<p>Given a string <code>s</code>, return <em>the number of <strong>palindromic substrings</strong> in it</em>.</p>

<p>A string is a <strong>palindrome</strong> when it reads the same backward as forward.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within the string.</p>

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

<pre>
<strong>Input:</strong> s = &quot;abc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Three palindromic strings: &quot;a&quot;, &quot;b&quot;, &quot;c&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aaa&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> Six palindromic strings: &quot;a&quot;, &quot;a&quot;, &quot;a&quot;, &quot;aa&quot;, &quot;aa&quot;, &quot;aaa&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution {
private:
    int ans;
    bool searchPalindrome(string &s, int l, int r, vector<vector<int>> &memo) {
        if(l>r) return true;

        if(memo[l][r] != -1) return memo[l][r];

        memo[l][r] = false;
        // cout<<"l: "<<l<<" r: "<<r<<endl;
        if(s[l] == s[r]) {
            if(searchPalindrome(s, l+1, r-1, memo)) {
                ans++;
                memo[l][r] = true;
            }
        }
        searchPalindrome(s, l+1, r, memo);
        searchPalindrome(s, l, r-1, memo);
        return memo[l][r];
    }
public:
    Solution() : ans(0) {}
    int countSubstrings(string s) {
        vector<vector<int>> memo(1000, vector<int> (1000, -1)); // -1 => not visited, 0 => false, 1=> true 
        searchPalindrome(s, 0, s.size()-1, memo);
        return ans;
    }
};
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