<p>Given a string <code>s</code>, return <code>true</code> <em>if it is possible to split the string</em> <code>s</code> <em>into three <strong>non-empty</strong> palindromic substrings. Otherwise, return </em><code>false</code>.​​​​​</p>

<p>A string is said to be palindrome if it the same string when reversed.</p>

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

<pre>
<strong>Input:</strong> s = &quot;abcbdd&quot;
<strong>Output:</strong> true
<strong>Explanation: </strong>&quot;abcbdd&quot; = &quot;a&quot; + &quot;bcb&quot; + &quot;dd&quot;, and all three substrings are palindromes.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;bcbddxy&quot;
<strong>Output:</strong> false
<strong>Explanation: </strong>s cannot be split into 3 palindromes.
</pre>

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

<ul>
	<li><code>3 &lt;= s.length &lt;= 2000</code></li>
	<li><code>s</code>​​​​​​ consists only of lowercase English letters.</li>
</ul>

class Solution {
public:
bool check(string &s){
        if(s.length()==1)return true;
        int n = s.length();
        int i=0;
        int j=n-1;
        while(i<j){
            if(s[i]!=s[j])return false;
            i++;
            j--;
        }
        return true;
    }
    bool f(int ind,string &s,int count,int k,vector<vector<int>>&dp){
        if(ind == s.length()){
            return count==k;
        }
        if(dp[ind][count]!=-1)return dp[ind][count];
        int ans=false;
        string temp;
        if(count<k-1){
            for(int i=ind;i<s.length();i++){
                temp+=s[i];
                if(check(temp)){
                   ans|=f(i+1,s,count+1,k,dp);
                }
            }
        }
        else{
            for(int i=ind;i<s.length();i++){
                temp+=s[i];
            }
            ans=check(temp);
        } 
        return dp[ind][count]=ans;
       
    }
    bool checkPartitioning(string s) {
        int n = s.length();
       vector<vector<int>>dp(n+1,vector<int>(4,-1));
       return f(0,s,0,3,dp);
    }
};
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