<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 dp[2005];
    
    vector<vector<bool>> is_palin;
    
    
    void fill_palin(string str)
    {
        int n = str.size();
        
        for(int gap = 0; gap < n; gap++)
        {
            for(int i = 0; i + gap < n; i++)
            {
                int j = i + gap;
                
                if(gap == 0)
                {
                    is_palin[i][j] = true;
                }
                else if(gap == 1)
                {
                    is_palin[i][j] = (str[i] == str[j]);
                }
                else
                {
                    if(str[i] == str[j])
                    {
                        is_palin[i][j] = is_palin[i + 1][j - 1];
                    }
                }
            }
        }
    }
    
    int helper(string& str, int i, int n)
    {
        
        if(i == n)
            return 0;
        
        
        if(dp[i] != -1)
        {
            return dp[i];
        }
        
        
        int mini = INT_MAX;
        
        for(int j = i; j < n; j++)
        {
            if(is_palin[i][j])
            {
                mini = min(mini, 1 + helper(str, j + 1, n));
            }
        }
        
        
        return dp[i] = mini;
    }
    
    int minCut(string str) {
        
        int n = str.size();
        
        
        
        
        is_palin.resize(n);
        
        is_palin.assign(n, vector<bool> (n, false));
        
        
        fill_palin(str);
        
        
        memset(dp, -1, sizeof(dp));
        
        return helper(str, 0, n) - 1;
    }
};
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