<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 {
public:
    bool isPalindrome(string s) {
        int l = 0;
        int r = s.size()-1;
        while(l<r) {
            if(s[l] != s[r]) {
                return false;
            }
            l++;
            r--;
        }
        return true;
    }
    int brute(string s) {
        int n = s.size();
        int count = n;
        vector<vector<bool>> cache(n, vector<bool>(n, false));
        for(int i=0; i<n; i++) {
            cache[i][i] = true;
        }

        for(int start=0; start<s.size(); start++) {
            for(int end=start+1; end<s.size(); end++) {
                if(s[start]==s[end]) {
                    if((start+1)<=(end-1) && cache[start+1][end-1]) {
                        cache[start][end] = true;
                        count++;
                    }
                    else if(isPalindrome(s.substr(start, end-start+1))) {
                        cache[start][end] = true;
                        count++;
                    }
                }
            }
        }
        return count;
    }
    int countSubstrings(string s) {
        return brute(s);
    }
};
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