<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:
    string s;
    int n;
    int pal[2001][2001];
    int dp[2001];
    int pali(int l,int r)
    {
        if(l>=r)
        {
            return 1;
        }
        if(pal[l][r]!=-1)
        {
            return pal[l][r];
        }
        if(s[l]==s[r])
        {
            return pal[l][r]=pali(l+1,r-1);
        }
        return pal[l][r]=0;
    }
    int rec(int l)
    {
        if(l>=n)
        {
            return 0;
        }
        if(dp[l]!=-1)
        {
            return dp[l];
        }
        int ans=n+1;
        for(int i=l;i<n;++i)
        {
            if(pal[l][i])
            {
                ans=min(ans,1+rec(i+1));
            }
        }
        return dp[l]=ans;

    }
    int minCut(string p) {
        n=p.length();
        s=p;
        memset(pal,-1,sizeof(pal));
        memset(dp,-1,sizeof(dp));
        for(int i=0;i<n;++i)
        {
            for(int j=i;j<n;j++)
            {
                pali(i,j);
            }
        }
        return rec(0)-1;
    }
};
25568