_index = s.length() - 1; end_index >= start_index; end_index--)
        {
            if (isPalindrome(s, start_index, end_index))
            {
                int check_forward = minCutRecursive(s, end_index + 1, memo);
                
                if (check_forward != INT_MAX)
                {
                    min_count = std::min(1 + check_forward, min_count);
                }                
            }
        }

        memo[start_index] = min_count;

        return min_count;
    }

    bool isPalindrome(std::string& s, int i, int j)
    {
        while (i < j)
        {
            if (s[i] != s[j])
            {
                return false;
            }

            ++i; --j;
        }

        return true;
    }
};
10028